r'.!^		' ^y
NAV. -		.- SCHOOL
MOWTEP.tY,	, CALli-.	3J940

NAVAL POSTGRADUATE SCHOOL

Monterey, California

	THESIS
	APPLICATION OF ADDITIONAL SECONDARY
	FACTORS TO LORAN-C POSITIONS	FOR
	HYDROGRAPHIC OPERATIONS
	by
	Gerald Eo Wheat on
	October 1982
Thesis	Advisor: Gers	.Id Bo Mills

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3. OOVT ACCCSSIOM NO.

4. TITLE fanrf Su*(lffa)

Application of Additional Secondary Factors Co LORAN-C Positions for Hydrographic Operations

7. AuTMOni'«>

Gerald E. Wheaton

S. PCArOMMINC OnOANlZATION NAME ANO AOOKCtS

Naval Postgraduate School Monterey, California 93940

n CONTWOLLIMC O^riCe NAMC AMO AOOKCSS

Naval Postgraduate School Monterey, California

TT MONlToniNC ACCNCY NAMC * AOOnCSSff/ ^IH»rwnt Irom Caturotllng OlUem)

Naval Postgraduate School Monterey, California 93940

READ INSTRUCTTDNS BEFORE COMPLETTNO FORM

1 RECl^ltNT'S CATALOG NUMBEI

5. TYPE OF «CPO»T « PCmoO COVERCO

Master's Thesis October 1982

«. PCWFOWMING ORG. HEPOWT Nu

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•• CONTNACT OI» GHAnT NLMSERraj

"*• tSS^VA^^''*'*'^ '•'•OJtCT TASK AHCA • WOKK UNIT NUMBEHS

12 (lEPOUT OATE

October 1982

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129

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Unclassified

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l«. SUPPLEMENTARY NOTES

19. KEY WORDS (Coftllnu* art rmirmf tld» II n*c««aarr an« l^mnltlt »V MocA nuai**r>

LORAN-C; Hydrographic Surveying; Additional Secondary Factors; Calibration;

20. ABSTRACT (Conllm— on ravwa* »ldm II naeaaaarr «•' ItfaMKfr *7 Moe* mmt^ar)

The application of LORAN-C in the hyperbolic mode as a positioning system for hydrographic surveys was investigated. Observed LORAN-C time differences from a field test conducted in Monterey Bay, California were compared to calculated time differences determined from geographic positions based on a microwave positioning system. Four methods were used to determine the calculated time differences. The first three methods were (1) applying only the seawater Secondary Factor,

DO I JAM 7j 1473 EDITION or 1 NOV •• IS OBSOLfTE

S/N 0 102-014- ««0I

1

IKCURITY CLASSIFICATION OF THIS RAOB (9hmn Oaf Mnfrad)

<*eij««»'

i'"^«" n«t« *■••»•«

(2) computing the time difference based on a Semi-Empirical TD Grid, and (3) applying ASF Correctors from the DMAHTC LORAN-C Correction Table. The final method applied multiple observed ASF Correctors at five minute latitude and longitude intervals. By applying multiple observed ASF Correctors, which was the most accurate method, a 38.3 meter 1 drms with a lane offset of 3 to 12 meters using the 9940 X-Y LORAN-C combination was obtained. Based upon the results presented, it may be possible to use LORAN-C for hydrographic surveys at scales of 1:80,000,

DD Form 1473

1 Jan 73 S/N 0102-014-6601

•tcu«t»v CLAMiriCATioH or THU PAairmt*)' o««« t«««»»*»

Approved for public release: distribution unlimited

Application of Additional Secondary Factors to LORAN-C Positions for Hydrographic Operations

by

Gerald E. WheatDn

Lieutenant , NOAA B.S., California State University, Humboldt, 1975

Submitted in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE IN OCEANOGRAPHY (HYDROGRAPHY)

from the NAVAL POSTGRADUATE SCHOOL October 1982

y^ I U II

a, I

MONTEREY, CALIF. 93S40

ABSTRACT

The application of LORAN-C in the hyperbolic mode as a positioning system for hydrcgraphic surveys was investi- gated. Observed LORAN-C time differences from a field test conducted in Monterey Bay, California were compared to calculated time differences determined from geographic posi- tions based on a microwave positioning system. Four methods were used to determine th? calculated time differences. The first three methods were (1) applying only che seawater Secondary Factor, (2) computing the time difference based on a Semi-Empirical TD Grid, and (3) applying ASF Correctors from the DMAHTC LORAN-C Correction Table. The final method applied multiple observed ASF Correctors at five minute latitude and longitude intervals. By applying multiple

observed ASF Correctors, which was the most accurate method, a 38.3 me-cer 1 drms with a lane offset of 3 to 12 me-ers using the 9940 X-Y LORAN-C combination was obtained. Based upon rhe results presented, it may be possible to use LORAN-C for hydrographic surveys at scales of 1:80,000.

TABLE OF CONTENTS

I. INTRODUCTION 9

A. USE OF LORAN-C 9

B. APPLICATION OP ASF CORRECTORS FOR NAVIGATION . 11

C. APPLICATION OF ASF TO HYDROGRAPHIC POSITIONING 13

D. OBJECTIVES 14

II. NATURE OF THE PROBLEM 18

A. THE PRINCIPLES OF LORAN-C 16

B. PHASE LAG 19

C. TD MODEL 22

D. SEMI-EMPIRICAL TD GRID CALIBRATION MODEL ... 24

1. Technical Approach 25

2. Generalized Range/Bearing Model 27

E. DMAHTC MODEL 31

1. Sea SF Model 31

2. Land SF Model . . . .- 31

3. Table Descri p-^.ion 34

F. ATTEMPTED DETERMINATION OF ASF CORRECTORS 3Y HYDRO FIELD PARTIES 38

III. EXPERIMENTAL PROCEDURE 42

A. FIELD PROCEDURES 42

B. MICROWAVE SYSTEM POSITIONING 45

C. LORAN-C COMPUTATIONS 46

1. Seawa-er Secondary Factors (SF) 47

2. Semi-Empirical TD Grid 49

3. Calculated Table ASF Correctors 51

4. Observed ASF Correctors 52

IV. RESULTS 54

A. SEAWATER SECONDARY FACTORS 55

B. SEMI -EMPIRICAL T D GR ID 57

C. TABLE ASF CORRECTORS 59

D. MULTIPLE OBSERVED CORRECTORS 60

V. CONCLUSIONS 63

APPENDIX A: PROGRAM GPBYLQ 65

APPENDIX B: PROGRAM LORAN 78

APPENDIX C: PROGRAM LOPLC 88

APPENDIX D: PROGRAM LORTAB 101

APPENDIX E: PROGRAM ASFSEL 112

BIBLIOGRAPHY 123

INITIAL DISTRIBUTION LIST 127

LIST OF TABLES

I. Phase Retardation or Lag of Radio Waves 10

II. Coding Delay 9940 LORAN-C Chain 24

III. TD Bias (b) - jisec 29

IV. Seawater Coefficisnts 30

V. Land Coefficients 31

VI. Sea SF Model Coefficients 32

VII. Geographic Names and Positions 42

VIII. Microwave Positioning Equipment 45

IX. LORAN-C 9940 Chain Data 47

X. Data Set Parameter 55

XI. Seawater Secondary Factor Errors 56

XII. Semi-Empirical TD Sr id Correction Errors 58

XIII. Multiple LORAN-C Correction Table Errors 59

XIV. Multiple Observed Correction Errors 61

LIST OF FIGURES

2.1 Hyperbolic Fix (From Coast Guard LORAN-C User Handbook, 1974) 18

2.2 Transmitted Radiation 19

2.3 Phase Lag 21

2.4 Location of West Coast LORAN-C Stations .... 26

2.5 Mixed Path TD Geometry 28

2.6 Composite Land-Ssa Path 33

2.7 99aO-W ASF Correction Table 35

2-8 9940-X ASF Correction Table 36

2.9 ■ 9940-Y ASF Correction Table 37

3.1 Location of Test Areas in Monterey Bay 44

I. INTRODUCriON

A. USE OF LORAN-C

In recent years there has been an increasing usage of a LORAN-C receiver and the LORAN-C network as rhe primary horizontal control for such scientific studies as deep ocean dumpsites, marine fisheries studies [Rulon, 1979], bathyme- tric surveys, and recently, a recDnn aissance hydrographic survey. Examples of bathymetric surveys conducted by the National Oceanic and Atmospheric Administration (NOAA) , which have used Loran-C for positioning are:

1) Su-100-1-79 Gulf of Alaska [NOAA H-9822, 1979],

2) SU-100-2-79 Gulf of Alaska [NOAA H-9823, 1979],

3) S-D902-WH-82 U.S. West Coast [NOAA Ship Surveyor, 1982].

Recently an attempt was made ♦:o use LORAN-C as the sounding position control for a reconnaissance hydrographic survey S-K902-WH-82 [NOAA, 1982]. This was a special survey conducted by the NOAA Ship Whiting in May 1982. Special surveys are field examinations of very limited extent or scope and frequently require unique survey or data collec- tion procedures [Umbach, 1976]. The purpose of this project was to verify the existence and extent of reported shoaling in three safety fairways in the Gulf of Mexico [NOAA, 1982].

The use of Loran-C as a positioning system for basic hydrographic surveys has been very limited due to the abso- lute accuracy of the long range system. A basic hydro- graphic survey is defined as a survey which is so complete that it need not. be supplemented by other surveys. "It must be adequate to supersede for charting purposes all prior

surveys" [Umbach, 1976]. Variables which affact the accu- racy of LORAN-C are signal propagation variations, weather, and sky waves. The affects of weather and sky waves on LORAN-C propagation are best described by Samaddar [1980] and the American Practical Navigator, [DMA, 1977] respec- tively.

Signal propagation variations are due to the phase retardation of the signal as it passes over an all seawater path, over land paths, or partial seawater-land paths as compared to free space. Table I sammarizes phase retarda- tion changes [Mortimer, 1978]. Errors due to an all sea

TABLE I Phase Retardation or Lag of Radio Waves

Propagation Path

ReDr=s entation Propa gation V9l ocity (kffl/secf

Vacuum

299792.5

Direct wave through 299 691 earth's atmosphere

Ground wave over

sea water

Ground wave over rugged mountains

299560

298 899

Difference in Phase Lag at 500 km Compared with Wave in Line Abcv5 (m)

170

220

1,300

water path are known as the Secondary Factor (SF) and errors due to a land path or mixsd path are known as the Additional Secondary Factor (ASF) [Speight, 1982].

10

ASF Corrections in ths LORAN-C system can b9 as large as plus or minus four microseconds, which is 600 meters on t.he baseline. In other areas with the same LORAN-C coverage, these corrections may be much larger due to the expansion of the distance between adjacent hyperbolic lines of position. For example, at 32° N and 80° W, using lattice pair 9960-X, a four microsecond (jisec) error will offset the 9960-X line of position approximately 2438 meters [Speight, 1982].

B. APPLICATION OF ASF CORRECTORS FOR NAVIGATION

To compensate for the Loran-C positional errors caused by the ASF Correctors, the Secretary of Transportation tasked the Defense Mapping Agency aydrographic/Topographic Center (DMAHTC) , the National Oceanic and Atmospheric Administration (NOAA) , and the United States Coast Guard (USCG) with the job of determining and applying the Additional Secondary Correctors for each Loran-C chain. This task was published in the Department of Transportation (DOT) National Plan for Navigation in the July 19, 1974 Federal Register. These corrections should provide 95^ assurance that a vessel could fix its position to a pred- icted accuracy of 1/4 nautical mile (NM) within the U. S. Coastal Confluence Zone (CCZ) and the Great Lakes. The CCZ is defined as:

"the seaward approaches to land, the inner boundary of which IS the narbor entrance and the cuter boundary of which is 50 nautical miles offshore or the edge of the Continental Shelf (100 fathom contour) whichever is greater. "

The 1/4-NM accuracy reguirement also affects the

nautical chart. The National Ocean Survey (NOS) , which

publishes charts for the CCZ, engaged in a program with the

USCG and DMAHTC to provide the coastal navigator with charts

overprinted with lattices which meet 1/4-nm accuracy. The

OSCG, as operator of the LORAN-C radionavigation system.

11

conducts surveys to ensure that LORAN-C coverage exists within the CCZ and will be reponsible for the verification of 1/U-NM accuracy for all coastal LORAN-C service. In

conjunction with NOS , it assists in surveys of coastal waters of the United States to allow production of LORAN-C charts based on observed field data to meet the standards set forth above [Speight, 1982].

DMAHTC, for LORAN-C civil need, prepares grid predic- tions from its data base. Based on analysis and verifica- xion of the predicted grid from a USCG and/or NOS survey, it produces revisions to the initial grid predictions [ Speight, 1982]. At present, DMAHTC has provided NOS with ASF Corrected LORAN-C Lattices which are overprinted on the NOS Charts. Each chart with ASF Correctors applied contains one of the following notes:

"The LORAN-C lines of oosition overprinted en this chart have been prepared for use with groudwave sianals and are presently compensatsd only for t heoretical' prooaga- tion delays, wnich have not yst been verified by observed data. Marinsrs are cautioned not to rely entirely on the lattices in inshore waters. Skywave corrections are not provided".

or

"The LOEAN-C lines of position overprinted on this chart have been prepared for use with groundwave signals and are compensated with propagation delays cofflDu.ed from observed data. Mariners are cautioned not to rely entirely on the lattices in inshore waters. Skywave corrections are not provided" [Speight, 1982].

Presently, all of the NOS Charts of 1:80,000 to

1:120,000 scale covering the east coast. Gulf coast, and

Great Lakes show LORAN-C lattices that have been compensated

for Additional Secondary Factors. Most of 'h= lattices on

these charts have been constructed from DMAHTC data tapes

that provide adjusted LORAN-C readings for each rate at

every five minutes of latitude and longitude. A few

lattices were constructed using a single ASF Correction for

the entire chart area. Five minute data tapes were not

12

furnished by DMAHTC for constructing lines of position for LORAN-C rates on the West Coast Charts. On these charts a single average ASF Correction was used to adjust each lattice [NOAA, Marine Chart Division, 1982].

In addition to supplying corrected LORAN-C lattices for nautical charts, DMAHTC prepares, distributes, and periodi- cally updates unclassified ASF LORAN-C Correction Tables [Speight, 1982]. The ASF Correction Tables are for preci- sion navigation, utilizing digital computers to convert LORAN-C time differences to geographic coordinates [Speight, 198 2]. Presently, the ASF correctors found in the LOEAN-C Correction Tables were determined using theoretical propaga- tion delays. ASF correctors listed in the tables are going to be updated with observed data and reprinted the first quarter of 1983 [Wallace, 1982].

C. APPLICATION OF ASF TO HYDROGRAPHIC POSITIONING

Schr.ebele [1979] investigated the possibility of using Loran-C as an electronic positioning system for hydrographic surveying. He concluded that in Monterey Bay, California a single Additional Secondary Factor (ASF) applied to offshore lines of position gave a root mean sguare error (drms) of 66 meters for the West Coast 99U0 Y-W pair and a predicted U2 meter drms error for 9943 X-Y rates.

The 42 meter predicted drms is larger than Nelson's [General Electric Co., 1979] findings in San Francisco Bay. He demonstrated, in a dynamic mode, that the precision of LORAN-C was 60.8 meters 2 drms (30.4 meter 1 drms) with a worst case of 71.2 meters 2 drms (35.6 meter 1 drms) . A mean difference or offset between the measured time differ- ence and the calculated time difference was 34 nanoseconds for the 9940-X rate and one nanosecond for the 9940-Y rate.

13

He also obtained a precision of 38.0 meters 2 drms (19.0 meters 1 drms) in the static mode. Nelson also states, that the above precision is only achievable if the user has a LORAN-C receiver which has the performance capabilities of those used in the experiment. rh9 LORAN-C receiver must

have "comparable signal averaging time, extra notch filters, and attenua-ion of the signal" [General Electric Co., 1979].

D. OBJECTIVES

The National Ocean Survey requires that hyperbolic control systems used for hydrographic surveying exhibit a 1 drms of less than 0-5 millimeter at the scale of the survey [Umbach, 1976]. Although this requirement is generally for 2 mHz phase comparision systems, it can be inferred that it also applies to other hyperblic systems such as LORAN-C. The scale routinely used" for coastal surveys is between 1:40,000 and 1:80,000 [Umbach, 1976] yielding an allowable error of 20 to 40 meters not including systematic errors. Schnebele [1979] concluded that hyperbolic LORAN-C, after applying a single ASF Corrector, is unsuitable for basic hydrographic surveying.

Whether or not applying multiple Additional Secondary Factors (AS?) to LORAN-C lines of position will reduce the drms sufficiently to meet the accuracy standards set by the National Ocean Survey Hydrographic llanual will be ascer- tained in this study. The term multiple ASF Correctors refers to the applicatioQ of more than one corrector to LORAN-C lines of position over a given area. The variable ASF Correctors result from varying delays of the electromag- netic wave as it propagates over different land segments.

Three methods of applying multiple ASF Correctors were tested. The first method was the application of a

14

Semi-Empirical Time Difference Grid Calibration Model devel- oped by The Analytic Science Corporation [1979]. The spon- soring agency was the Onited States Coast Guard. The Semi- Empirical Model applies Secondary Factors and Additional Secondary Factors for each geodetic position based on the distance over land, the distance over water, and the total distance using mean se^ water and land conduc- tivities.

The second method which was investigated applies ASF Correctors found in the DMAHTC LORAN-C Correction Tables [DMAHTC, 1981] to LORAN-C lines of positions. These correc- tors were derived from the ground conductivities which have been determined in the field by a Coast Guard calibration team [U.S. Naval Oceanograp hie Office, 1982].

Finally, a third method was pursued. ASF Correctors, which were determined by field observations, were applied to the LORAN-C lines of position. These were derer mined by

computing the difference between the observed LORAN-C rates and the expected time difference which was calculated using four lines of position from a very accurate microwave posi- tioning system. These ASF Correctors were determined at five minute latitude and longitude intervals.

15

II. MIHRJ Ql IHI EIQBLEM

A. THE PRINCIPLES OF LORAN-C

To understand the problems associated with LORAN-C when used during hydrcgraphic operations, one must first under- stand its principles of operation. LORAN-C is a low frequency, pulsed signal, hyperbolic, radio navigation system, employing time difference measurements of signals received by the navigator from an laast three ground tran- smitting stations [Speight, 1982]. The stations ar9 comprised of a master transmitting station, two or more secondary transmitting stations which are strategically spaced several hundred miles apart and, if necessary, a System Area Moniter (SAM) Station [U.S. Coast Guard, 197U].

System Area Monitor (SAM) stations associated rfith each LORAN-C chain apply differential-type corrections to the rates in real-time. SAM stations continuously monitor the signals from all transmitters in the chain. If the oberved time difference deviates by- more than 0.05 jusec from the expected value, then the appropriate secondary adjusts its emission delay time in order to remove the error [Schnebele, 1 97 9 ] .

The master and at least two secondary stations are located such that the signals from the transmitting stations can be received throughout the desired coverage area. The master station is designated by the letter "M" and the secondary stations or slave stations are aesignatisd W, X, Y, or Z [.U.S. Coast Guard, 1974].

All stations transmit on the common frequency of 100 kHz. Interference between transmitters is avoided through the use of time separation [Poppe, 1982]. After the master

16

station transmits a pulse, each secondary station delays its own transmission for a fixed time, called the secondary coding delay. This ceding delay is synchronized through the use of cesium frequency standards at each station. The high stability and accuracy of these standards permit each station to derive its own time of transmission without reference to another station [DMA, 1977]. Secondary coding delays are predetermined by system propagation times and equipment characteristics [ Laurila, 1976].

The pulse from the master transmitter is distinguished from those of the secondaries through phase coding of the pulses. Phase coding refers to the inversion of the nega- tive and positive peaks of the sine wave comprising the 100 kHz carrier portion of the pulse. The purpose of the phase coding is twofold:

"Firs-, it permits automatic discrimination between the master and the various secondary stations, thereby permitting all stations to be identified by their rela- tive timing with respect to the master"

"Second, the phase coding nrcvides protection against excessively long skywave delays which would cause the late arrival of the proceeding pulse to coincide with the leading edge or groun dwave portion of a oulse being tracked" [Poppe, 1982].

The signals are received by a mobile receiver where the differences in time of arrival of the master signal and various secondary signals are measurad and displayed en the indicator portion of the LORAN-C set. The accuracy of this time difference is increased by phase comparision "of the synchronized 100 kHz carrier within the master and secondary pulses" [Laurila, 1976]. This measured time difference (TD - in microseconds) represents a hyperbolic Line of Position (LOP) [U.S. Coast Guard, 197a]. The intersection of two or

17

SECONDARY ( X )

THE LOCUS OF ALL POSITIONS WHERE THE OBSERVED TIME DIFFERENCE BETWEEN THE TIMES OF ARRIVAL OF THE M & X SIGNALS IS CONSTANT.

OBSERVER ( HYPERBOLIC FIX )

SECONDARY ( Y)

J

Figure 2.1

Hyperbolic Fix (From Coast Guard LORAN-C User Handbook, 197U)

more LORAN-C LOP*s defines the posi*:ion of the observer (Figure 2.1). When plotted en a chart, the intersection of the resultant hyperbolic lines defines a geographical position [Speight, 1982].

18

B. PHASE LAG

In a vacuum, the velocity of radiated energy from an antenna for LORAN-C is 29979 2,458 Icm/sec. Since radiated energy cannot be shown pic^orially, the phase of "che transmitted radiations is used. The lines of constant phase of the transmitted radiation are shown in Figure 2.2 by the curved lines labeled aa' , bb' , and other similar designa-ions. They define the wave front as it proceeds outward from zh=i antenna in all directions. The distance between each line of constant phase is one wavelength (x) [Admiralty Manual, 1 96 5 ] .

\ (meters) = 29 9792.4 58 km/sec t frequency in kHz

"1

Antenna

A

< X ^\< X >

< X >

I

J

Figure 2.2 Transmitted Radiation

The velocity of the radiated energy in air depends on :empera-ure, pressure, humidity, and the narure of the

19

surface over which the transmissions pass. The retardation of a -cransmitted wave is known as phase lag. When low frequencies are employed, such as LOHAN-C at 100, kHz, the effects of change of temperature, pressure, and humidity are swamped by the effects caused by changes in the na-ure of the surface over which the transmissions are traveling [Admiralty Manual, 1965]. The Genaral Electric Company, TEMPO division, conducted a LORAN-C Signal Analysis

Experiment under the direction of the U.S. Coasr Guard. This experiment was conducted along the U.S. Wesx Coast. The General Electric Company recorded an overall change of 108 nsec and 116 nsec time of arrival from -tha master and X-secondary stations respectively after a storm [Samaddar, 1980]. If ASF Correctors are as large as two microseconds on the West Coast [DMAHTC, 1981] then the ASF Corrections are 20 times larger in magnitude than weather effects for the 9940 West Coast LORAN-C chain.

The change in transmission ratas or phase lag are a result of the amount of energy transferred from -^he tran- smitted radiation. This energy transfer depends en the absorption qualities (inversely related to conductivity) of the surface over which they are passing and their wavelength (or frequency) . The lower the conductivity and the longer the wavelength (or lower the frequency) the greater the transfer of energy, and vice versa. Seawater has a rela- tively high conductivity (5.0 mhos/meter). Land has a much lower conductivity, which varies from marsh (fairly high) to dry sand and rock (very low) [Admiralty Manual, 1965]. Two excellant papers that discuss the electrical properties of soil are those of Smith-Rose [1934] and Pressey, Ashwell, and Fowler [1956]. Smith-Rose [1934] found that the conduc- tivities for soil ranged from 0.18 mhos/meter for a grey clay with salt to .00001 mhos/meter for granite.

20

Antenna

A

^0 120 160 Distance from Antenna (km)

Sea Level

Figure 2.3 Phasa Lag

Phase lag is illustrated in Figure 2.3, The lines of

constant phase , aa', bb ' , and cc' become distorted as they progress along the sea surface. The dotted lines represent the position of the lines of constant phase in the absence of the sea surface. The wavelength (X) in meters, measured at heights of several wavelengths above the sea, remains about the same as the direct wave through the earth's atmo- sphere at 299691 km/sec i- freguency in kHz. Near sea level the absorption of energy retards -he progress of -he wave- front, and makes the sea level wavelength ( x' ) less than A. As the lines of constant phase progress away from, the antenna the phase lag increases with distance. This is known as the Secondary Factor (SF) [Admiralty Manual, 1965].

The most intriguing feature of phase lag occurs at the coastal interface where there is an extreme change in the conductivites between land and sea. Visualizing the wave front in three dimensions, the lower part of the wave, slowed by the drag of the ground, lags further and further behind the upper part as the wave crosses the land. At the

21

coastline it suddenly encounters the much lower impedance of the sea, and in a very short distance the bottom of the wave tries to catch up with the top, as though the whole wave front were an elastic balloon. This is known as "phase recovery" [Eaton, 1979]. Phase recovery was verified during tests on Decca transmissions across the south coast of England by Pressey, Ashwell , and Fowler [1956]-

The determination of the Secondary Factor for seawater is fairly direct since the conductivity of seawater (5.0 mhos/meter) is fairly constant. But for land the conduc- tivity can vary depending on the type of soil and its water content [Smith-Rose, 1934].

Phase lag for radiated energy over land can be deter- mined two ways:

1) Assign an average land conductivity to the ASF Model, For example, the average conductivity for the soil on the west coast is 0.003 mhos/meter. The average land conductivity will determine the average phase retardation of the path [The Analytic Science Corporation ,1979].

2) Determine every conductivity for each portion of a line segment from the transmitter to the receiver. The total of these conductivity segments constituting a land-water profile will determine the total phase retardation of the path [Speignt, 1982].

C. TD MODEL

Positional fix accuracy using LORAN-C is primarily dependent on a chart makers ability to accurately compute the expected difference in time-of-acri val (TOA) of received groundwave signals from the transmitting s-^ations. Time

22

differences (TD) , are the differences between the TO As of

the secondary and master transmitters.

TD = TOA - TOA (2.1)

i 1 m

i = Secondary Station m = Master Station

TOA computations are dependent, upon an accurate knowledge of the signal phase delay.

The phase delay of a groundwave signal is generally

expressed as:

T + SF (2.2)

nR

C

SF

where n is the surface refractive index, C is the speed of light in a vacuum, R is the range between the raceiver posi- tion and the trajismi-t; ting station. The primary phase delay, T, is the computed travel time of the LOEAN-C pulse over a distance equal to the tran smit ter-tD-receiver greax circle path length, taking into account the veiccitv of electromag- netic waves and the index of refraction of the atmosphere. The secondary factor (SF) is a correction to the primary phase delay and accounts for the phase lag. The dominant term in (2.2) is the primary phase dslay (T) . The SF is

usually an order of magnitude smaller [The Analytic Science Corporation, 1979].

Thus, time-of-arr ivals can be expressed as:

TOA = T + SF + CD (2.3)

i i i i

TOA = T + SF {2,'i)

m mm

where CD is the true emission delay or coding delay for the LORAN-C chain [The Analytic Science Corporation, 1979]- The coding delay is equal to a time delay plus a computed one

23

way baseline time (Be) which includes the secondary phase correction for an all seawater path. The oneway baseline time (Be) is equal to the distance between the masx.er and secondary transmitters in meters divided by the propagation velocity of LORAN-C through the earth's atmosphere (299.691 meters per microsecond [Navigation Department DMA, 1982]). See Table II for Coding Delay values for the 9940 chain

TABLE II Coding Delay 9940 LORAN-C Chain

Pair 9940-W: 9940-X: 9940-Y:

CD CD CD

+ Be = 1 1000 + Be = 2 7000 + Be = 4 0000

■•• 2796.90 = 13796.90 + 1094.49 = 28094.49 + 1967.27 = 41967,27

|isec /isec ;us6c

1 1 1 J

[Riordan, 1979]. Combining equations 2.1, 2.3, and 2.4, the true TD is given by equation 2.5 [The Analytic Science Cor po rar io n , 1979].

TD = (T - T ) + (SF - SF ) + CD (2.5)

i i m i m i

D. SEMI-SaPIRICAL TD GRID CALIBRATION MODEL

The Semi-Empirical TD Model was developed by The Analytic Science Corporation [1979] in Reading,

Massachusetts for the »est Coast 9940 LORAN-C chain. Similar "time difference (TD) grid calibration techniques have been successfully employed to develop an accurate (approximately 100 nsec drms) calibra-ed grid for St. Marys River LORAN-C chain", [The Analytic Science Corporation, 197 9].

24

^ • l^chnical Approach

The Semi-Empirical Model is based on Millington* s empirical approach for computing the secondary factor over a mixed (multiple-homogeneous segment) path which combines land and sea phase delays. The generalized semi-empirical polynomial functional form for the SF of the LORAN-C station is given by:

K

2 L

SF = SF(T ,6)= I AT +S(C 5inl6 ♦ D ccsl B ) (2.6)

j j j k=-K^ k j 1=1 jl j jl j

where

j = secondary (W,X, or Y) cr master (M) station,

nS ,

T = = jth station-to user primary phase delay,

j c

R = jth station-to-user great-circle path length, j

8 = user path bearing angl=^ at the jth station, j

K , K and L are oositive integers, 12

C and D are the station-dependent coefficients jl jl

of harmonic terms in the model, A is the range-da pandent coefficient of -he model

which may in general be station-dependent.

Data from 27 coastal sites distributed along the West Coast and 122 land-sea sitas distributed in the Southern California CCZ (between Point Arguallo and San Diego - see Figure 2.4) were used in a Kalman estimation algorithm to compute the uncertain coefficients of the land and sea models of the TD grid calibration algorithm. (An

explanation of Kalman filtering for the layman is presented by Roger M. du Plessis [1967].) The calibrated algorithm

25

(X) Middletown V /\ California \ ^Tn

Monterey Bay

Point Arguello

Figaro 2.4 Loca-iOx' of West Coast LORAN-C Statio:

26

was used to compute TDs at each data site and the TD resi- duals (difference between measured aad calibrated TDs) were examined. Adjustments were then made to the TD model struc- ture in an attempt to further reduce the residuals. This process of adjusting the aodel structure is repeated until the residuals agree with the expected theoretical covariance associated with the TD model. The model which exhibited the "best" performance was selected as the West Coast TD grid model.

2. Generalized Ranqe/B earing Model

The Generalized Range/Bearing (GRB) Model was selected as the "best" semi-empirical calibration model for the West Coast chain. The semi-empirical function is:

L S? = AO + A1T + E (C sinlS + D cosl 6 ) usee (2.7)

J j 1=1 jl j jl j "^

where AO , A1 , C and D are the model coefficients, is the path bearing angle measurad positive clockwise from north at the jth ( W,X,Y or M) station and I is nhe path range to -he jxh station. The GRB model is rela-cively complex and is

expected to exhibit superior performance. The extensive mcdel is based on knowing the distance overland (TL) , -he distance over water (TS) , the total distance (T) , and the path bearing angle 3 (Figtirre 2.5).

It was noted that the calibrated mcdel was expected to be accurate and applicable only over the extent of ranges and bearing angles embodied in the calibration data. Hence, outside the region covered by the calibration data the model may not be as accurate as within the data coverage region. Osing the GRB model, a drms value of approximately 0.3 jisec was expected in areas where land data alone was used to calibrate the model. Inclusion of sea calibration data

produced a drms value of 9.35 to 0.50 jis<5c.

27

r"

USER :

MASTER STATION

D'.

,^ECONDARY STATION

Figure 2.5 Jlixed Path ID Geomezzj

The time difference (TD) is expressed by -he

following equation:

TD = (T - T ) + (SF. - SF ) + CD. + b. /isec (2.8)

i i m 11 11

28

where

n R.

T = |isec,

i c

n R m

T = )isec,

m c

R = ith secondary s-at ion-to-user great-circle path length, i

c = -he speed of an al ectromagnetic wave in a vacuum = 2.99792458 X 10^ m/sec,

n = surface refractive index = 1.000338,

R = master station-to- user great-circle path length, m

CD.= coding delay found in Table II,

b = TD bias associated with the ith secondary i

station (psec) (Table III) .

TABLE III TD Bias (b) - jasec

r-				"T
	TDW	-0.	BbU	1
	TDX	-1.	,173	1
c-	TDY	-0.	353	1 -J

SF,= 0.5 {-SI + S2 + S3 - 34 + S5 + S6) (2.9)

1

The term SI is -he SF of a land path of length T (;isec) from the jth station:

SI = 0.795/T + 0.439 + (0.00245) T usee. (2.10)

sj sj

The terms S2, S3, and S4 combine to make up the secondary factior for the seawater path Isngihs.

29

S2 is the SF for the total path. S3 is the SF using the seawater coefficients for the portion with seawater, and S4 is the SF using the seawater coefficients for the land path distance. The seawater coefficients are found in Table IV.

TABLE IV Seawater Coefficients

a1

a2 a3

b1 b2

b3

128.8 0. 187 0.000652

3.188 I

-0.594 I

0.000329 I

SF (T)

SF (T)

s

bl/T + b2 + (b3) T ;isec,

if 10 < T < 540 ;isec.

al/T + a2 ^- (a3) T if T > 540 jasec.

;isec.

(2.1 la)

(2. lib)

Term S5 and S6 are the SFs of land paths of length

T and T . SF5 is the Secondary Factor for the

J Ij total length using the land coefficients whereas

SF6 is the Secondary Factor for the distance over

land using •^. he land coefficients. The land

coefficients are found in Table V.

S5 = SF (T , 8 ) ,

L J J

S6 = SF (T ,6 ) ,

L Lj y

w he r e

SF (T , 3 ) = \0 ^ (A1) r + I (C sinl 3 + D cosl 3 ) (2.12)

L j j j 1=1 jl j jl j

30

TABLE V

Land Coefficients

AO	=	1.428	D x2	=	0.9U2
A1	=	0.00158	C	=	0.0
C	=	0.0	c	=	0.588
Wl			y2
C	=	-0.711	D	=	0.0
w2			yi
D	=	0. 323	D	=	0.0
wl			y2
D	t=	0.0	c	=	1.010
w2			ml
C	=	0.0	c	=	-0.196
xl			in2
C	=	0.0	D	=	-0.893
x2			ml
D	=	0,0	D	=	-0.355
Xl			m2		._ J

S. DMAHTC MODEL

1 . S6 a S F Model

The equations for the Sea SF Model is:

SF = (B1/T) + 32 + (B3 T) usec, if ID < T < 537 jis^c, (2.13a) SF = (A1/T) + A2 + (A3 T) a sec, if T > 537 jtisec, (2.13b)

where T is -he primary phase delay (or range) in microse- conds (usee); Ak and Bk (k = 1, 2, and 3) are the sea model coefficients used by DMAHTC in program TDGRID [Funakoshi, 1982]. The coefficients are found in Table VI.

2. Land SF Model

The solution used to resolve DMAHTC Taoles ASF Corrections is called Millington's Method [DMAHTC, 1981].

31

TABLE VI

Sea SF Model Coefficients

A1 A2 A3

B1 iB2

|B3

129.04323 -0.40758 0.00064576813

2.741282 -0.011402 0.00032774815

— I

This method is based on the premise that the phase distor- tion due to a composite land-sea path is the arithmetic average of the phase distortion foand in the forward and reverse paths of the propagated signal [ DMAHTC, 1981]. For example, in Figure 2.6 two azimuths have been drawn on the map and are labeled as 210° and 235o. Also placed on the map are the proper ground conductivities which have been determined in the field by the Coast Guard calibration team. A great circle drawn on the appropriate chart or charts from the LORAN-C Station coordinates to the area undsr considera- tion spans various lengths of land and seawater. Each length or segment will have a specific conductivity and distance. The total of these conductivity segments, consti- tuting a land-water profile, will determine the total phase retardation along that path [U.S. Naval Oceanographic Office, 1982]. All azimuths and distances are computed based on the World Geodetic Systsm (WGS) datum [DMAHTC, 198 1]. The values of phase retardation for a given ground conductivity are tabulated in the National Bureau of Standards (N3S) Circular 57 3 [Speight, 1982].

The formula used to derive the ASF Correction for the time difference for a master-slave transmitting station pair is:

ASF Correction = (-Slave Error) - (-Master Error)

32

TRANSMITTER

(,003 mhos/m)

SEAWATER (5.0 mhos/m)

^

Figure 2.6 Composite Land-Sea Path

The mean values derived for one station from the

forward and reverse solution of Millington's Me-hod are

subtracted from the Sea SF Model. The differences are

33

presented in an azimuth array. This array is a series of geodetic azimuths radiating from the transmitter with corrections computed at incremented distances along each azimuth. After the valaes are computed in the azimuthal array a compu-cer program rearranges them into a matrix form. The matrix form is the arrangement of corrections into rows and columns covering a specified geographical area at a constant spacing. The purpose of the matrix is to enable the corrections from two LORAN-C transmitters to be added algebraically, combined into a single matrix, and arranged in the desired tabular form. This tabular form is the body of the table [DMAHTC, 1981].

3 • Ta b le Description

Each table contains a complete chain. Figures 2.5, 2.6, and 2.7 depict LORAN-C ASF Correctors for chains 9940-W, X, and Y for Monterey Bay, California. A table section is prepared for each station pair (master station and one slave station) in a LORAN-:: chain. As a rule the limits of the table coverage are determined by the range of the groundwave transmissions for t-hs LORAN-C chain. Each page of corrections in the table covers an area three degrees in latitude by one degree of longitude, with correc- tions printed in increments of five minutes of arc. Rate designation and page numbers are printed at the top of each correction page. Those pages where latitude and longitude limits contain both land and sea are included but correc- tions apply only for the area covered by the a.S. Coastal Confluence Zone (CCZ) . Large land bodies and areas ouside the CCZ are represented by blank spaces on the page. ASF correcticn values can be either positive or negative (posi- tive values are shown without sign). Areas requiring no correction show a zero value which in some cases in preceded

34

	122"		LONGITUDE WEST	1 121
	0' 55 50	45	40 35 30 25 20 15	10 5 0 •
39* O'
55
50
45
40
35
30
Z'j
20
15 10			-
L 0 \ A 38 0
T
I 55
T 50
U 45
0 40
E 35
30
25
20
N 15
0 10
R 0 5, T 37 0
H
55	-1 .6 -1 .6
50	-1.6 -1 .5 -1.4
1 ^5	-1 .5 -1 .4 -1.6
i 40	-1.4 -1 .3 -1.5			,
i 35	-1.3			■ j
1 30	-1 .4			■
1 25	-1 .4 -1.5
20	-1 .2 -1.1
15	-1 .4 -1 .3 -1 .6
10	-1.3 -1.3 -1.7	-1.7
0 5	-1.3 -1.4 -1.7	-1 .7	-1.8
36 0'	-1 .2 -1 .6 -1 .6 • 1	-1 .7	-1.7 -1.7 -1.8
			III 1	i

Figure 2.7

9940-v* ASF Correction Taole

by a negative sign indicating that the zero results from the rounding off of a value slightly less than zero (indicates the trend of the correction).

35

1 1 1	122"			LONGITUDE WEST	121"
1 1	0*	55	59	45 40 35 30 25 20 15	10 5 0 '
39° O'
55
! 50
i 45
40 35				*
30
'
25
20
15
10
>- 0 5, A 38 0				-
T
1 55					1
T 50					1
U 45					1
0 40					f
E 35					1
30				•	1
25					1 1
20
N 15					1 1
0 10					1 1
R 0 5
T 37 0'
H
55	0.9	0.9
50	0.9	0.9	0.8		*
45	1 .0	1 .0	1 .0
40	1 .0	1.2	1 . 1
35	1.1
30	1 .0
25	1 . 1	1 .0			1
20	1.3	1 .4
15	1 .2	1.3	1 .1
10	1 .3	1.3	1 .0	1 .0	1
, 5	1 .3	1.3	1 . 1	1.1 0.9	j
36 0'	1 .3	1.3	1.2	1.2 1.0 1.0 0.7	1 1
I				" " " ■

Figure 2.8 99aO-X ASF Correction Tacls

The table can be entered directly by using the ship's position determined to the nearest five minutes of arc in la-irude and longitude either by dead reckoning or

36

		LONGITUDE WEST	1
	122'		121 'i
	0' 55 50 45	40 35 30 25 20 15	10 5 0 '
0 > 39 0
55
50
45
40
35
30	■
25
20
15
10
A 38 0		-
T
I 55
T 50		•^
U 45
0 40
E 35
30
25		.
20
H 15
0 10
R 0 5
T 37 0
H
5 5	-0.2 -0.2
50	-0.3 -0.3 -0.3
45	-0.3 -0.2 -0.4
40	-0.4 -0.3 -0.6
35	-0.5
30	-0.7
25	-0.6 -0.8
20	-0.5 -0.6
15	-0.4 -0.3 -0.3
10	-0.2 -0.2 -0.2 -0.2
, 5	-0.1 -0. 1 -0.1 -0.1	-0.2
36 0'	0.0 0.0 0.0 0.1	-0.1 0.0 0.0
^		,	_ _ , J

Figure 2.9 9940-Y ASF Correction Table

scr^e other means. To find the page with the appropriate correction, the Page Indexes of the table should be utilized. These indexes show the limi-s and page number of

37

all pages in the table. To locate the number of the page on which the desired correction is to be found ihe Page Index is entered with the ship's position. In some cases the

ship's position will fall on the page limit in either lati- tude or longitude or both. These positions are repeated on both pages and either page may be used.

The ASF Correction is added algebraically to the time difference for the LOR AN-C pair. Interpolation of this data will not necessarily improve the accuracy due to the method used to determine ASF Correctors [DMAHTC, 1981]. Since the correctors are computed in the azimuthal array and are based on the conductivity and distance over which the LORAN-C electromagnetic wave travels, the ASF Corrector between the published AS? Correctors in the tables may not be the linear interpolated values. For example, the ASF Corrector for a distance of 500 m with an azimuth of 180° is equal to 1.5 jisec. The ASF corrector for a distance of 500 m with an azimuth of 181^ is equal to 1.6 psec. The inter- polated value between 1.5 and 1.6 is 1.55. The true ASF Corrector for the 180° 30* azimuth is 1.U since the land distance for the same azimuth is less than the land distance for the 180O and 181 o azimuth. The LORAN-C signal passed over a harbor [Dansford, 1982]-

F. ATTEMPTED DETERMINATION OF ASF CORRECTORS BY HYDRO FIELD PARTIES

One of the major problems encoantered by hydrographic survey operating units when using LORAN-C for position control is the determination of the AS? Correctors for the survey area. The four surveys mentioned in the Introduction all made attempts to determine the correctors by comparing the LORAN-C rates to a second source.

38

Bathymetric Surveys H-9822 [NOAA H-9822, 1979] and H-9823 [NOAA H-9823, 1979] Gulf of Alaska, compared the rates from an Internav LC-20U LORAN receiver to computed rates from a position obtained from a JMR-1 Satellite Navigation Receiver when available. Shore ties using radar ranges, visual bearings, and sextant angles in comparison to LORAN-C rates were also made prior to and after each survey. The calibrations of LORAN-C rates were based on the satel- lite positions only since the positional computation of LORAN-C and JMR Doppler Satellite were made on the WGS 1972 datum whereas the land ties were based on the NAD 1927 datum.

Bathymetric survey SU- 40-7-82 which extended along the Washington, Oregon, and California Coasts used LORAN-C as navigational control. LORAN-C time differences were

compared with SATNAV positions. The report did not indicate whether any correctors were applied [NOAA Ship Surveyor, 198 2]-

Finally, Hydrographic Survey S-K902-Wh-82,

Reconnaissance Survey of Safety Fairways, Gulf of Mexico used LORAN-C as a pcsizioning control system. The posi-

tioning unit was an LC-20'i receiver. LORAN-C rates were input via the HIDROPLOT Controller, a special purpose input-outpu"*- interface which is the nucleus of the computer system hardware [dmbach, 19 76]. Positions were computed and plotted by Program RK121, LORAN-C Real-Time HYDROPLOT [Backus, 1980].

ASF Correctors for LORAN-C were achieved by visual cali- bration using three poirn: sextant fixes using charted oil rigs as control in the vicinity of the survey area. A

three-point sextant fix is a convenient and accurate method for determining the position of a hydrographic survey vessel. Sextants are used to measure two angles between

39

three objects of known geographic positon. The center object is common to both angles. The position of the obser- vers taking rhe angles is fixed by the intersection of three circular lines of position [Umbach, 1976].

These sextant angles were recorded and later tranf erred onto their respective charts using a plastic rhree-arm protractor. A plastic three-arm protractor is transparent and made up of one fixed arm and two movable arms which contain an etched line that is radial with the center of the protractor [Ombach, 1976]. Sextant angles observed in pairs for a resection fix with a common center mark may be plotted directly by this instrument. When the three arms are placed at the angles observed and fitted sd as to pass through the plotted positions of the observed stations on the field sheet, the hole at the center of the three-arm protractor is the fixed positon of the vessel [Ingham, 1975].

Partial correctors for each area surveyed were defined by comparing the observed rates and the determined rates plotted on the nautical chart. The partial correctors were applied via the HYDROPLOT Controller. However, even after applying these correctors, the plotted position still disa- greed with the ship's determined postion with respect to the oil rigs. Ship's personnel attributed the discrepancies to one or more of the following:

1) Accuracy of the charted rigs,

2) Weather effect on LORAN-C,

3) Time of day,

4) Propagation of signal over land path,

5) Three-arm protractor accuracy, and

6) Error in the conversion by the software of the LORAN-C rates to latitude and longitude [NO\A, 1982].

UO

There is an apparent need for a LORAN-C calibration routine aboard NOAA ships which provides the ASF Correctors for program RK121, LORAN-C Real-Time HYD20PL0T. The routine should use the same geodetic distance computation found in RK121 and use the same datum as that of the nautical chart of the survey area.

The above mentioned discrepancies illustrate the defi- ciencies in applying a single ASF Corrector -o LORAN-C data. The accuracies for hydrography cannot be met using single correctors because the errors are non-linear and systematic. They cannot be distributed like residuals in a traverse. Schnebele [1979] has already proven that single ASF area correctors to LORAN-C positions do not meet the accuracy s-andards of the NOS Hydrographic Manual.

Based on visual inspection of the DMAHTC LORAN-C Correction Tables, ASF Correctors should be updated every five minutes of Latitude or Longitude change. In Monterey Bay, California, there is approximately 0.1 to 0.2 usee difference for every five minures of change, a poten-ial error of 55 to 110 meters.

41

III. EXPERIMENIAL PROCEDURE

A. FIELD PROCEDURES

In order to compare the use of differential LOHAN-C with ASF multiple correctors, typical survey operations were planned for the southern portion of Monterey 3ay, California. This survey was conducted in con juncxion with a comparative evaluation of multiple lines of positon for selective positioning methods [Anderson, 1982]. Four micro- wave ranging systems were set on Known geographic positions

TABLE VII Geographic Names and Positions

Microwave System

Stations

Seaside 4 (1964)

Use Hon Ecc. Geoceiver Sec. Mussel Sec. Park (1931) Mulligan RM1 Range 7 (197 2) Mussel (1932)

Geographic Position (NAD 19 27)

35 0 36 1210 51

360 36

1210 52

36 0 36 121 0 53

36 0 36

1210 54

360 53

121 0 49

360 44

121 0 47

360 39

1210 49

36 0 37

1210 54

23.44596" 38.83281"

04,73031"

35.98040"

32.49281" 25.21162"

18.25484" 11.49661"

13.30600"

46.743 00"

5 6.49531" 52.31090"

02.47787"

08.58202"

18.15100" 11.49661"

^§l£§ !^§^d. June 3-5,1982

June 3-5,1982

June 3-5,1982

June 3-5,1982

June 6-7,1982

Jane 6-7,1982

June 6-7, 1982

June 6-7, 1982

42

listed in Table VII. A series of tracklines were run in two separate areas as shown on ?igure 3-1. To ensure that the microwave postioning system was working properly, the equip- ment was calibrated over known baselines of 1497.47 meters and 7877.3 1 meters at the beginning and end of the project. Trackline observations were only made during the daytime in fair weather conditions so as to eliminate sky waves and weather changes that influence LORAN-C signal propagation characteristics [Samaddar, 1982]. The vessel used was the 126 foot R/V Acania which is operated by the Naval Postgraduate School.

The positioning equipment consisted of a Micrologic ML- 1000 LORAN-C receiver (0.0 1 usee resolution) and a Trisponder Microwave System provided by Racal-DECCA Survey, Inc. The Trisponder Microwave System consisted of four DNT1 Model 217C transponders, four DNT1 Model 21017 HP sector antennas with 87o by 5° beam widths, cne DNT1 DDMU (Digital Distance Measuring Unit), two Omni DVTI Model 2 1019 HP antennas, a Houston Instruments Model DP3-M2D/RC3 plotter, and a Texas Instruments 743 terminal (Table 7III) . The

manufacturer's published accuracy for the positioning equip- ment is ± 1 m for a single range [ Ra::al-DECCA Survey, 1981]. Anderson [1982] discusses the accuracy of four lines of position. The four Decca Trisponder distances were recorded via a Texas Instruments 743 data terminal while the LORAN-C rates were manually logged. The data was acquired at one minute intervals while the ship maintained constant course and speed. The recorded LORAN-C rates were 9940-W, X, and Y of the West Coast chain.

To test the potential for calibrating the LORAN-C System using the Semi-Smpirical Model, the correction tables, and multiple observed field correctors, the positions derived from the microwave system n easurement s were used to compute

43

122*

122

Figure 3.1 Location of Test irsas in Mcntsrey Bay

44

TABLE VIII

Microwave Positioning Equipment

Eauipment			S/N
DNT1 Model 217C Transponders (Code (Code (Code (Code	72R] 74R 76R 78R	1 1	3323 3320 3321 3322
DNT1 Model 2107 HP Sector Antenna (870 by 50 Beam Widths)			185 186 187 191
DNT1 DDMV Model 540			426
Omni, DNT1 Antenna Model 2 1019 HP			194 200
Houston Instruments Plotter Model	jP3-	12D/RC3	10722-10
Texas Instruments 7U 3 Terminal			34418 — _ _ _j

expected LORAN-C time differences at each point. The

difference or offset between these expected time differences and the observed values were computed for the three methods. The mean offset, standard error, and drms values were also computed and compared.

3. MICROWAVE SYSTEM POSITIONING

The geographic position of the ship based on four lines of position was determined using a computer program callei GP3YLQ (Geographic Position by Least Squares) written by the author (See Appendix A) . GPBYLQ contains subroutine LSQR (Least Squares), which is a least squares adjustment written by Paul R. Wolf, Ph.D. [1974] and revised by LCDR D. Leath [1981]. Geographic postions were converted to X,Y (meters) which in turn were converted to geographic position via subroutines GPTOXY and XYTOGP, respectively [Wallace, 1974],

45

Subroutine GPTOXY and XYTOGP are based on the Modified Transverse Mercator Grid srfhich was centered in the survey area.

The Modified Transverse Mercator (MTM) projection is used by the National Ocsan Survey and is similar to the projection used in the Universal Transverse Msrcaror (UTM) system. The main difference is that in the MTM a Central Meridian is picked that is near the survey area instead of being fixed at a particular meridian [Wallace, 1971]. Central Meridian (CMER) , False Easting (FEST) , and Controlling Latitude (CLAT) are the three parameters which define the MTM projection. CMER is the mean longitude computed using the maximum and minimum longitudes of the survey limits, FEST is the X-Coordinate that is assigned to the Central Meridian, and CLAT is the distance in meters from the equator to seme reference latitude [Wallace, 1971], The Central Meridian, False Easting, and Controlling Latitude used for Monterey Bay, California referenced to NOS Chart 18685 are:

CMER = 1210 56' 00 .0",

FEST = 20000 .0,

CLAT = 4050000.0, To be consistent with the National Ocean Survey charts of the area, all computations were done relative to North American Datum (NAD) 1927 geographic positions. All

programs were executed on an IBM 30 33 computer located at W.R. Church Computer Center, Naval Postgraduate School, Monterey, California.

C. LORAN-C COMPUTATIONS

The differences or offset between the observed and computed LORAN-C rates using the Semi-Empirical TD Model, ASF LORAN-C Correction Tables, or the Multiple Observed

U6

TABLE IX

LORAN-C 9 940 Chain Data

r Station	Geogrj	aphic Position (NAD 1927)
Master - Fallon, Nevada	390 1180	33' 49'	07.03"N 52.23"W
Slave - George. Washington 9946-W	470 1190	03' 44"	48.82"N 34.78"W
Slave - Middletown, California 99 40-X	380 1220	46' 29'	' 57.49"N 40.04"W
Slave - Searchlight, Nevada 9940-Y	350 1140	19 48'	• 1 8 . 3 2 •• N ' 13.95»W
t -			_ J

Correctors were compared to the offsets between the observed TD rates and the computed rates for which only the seawater Secondary Factors (SF) were applied. The comparison of the offsets between the four methods illustrates the improvement in positional accuracy after applying ASF Correctors.

^ • Sea water Secondary Factors (SF)

Time differences using only the seawa'rer Secondary Factors for each of the geographic positions were computed using program LORAN written by the author {Appendix C) . Seawater Secondary Factors (SF) were computed using formula 2.13 and the coefficents found in Table VI. All TOA

distances in meters were determined using subroutine INVER1. INVER1 is a geodetic inverse routine using T. Vincenty's modified Rainsford's method with Helmert's elliptical terms, programed by LCDR L. Pfeifer, NOAA [1975]. Subroutine INVER1 is accurate to 0.0 001 m halfway around the world [Pfeifer, 1982]. All distances were converted to microse- conds using 299.792458 m/|iS€C. Time differences (TD) were

47

computed from equation 2.5. North American Datum 1927

geographic positions were used for all computations. See Table IX for the positions of LORAN-C 9940 transmitters [Riordan, 1979].

To ensure that subroutine INVER1 was functioning properly the distances between ths master and secondary stations were compared to the NOS published baseline distance [Riordan, 1979]. The published distances and -he results from routine INVER1 are lisred below.

Published Baseline Commuted Baseline

Dis-ance (m) Distance z INVERT (m)

99U0-W 837,777.0929 837,777.115

99U0-X 327,886.3720 327,886.316

99aO-Y 589,298.5712 589,298.589

The difference between the publishei and computed baselines ranged from 0.02 to 0.06 m.

Differences or offsets (x . ) were obtained by subtracting the observed LORAN-C rates from the computed values from the various methods. The mean difference or

offset (X) and standard deviation (s) in microseconds for each rate were determined using equations 3.1 and 3,2 [Wonnacott, 1935]:

n 1 Mean offset (/isec) : x = - Z x (3.1)

n i

i=1

where: x = original observation in usee, i

n = number of observations;

n Standard 1

error: s = Z (x - x)2. (3.2)

(;isec) n-1 i

48

The mean offset in microseconds can be converted to meters using equation 3.3 [Heinzen, 1977]:

Mean offset (meters)

where w

1 =

X w

sin 01

(3.3)

= distance corresponding to one microsecond

on the baseline = 149.396229 meters [Bigelow, 1963].

= one-half the angle between the

radius vectors from the position to the master and secondary stations.

Equation 3.4 was used to compute drms values in meters [Heinzen, 1977]:

drms=

sin ( + ) 1 2

\1

(S^W)2 2 sin a 1	(S^W)2 + + 2 sin a 2	2 pcos ( a + a ) s w 1 2 1	\ s w 2
(sin 01 ) (sin a )

(3.4)

where:

= correlation coefficient = 0.33,

s and a are as above with the subscript

denoting the appropria-^e secondary station.

The correlation coefficient (p) is a resuli of the secondary station having a common line of position with the master station. Although often ignored, various authors assign values ranging from 0.33 to 0.40. Bigelow [1963] chooses P = 0.33.

2 . Semi-Empirical TD Grid

To determine if the Semi-Empirical TD Grid would reduce either the drms value or the offset between the observed and expected TD rates, program LOPLC (Line of Position - LORAN-C) was written by the author (Appendix B) . Program LOPLC computes the distance over land, distance over water, the total distance, and the azimuth from north for the transmitting station using Subroutine INVER1. The

49

land-sea distances were computed by selecting a point which was located along the coast of Monterey Bay, Subroutine SHORPT (Shore Point) interpolated a geodetic position from 23 geodetic points which outlined Monterey Bay, California, The land/sea Secondary Factor was determined in Subroutine SECFAC which is found in program LOPLC using eguations 2,8 through 2.12, All corapu taxions ware based on NAD 1927 geodetic datum.

Tests were made on program LOPLC using data found in the Semi-Empirical TD Grid article [The Analytic Science Corporation, 1979] using the WGS 1972 datum. Station TASC 55 located at latitude 3ao 34* 18,3" N and longitude 120o 39* 40. 3" W, was selected from The Analytic Science

Corpora-ion article. It was one of the stations used to

calibrate the coefficients for the Semi-Empirical TD equa- tions discussed earlier. The only distances listed for TASC 55 were the individual distances ov=r land and over water. The total distance between the transmitters and TASC 55 was computed by adding the land and sea distances. The

following station-tc-site pazh segment lengths are listed for TASC 55:

TASC 55 OI2R2

Distance Dist ance Distance Distance

Station (km) (km) (km) (km)

Master 540,730 35.548 575.278 576.083

X-Secondary 369,248 126,096 495.344 495.178

Y-Seccndary 525,659 15,832 541.491 541.308

Using the land distances, sea distance, and total distances to TASC 55, and the computed azimth from subroutine INVER1, program LOPLC produced offsets of 3.86 jisec and 1.13 jisf^c for 9940-X and 9940-Y respectively when compared to the expected time differences at TASC 55.

50

An attempt was made to determine if this discrepency was due to program LOPLC. A comparison of the total

distances in the report between the transmitters and TASC 55 were compared to the total distances computed by INVEE1. The difference in distance between Subroutine INVER1 and the total distances from the Semi-Empirical TD 3rid acticle ranged from 160 - 200 m corresponding to 0.5 to 0.65 usee. This results in time difference errors of 0.04 usee for the 9940-X rate and a 0.10 ;isec for the 9940-Y rate, implying that the offsets, 0.86 psec and 1.13 fisec, are caused in part by the method in which the azimuth from north is deter- mined. Unfortunately, azimuth data from TASC 55 was not presented in the article. The Ar;alytic Science Corporation has been contacted on numerous occasions in an attempt to ascertain their method of determining distance and azimuth. As of this date there has been no response.

Nevertheless, ttie data from Monterey Bay was utilized in Program LOPLC to obtain results that could be compared to that obtained by the other methods. If this

method is accurate enough, AS? Correctors could be deter- mined via computer for each individual position without using tables or field determined correctors. The mean offset (X) and standard arror (s) in microseconds between the observed and calculated rates w=re computed using equa- tions 3.1 and 3.2, respectively. The mean offset (1) and drms in meters were computed using equation 3.3 and 3.4, respectively.

3. Calculated Table ASF Correctors

The offset between the observed LORAN-C rates and the expected values with applied ASF Correctors from the LORAN-C Correction Tables and the seawater Secondary Factor (equation 2.13) were determined using program LORTAB which

51

was written by the author (Appendix D) . The ASF Corrector for each position was selected using subroutine TABLE. Subroutine TABLE, which is found in program LORTAB deter- mines an AS? Corrector for each data point based on its geodetic position. The ASF Correctors used in subroutine

TABLE (see Figures 2.5, 2.6, and 2.7) are located between latitude 36° 35' N and 36o 55'N and longitude 121° 50' W and 1220 00' W. The difference in sign between the ASF

Correctors in subroutine TABLE and those found in ths LORAN-C Correction Table is due to the difference in their application. ASF Correctors from the tables are applied to observed rates while ASF Correctors from Subroutine TABLE are applied to the calculated LORAN-C rates. Negative ASF Correctors from the LORAN-C Correction Table were applied to the calculated time differences ro be consistent with the application of Secondary Factors to the computed primary phase delay.

As before equations 3.1 through 3.4 were used to compute "he the mean offset , standard error, and drms. If this application of LORAN-C Correction Tables is accurate enough, it precludes the need to determine ASF Correctors in the field.

'* • Observed ASF Cor rec tors

Observed ASF Correctors were determined using Program ASFSEL (ASF Selection) which was written by the author (Appendix E) , Schnebele's prior data [1979], and the June 1982 data. Program ASFSEL (ASF Selec-ion) was writ-en by the author. This program computes the ASF Correctors by subtracting the observed LORAN-C rates from the expected values. Only the seawater Secondary Factors from equation 2.13 have been applied to the calculated time differences.

52

The mean ASF Correctors for the LORAN-C rates were deter- mined at every minute of latitude and longitude between 36° 50* N and 36° 35' N and 122° 04»W and 122o 49' W. See

j Appendix E for mean ASF Correctors at one minute intervals.

The ASF Correctors were then selected and assigned to subroutine TABLS in Program L0RTA3 at five minute latitude and longitude intervals. All values were entered to the

I nearest hundredth of a microsecond. Equations 3.1 through

3.4 were used as before for computations. This determina- tion of ASF Correctors in the field, if accurate enough, may allow the use of LORAN-C as a positioning system for hydro- graphic surveying in the future.

53

IV. RESULTS

A total of 620 time differences (TD) and geographic positions based on four lines of position were recorded in the southern portion of Montery Bay in order to compare the use of differential LORAN-C with ASF Multiple Correctors. The data was divided into four sets. The first data set is Schnebele's [1979] prior data consisting of a tozal of 130 data points collected on two separate days, Juna 12 and July 25, 1979 between latitude 36° 38» N and 36° 47' N and longitude 121o 49' W and 12 20 02' W. The recorded LORAN-C time difference rates were 9940-Y and 9940-W.

The second data set consists of 193 time differences collected en June 7, 1982. The recorded LORAN-C rates were also 9940-Y and 9940-W. Data set Number 2 is located

between latitude 36o 40' N and 36° 45' N and longitude 1210 54' M and 122° OO'W. See Figure 3.1 for the location of test areas in Monterey Bay, California.

Data set Number 3 is located in the same area as data set Number 2, between latitude 36o 40' N and 36° U5' N and longitude 1210 W 54» and 122° 00' W. This set, consisting of 128 points with recorded rates 9940-X and 9940-Y, was recorded on June 6, 1982.

The final set, data set Number 4 was recorded between June 3 and iJune 5, 1982. It contains 169 points located between latitude 36o 36 N and 36o 39' N and longitude 121o 53' W and 121° 58' W. The recorded rates were 9940 -X and 9940-Y which are the same as data set three. The dana for rates 9940-X and 9940-Y was Icepr separate so as to determine if there was a significant difference between the offshore (data set three) and inshore (data set four) drms values due to phase recovery (see Chapter Two) .

54

TABLE X

Dara Set Parameter

Set Number	Collection Date	TD R ates	N Da	amber of ta Points	Area Lit	Limits Lon
1	June 12, 1979 July 25, 1979	9 940-Y 9 9U0-W		130		36/38 36/47	121/49 122/02
2	June 7, 1982	9 940-Y 9940-W		193		36/40 36/45	121/54 122/00
3	June 6, 1982	9 940-X 9940-Y		128		36/40 36/45	121/54 122/00
4	June 5, 1982	9 94 0-X 9940-Y		169		36/36 36/39	121/53 121/58 J

Table X provides a convenient breakdown of the parame- ters for each of the data sets. The table consists of the data set number, the date the data was collected, the LORAN-C time difference rates, the number of data poinxs, and the area limits in latitude and longitude. It defines the parameters for the four data sets of Tables XI (Seawater Secondary Factor Errors) , XII (Semi-Empirical TD Grid Correction Errors), XIII (Multiple LOP.AN-C Correc-ion Table Errors) , and XIV (Multiple Observed Correction Errors) . All basic data and computarion s are kept on file with the NOAA hydrography instructor at the Naval Pos-graduate School, Monterey, California. (Individuals seeking this information should contact the Oceanography Department.)

A. SEAWATER SECONDARY FACTORS

LORAN-C rates were computed using only the seawater Secondary Factor (equation 2. 13) . The LORAN-C computed time differences are basically uncorrected rates since no Additional Secondary Factors were applied. Offsets between

55

TABLE XI

Seawater Secondary Factor Errors

Rates

Mean Offset

Mean Offset

Standard

Error (s-^sec)

a)

b)

c)

d)

Set Y W .

Set Y W

Set X Y

Se-c X Y

(Schnebele's data. 130 data points) -0.508 -148.636 0.088

-1.2U1 -683.693 0.134

(June 7- 1982, 193 data points) -0.526 -154.295 0.077

-1.283

-701.947

0. 124

(June 6, 1982, 128 data points)

1.565 535.449 0.059

-0.550

-161.404

0.083

(June 3-5, 1982, 169 data points)

1.582 550.089 0.055

-0.817 -237.109 0.187

drms (1)

110.4

101.3

38.6

68. 1

the observed and calculated rates using only the seawater Secondary Factor were computed to illustrate -he improvement in posi-^,ion after applying the Semi-Empirical TD Model, ASF Loran-C Correction Tables, or nhe Multiple Observed ASF Correctors. The mean offset in microseconds and meters, standard error, and the drms are found in Table XI. Examples of offsets for several data points are listed in Appendix 3 after program LORAN.

It was stated earlier in Chapter One that Schnebele obtained a 66 m 1 drms using Y and W rates. The drms of 66 m was obtained using 48 data points which were located 10 km or more offshore. The 110.4 m 1 dris for the Y and W rates in Table XI is a result of combining the 130 inshore and offshore positions. The increase from 66.0 m 1 drms for the offshore positions to 110.4 m for combined offshore and inshore positions indicatas that the application of a single

56

ASF Corrector is dependant on the size of the area. The 48 data points were located between latitude 36° 41 » N and 360 46» N and longitude 121o 55 • W and 122° 02« W.

Schnebele also obtained the 66 m 1 drms by adjusting the LORAN-C observed time differences which were skewed due to the ship's motion and the five second averaging interval of the LORAN-C receiver. These caused the observed TDs to be several seconds old in comparison to the microwave system measurements [Schnebele, 1979]. Due tc the large amount.s of data from the June 1982 survey operations, no deskewing was done.

The offset, standard error, and drms for data set Number 2 (June 7, 1982) compares well to data set Number 1 (Schnebele's data - all). Also, the 38.6 m 1 drms for the X-Y rates is between Schnebele's U2.0 m 1 drms prediction [Schnebele, 1979] and Nelson's findings of 30 m 1 drms in San Francisco Bay [General Electric 3o. , 1979]. The large drms of 68.1 m for data set Number 4 (X-Y rates) is probably due to the phase recovery of the electromagnetic wave from The 99aO-Y transmitter located in Searchlight, Nevada. Finally, if ASF Correctors are not applied, drms values ranged from 38.6 m for 9940 X-Y to 101.4 m for 9940 Y-W for data sets 2 and 3. The large offsets for all data sets

indicate a systematic error, ranging from 150 m to 700 m, which precludes the use of zhis method for hydrographic surveying.

B. SEMI -EMPIRICAL TD GRID

To determine if the Semi-Empirical TD Grid would reduce the offset and drms for hydrographic surveying, program LOPLC (Appendix C) was applied to data sets 1 through 4. The Semi- Empirical TD Grid applies a Secondary Factor and an Additional Secondary Factor to the primary phase delay based

57

or. the distance overland, the distance over water, and the total distance using mean land and water conductivities. The mean offset in meters and microseconds, standard error, and drms are listed in Table XII. Examples of offsets for several data points can be found in Appendix C after program

TABLE XII Semi-Empirical TD Grid Correction Errors

Rates

Mean

Offset

(xz^sec)

Wean Offset (111)

Standard Error

a)

b)

c)

d)

Set Y W

Set Y H

Set X Y

Set X Y

(Schnebele's data, 130 data points) 1.131 330.672 0.086

1. 145

630.278

(June 7, 1982 data, 193 data

1.108 324.975

1.105 603,926

(June 6, 1982 data, 128 data

1.131 386.940

0.5 89

(June 3-5, 1.0 50 0.341

172. 923

0. 139

points) 0.077 0. 126

goints) .061 0.084

1982 data, 169 data points) 365.113 0.052

99.084 0.189

drms (iS)

113.5

112.7

39.4

63.2

LOPLC. Earlier, Program LOPLC had been tested with data found in the article by The Analytic Science Corporation [1979], Program LOPLC produced offsets of 0.86 ;isec and 1.13 }is(^c for the time differences from rates 9940-X and 9940-Y, respectively. As previously stated, the large

offsets may be due to the method by which the distance and azimuth were computed. The drms, for the data from Monterey Bay, obtained with the Semi -Empirical TD Grid was similar to the drms errors for seawater Secondary Factor .lodel. This might be an indication that Program LOPLC is correct but the

58

bias needs to be adjusted to reduce the large offset between the observed and calculated TD rates. The mean offset

ranged from 99 to 630 m« Bias reduction could be achieved by applying land-sea data for the entire West coast to the Semi-Empirical model. Again, the existence of large offset values precludes the use of this method for hydrographic surveying.

C. TABLE ASF CORRECTORS

To determine if the multiple ASF corrections from the LORAN-C Correction Table would reducs the offset and drms to meex the NOS accuracy standards, program LORTAB (Appendix D) was applied to data sets 1 through !4 . ASF Correctors from

TABLE XIII Multiple LORAN-C Correction Table Errors

Rates

Mean Offset (iZ^sec)

Mean Offset

(iz^)

standard Error (sz^sec)

a) Set 1 (Schnebele's data, 130 lata points)

b)

c)

d)

Y W

Set Y

Set X Y

Set No

eas

-0.229 0. 169

-^7,068"

92.540

(June 7- 1982 data, 192 data -0.309 -90.614

0. 123

67. 189

(June 6, 1982 data, 128 data 0.559 19^.134

-0.319

-93.486

0. 104 0. 160

oints) .085 0, 144

points) 0.073 0. 101

arms (m)

123.6

1 16.9

47.3

4 (June 3-5, 1982 data, 169 data points) ASF Corrections listed in Table for the south- end of Monterey Bay next to the shore line.

the LORAN-C Correction Tables are determined from field observation of land conductivities by the U.S. Coast Guard

59

Calibration Team [Marine Science Department, 1982]. The results are listed in Tabls XIII.

When compared to the Saawater Secondary Factor Error in Table XI, ^he drms values using LORAN-C Corrsction Tables were increased slightly while the offsets were reduced substantially. The offsets ranged from 65 - 200 m. Since the drms ranged from 47.3 to 116.9 m for rates 9940 X-Y and 9940 Y-W respectively, the application of ASF Corrector from the tables does not meet the NOS accuracy standard. Again, large offsets and the increase in drms precludes the use of this method for hydrographic surveying.

D. MULTIPLE OBSERVED CORRECTORS

To determine if multiple observed correctors would diminish the offset and drms values, mean ASF Correctors were selected at one minute latitude and longitude in-ervals using Program ASFSEL. One minute ASF Correctors are shown at the end of Program ASFSEL in Appendix E. From the one

minute grid, mean ASF Correctors were selected and entered into Subroutine TABLE at five minute latitude and longitude intervals in Program L0RTA3 . The following is an example of the 9940-X ASF Correctors at five mi.iute latitude and longi- tude intervals for the program:

122/00/00.0 121/55/00.0 121/50/00.0

36/50/00.0 -1.52 -1.63

36/45/00.0 -1.52 -1.56 -1.61

36/40/00.0 -1.58 -1.60

This is the same format used in the LORAN-C Correction Tables. Program LORTAB was applied to the four data s*=ts. The error results are listed in Table XIV.

The drms value obtained with multiple observed correc- tors were all reduced when compared to the irms for the

60

TABLE XIV Multiple Observed Correct icn Errors

-			Mean Mean Standard Offset Offset Error	_ _ — _ ^ drms
Rates	1	(X-jisec) l-ffl) (s-^sec) (Schnebels's data, 130 data points) 0.033 9.585 5.076 0.052 28.604 0.113	(I) 87.6
a)	Set Y W
b)	Set Y	2	(June 7, 1982, 193 data poinds 0.028 8.318 0.073 -0-016 -8. 944 0.116	89.3
c)	Set X Y	3	(June 6, 1982, 128 data points) -0.034 -11.490 0.055 0.010 2.913 0.086	38.3
d)	Set X Y	a	(June 3.5, 1982, 169 data points), 0.001 0.383 0.052 -0.008 -2.225 0.187	67.5

seawater Secondary Corrector. The idst: impressive reduction in drms was within Schnebele's data which covered an area of seven minutes of latitude and 12 minutes of longi-ude. The drms for seawater Secondary Correctors was 110.4 m whereas the drms for the same data using multiple observed correc- tors was 87.6 m. This is a smaller drms than that of the June 7, 1932 data (data set Number 2) which was obtained three years later. It appears that 87.6 m 1 drms is nearly the minimum error that can be obtained for the 9940 Y-W rates in Monterey Bay after applying multiple observed AS? Correctors at five minute latitude and longitude intervals. For the LORAN-C rates 9940 X-Y, a 38, 3 m 1 drms was obtained for same five minute area covered by data set Number 2 (June 7, 1982). LORAN-C rates 9940 X-Y were not obtained for the same size area covered by data set Number 1 (seven minutes of latitude and twelve minutes of longitude - 9940 Y-W) due

61

to the restriction of ship time and the length of time the Racal-DECCA Trisponder alrctronic eqaipinent had been loaned. The drms for the June 3-5, 1982 inshore data was only reduced to 67.5 m from 68.1 m for seawater Secondary Correctors. The small change in error at the coast is

probably a result of the erratic behavior of phase recovery discussed earlier in Chapter Two. The drms value could presumably be reduced if the correctors were applied at one minute intervals. This would be a very costly method of

calibrating Loran-C for hydrographic surveying.

62

V. CONCLUSIONS

It was noted in Chapter One that the smallest scale routinely used for coastal surveys Ls 1 ;80,000. This yields an allowable error of 49 tn 1 drms with no systematic errors. This paper determined whether or not applying multiple Additional Secondary Factors (ASF) Correctors to LORAN-C lines of position would reduce the drms sufficiently to meet the accuracy standards set by the National Ocean Survey.

Three methods of applying multiple ASF Correctors were tested. The first approach computes the time difference based on a Semi-Empirical ID Grid. The Semi-Empirical Xodel produced large offsets in the 9940-W, 99aO-X, and 99aO-Y time differences. The offsets ranged from 99 to 630 m. The drms for 9940 X-Y combination was 39.4 m and the drms for 9940 W-Y combination was 102.7 m.

The second method applies AS? Correctors found in the DMAHTC LORAN-C Correction Tables to LORAN-C lines of position. The application of the tables reduced the offset in the LCRAN-C time differences. The offsets were between

67 and 191 m. The drms was increased to 47.3 m for the 9940 X-Y combination and 116.9 m for the 9940 W-Y pair.

The final and most accurate method applies multiple observed ASF Correctors at five minute latitude and longitude intervals to LORAN-C lines of position. This

method again reduced the offset ia the time difference. This offset was between 3 and 12 m for the 9940 X-Y combination. Part of the offset may have been a result of the microwave positioning system. Reference is made to Anderson's [1982] paper (in preparation) on the evaluation of multiple lines of position.

63

The drms values were also reduced to 38.3 m for the 99U0 X-Y rates and 89.3 m for the 9940 W-Y combination. The 38.3 m 1 drms can be decreased by improving the sampling time for LORAN-C receivers. Nelson obtained 30 m 1 drms for the 9940 X-I rates with special LORAN-C squipment used in San Francisco Bay, California [General Electric Co., 1979]. Improving the sampling time for LORAN-C receivers used as positioning equipment for hydrographic surveys should be investigated.

With drms values of 38.3 m with the possibility of obtaining 30.0 m 1 drms and offsets ranging from 3 to 12 m, it may be possible to use LORAN-C for hydrographic surveys at scales of 1:80,000 or less using multiple observed ASF Correctors. The use of DMAHTC LORAN-C Correction Tables should not be ignored. After updating these ASF Correctors with observed data, the LORAN-C Correction Tables may allow LORAN-C to be used as a positioning system for hydrographic surveys.

64

APPENDIX A PROGRAM GPBYLQ

C PROGRAM GPBYLQ

C

C GENERAL PROGRAM FOR DETERMINING GP FROM KNOWN STATION

C POSITIONS AND THE DISTANCES FROM THEM USING LEAST

C SQUARES. GP TO XY AND XY TO GP ARE DETERMINED 3Y

C SUBROUTINES GPTOXY AND XYTOG? WHICH ARE BASED ON THE

C MODIFIED TRANSVERSE MSRCATOR PROJECTION (MTM) .

C

C PROGRAMMED BY GERALD E. WHEAION, LT. NOAA

C

C LEAST SQUARES ADJUSTMENT BY PAUL R. WOLF, PH.D. AND

C REVISED BY D. LEATH, LCDR

C

C PROGRAM INPUT VARIABLE NAMES

C TITLE = ANY JOB IDENTIFICATION NAMES OR NUMBERS

C M AND N = THE NUMBER OF EQUATIONS (M) AND UNKNOWNS (N)

C XO AND YO = BEST QUESTIMATE OF THE POSTION

C STA(I,1) = X COORDINATE OF KNOW STATION

C STA(I,2) = Y COORDINATE OF KNOW STATION

C STA(I,3) = DISTANCE FROM KNOW STATION

C A (I, J) = THE COEFFICIENT MATRIX

C EL (I, J) = THE CONSTANT MATRIX

C QLL{I,J) = THE WEIGHT MATRIX (WEIGHTS ARE ENTERED AS

C 1 • S IF THE SOLUTION IS EQUALLY WEIGHTED)

C

IMPLICIT REAL*8 (A-H,0-Z)

DIMENSION XCORD (30) ,Y CORD (30) ,WT (3 0) ,ISNO(30)

COMMON /ISTAT/ STA (30 , 3) , FXY (30)

COMMON /LSQX/ A (30 ,30 ) , EL ( 30 , 1) , QLL ( 30 , 30) , AT (30 , 30) ,

65

1AQ(30,30), QXX(30,30) , AQL(30,10), X(30,1), V(30,1),

2VAE(30) , TITLE(80) C

C READ AND WRITE OaTPOT TITLE

C

WRITS (6,509)

READ (5,710) TITLE

WRITE (6,710) TITLE C

C DEFINE NUMBER OF SI3NALS (NOT GREATER THAN 30) AND

C NUMBER OF DATA SETS.

C

READ (5,502) NSIG,NDATA

502 FORMAT(I5,I10) C

C DEFINE THE CENTRAL MERIDIAN (CMSR) , FALSE EASTING

C (FEST), AND CENTRAL LATITUDE (CLAT) .

C CMER IS EXPRESSED IN DEGREES, MINUTES, AND SECONDS.

C' FEST IS THE X-COORDINATS THAI IS ASSIGNED TO THE

C CENTRAL MERIDIAN AND IS EXPRESSED IN METERS.

C CLAT IS DEFINED AS THE CONTROLLING LATITUDE.

C IT IS USED TO REFERENCE THE Y-COORDIN ATES AND

C IS EXPRESSED IN METERS.

C

READ (5,503) ILO NC, ILM INC, RLSECC , FEST , CLAT

503 F0eMAT(1X,I3, 1X,I2,1X,F8. 5, 1X,?7. 1,F10.1)

CMER = ((IA3S (ILONC) * 60 + ILMINC) * 60) + RLSECC C

C DEFINE VARIABLE FOR:

C NUMBER OF EQUATIONS (M)

C NUMBER OF UNKNOWNS (N)

C IPAGE = NUMBER OF LINES PER PAGE.

C

IPAGE = 1

66

M = 4

N = 2 C

C NULL WEIGHTS C

DO 3 I a= 1,30,1

DO 3 JM=1,30,1 3 QLL(IM,JM) =0.0 C

C R2AD STATION NUMBERS , POSITION, AND WEIGHTS. C CONVERT POSITIONS (3P) TO SECONDS AND THEN TO XY. C

DO 12 J=1,NSIG,1

READ (5,80 0) I SNO (J) ,IL AT ,1 MIN, RS EC, JLON, JMIN , SSEC, WT (J) 800 FORMAT(1X,I3,IU,I3,F9 .5,I5,I3,F9.5,F5. 1) C

RMAST = ((lABS(ILAT) * 60 + IilIN) * 60) + RSEC

RMASTL = ((lABS(JLON) * 60 + JMIN) * 60) + SSEC C

CALL GPTOXY (RMA ST, RMA STL, XMETER, YMETER, FEST , CLAT , CMER)

XCORD(J) = XMETER 12 YCORD(J) = YMETER

C

C READ DATA (STATION NUMBERS AND THE DISTANCES)

C

15 DO 40 JC0UNT=1 ,NDATA ,1 READ(5,805) I F, IS, IT , lU ,NREC

805 FORM AT (515)

DO 16 IC0UNT=1 ,NSI3, 1 IF (ISNO (ICOUNT) .EQ. IF) IF=ICOUNT IF (ISNO (ICOONT) .EQ. IS) IS = ICOUNT IF (ISNO (ICOUNT) ,EQ. IT) IT=ICOUNT

16 I? (ISNO (ICOUNT) .EQ. 14) I4 = IC0UNT C

67

STA(1,1) = XCORD(IF)

STA(1,2) = YCORD(IF)

QLL(1,1) = WT(IF) C

STA(2,1) = XCOFD(IS)

STA(2,2) = YCORD(IS)

QLL(2,2) = WT(IS) C

STA(3,1) = XCORD(IT)

STA(3,2) = YCORD(IT)

QLL(3,3) = WT(IT) C

STA(a,1) = XCORD(IU)

STA(4,2) = YCORD(IU)

QLL(4,4) = WT(I4) C

C READ THE DISTANCE RECORD AND LORAN HATS.

C

DO 38 KC00NT=1, NREC,1

READ (5,507) STA (1, 3) , STA(2,3) ,STA (3,3) ,STA (4,3) , 1 RATE1,RATE2 507 FORMAT(6F10, 1)

C

C DETERMINE BEST GUESS COORDINATES XO AND YO

C WITH SUBROUTINE GUESS.

C

19 CALL GUESS (XO,YC) C

IJUMP = 0 C

C COMPUTE FXY, A AND L MATRIX

C

20 DO 25 1=1, M

FXY(I) = DSQRT (DA3S( ( XO-STA (I, 1) ) **2

68

1 (Y0-STA(I,2) )**2) )

A (1,1) = (X0-STA(I,1) ) / (FXY(I))

A(I,2) = (Y0-STA(I,2) ) / (FXY (I) ) 25 EL (1,1) = STA(I,3) - FXY(I) C

C CALL SUBROUTINE LSQR C

CALL LSQR (K,N) C

C COMPUTE THE NEW QUESSTIMATE FOR XO AND YO C

XO = XO + X (1 ,1)

YO = YO + X (2,1) C

C EXIT IF STANDARD ARE MET USING IJUMP OR C XO AND YO CUT OFF C

IF (DABS (X (1,1) ) .LE.1. 00 .AND. D AB3 (X (2, 1) ) . LE. 1 . 00) 1 GO TO 35

IF (IJUMP .EQ. 10) GO TO 35 30 GO TO 20 C

C COMPUTE ERROR ELLIPSE C 35 CONTINUE

CALL ELIPSE (SU, SV) C

C CONVERT XY TO GP

C

CALL XYTOGP (XO, YO, SEC lAT, SECLON , FEST , CLAT, CMER)

CALL TODMS (SECL AT, IDE GP,I MINP, RSECP)

CALL TODMS (SECLON, JDE GP ,JMINP , 3SSC?) C C PAGE AND CONTINUE WITH NEXT SET OF OBSERVATIONS

69

c

WRITE (6,505) IDEGP ,IM INP,RSEC?, JDEGP, JMINP , SSECP , 1 EATE1,RATE2 C WRITE(6,505) IDEGP ,IMINP, RSECP, JDEGP, JMINP, SSECP,

1 sa,sv

505 FORMAT (14, 13, F6. 2, 15, I3,F6 . 2, 2F9 . 2) C IF(IPAGE .EQ. 50) WRITE (6,509)

IF(IPAGE .EQ. 50) IPAGE = 0 38 IPAGE = IPAGE + 1

C

C FORMAT STATEMENTS C

710 FORMAT(80A1) 509 FORMAT (1H1)

UO CONTINUE

STOP

END

C======== = ======= = == ====== ====== = == = = = == ====== = = == = ======:

SUBROUTINE LSQR (M,N) Q

IMPLICIT REAL*8 (A-H,0-Z)

COMMON ASQX/ A (30,30) ,SL (30, 1) ,QLL (30,30) , AT(30,30) , 1AQ(30,30), QXX(30,30) , AQL(30,10), X(30,1), 7(30,1), 2VAR(30) , TITLE (80) C

C COMPUTE A TRANSPOSE 3Y TRANSPOSING THE A MATRIX (AT)

C

DO 6 1 I=1,M DO 61 J=1,N 61 AT (J, I) =A (I, J) C

C USING STEPS (1) , (2) , AND (3) COMPUTE THE INVERSE C OF THE TRANSPOSE (AT) * WEIGHTED MATRIC (QLL) * C MATRIX A = QXX.

70

c

C (1) COMPOTE AQ = AT * QLL

C

DO 7 1 1 = 1 ,N

DO 71 J=1 ,M

AQ (I,J)=0.

DO 71 K = 1 ,M 71 AQ (I,J)=AQ(I,J) +(AT(I,K)*QLL(K, J) ) C

C (2) COMPUTE QXX = AQ * A

C

DO 81 1 = 1, N

DO 81 J=1,N

QXX(I,J)=0.

DO 81 K=1,M 81 QXX(I,J)=QXX (I, J) +AQ (I,K) *A (K,J) C C (3) INVEST QXX MATRIX

C

DO 3 07 K=1 ,N DO 302 J=1,N IF (J-K) 304,302, 304 304 QXX(K,J)=QXX (K, J)/QXX (K,K)

302 CONTINUE QXX(K,K)=1./QXX (K,K) DO 307 1=1, N

IF (I-K) 305,307,305 3 05 DO 3 03 J=1,N

IF (J-K) 306,303, 306

306 QXX(I,J)=QXX (I, J) -QXX (I,K) *QXX (K, J)

303 CONTINUE QXX(I,K)=-QXX (I,K) *QXX (K, K)

307 CONTINUE

71

C USING STEPS (4) AND (5), COMPOTE THE UNKNOWNS X

C BY MULT THE INVERSE Q XX AND AQL.

C

C (U) COMPUTE AQL = A Q * EL

C

DO 101 1=1, N

AQL(I,1)=0.

DO 101 K= 1 , M 101 AQL(I,1)=AQL (I, 1) +A3 (I,K) *EL(K, 1) C C (5) COMPUTE X = QXX * AQL

DO 201 1=1, N C

X (I, 1)=0.

DO 201 K=1,N 201 X (I, 1) =X(I,1) +QXX(I,K) *AQL (K, 1) C

C (6) COMPUTE THE RESIDUAL (V = A * X -EL) C

DO 301 1=1, M

V{I,1)=0.

DO 3 01 K=1,N 301 7 (I, 1)=7(I, 1) +A (I,K) *X(K, 1)

DO 1 1=1, M 1 V(I,1)=V(I,1)-EL(I,1) C

C COMPUTE THE STANDARD DEVIATION OF UNIT WEIGHT SIGMA C DM - NUMBER OF OBSERVATIONS C DN - NUMBER OF KNKNOWNS

C

SIGMA=0.

DM=M

DN=N

DO 332 1=1, M

72

382 SIGMA=SIGMA+V (1,1) **2*QLL (1,1) SIGMA=DSQRT (SIGMA/(D M-DM) ) C

C COMPUTE THE STANDARD DEVIATION OF THE ADJUSTED UNKNOWNS

C QXX - ARE THE ELEMENTS OF THE COVARIANCE MATRIX.

C

DO 446 1=1, N 446 VAR(I) =DSQRT (QXX(I ,1) *SIGMA**2) C

5 10 CONTINUE RETURN END

C==r== ===== = == ============== = = ======== = = = = == = = = === = == = = ====== =

SUBROUTINE ELIP SE (SU, SV) C

c

C SOLVE FOR THE SEMI MAJOR AND SEMI MINOR AXIS OF

C THE ERROR ELLIPSE

C

IMPLICIT REAL*8 (A-H,0-Z)

COMMON /LSQX/ A (30 ,30 ) , EL ( 30, 1) , QLL (30 , 30) , AT (30 , 30) , 1AQ(30,30), QXX(30,30) , AQL(30,10), X(30,1), V(30,1), 2VAR(30) , TITLE(80) C

SUS = .5*(QXX(1,1) + QXX(2,2) + DSQRT (DABS (QXX ( 1 , 1) - 1 QXX (2,2) +4.0*QXX(1,2) *QXX (2, 1) ) ) )

SVS = .5*(QXX(1,1) + QXX(2,2) - DSQRT (DABS (QXX (1 , 1) - 1 QXX (2,2) +4.0*QXX(1,2)*QXX (2,1) ) ) ) C

SU = DSQRT (SUS) SV = DSQRT (SVS) C

RETURN END

73

C==:==s = =: == = ===== = = = = ======= ===== = = = = = = = === = == = == = = == = = = = == =

SD3R0UTINE G0ESS(XO,YO)

c

C SUBROUTINE GUESS DETERMINES THE BEST GUESS COORDINATES

C TO BE USED IN SUBROUTINE LSQR. USE RIGHT SIDE RULE FOR

C STATION ORDER.

C

IMPLICIT REAL*8 (A-H,0-Z)

COMMON /ISTAT/ STA (30 , 3) , FXY (30) C

C DETERMINE DISTANCE BETWEEN STATION 1 AND STATION 2

C

D = DSQRT ((STA (2, 1) -STA (1,1) ) **2+ (STA (2,2)-3TA (1,2) )**2) C

C DETERMINE ANGLE ALPHA BETWEEN XO , Y0/STA2/STA1

C

ALPHA=DARC0S ( (STA(2,3) **2-STA (1,3) **2 + D**2) / 1 (2.0*STA (2,3)*D) ) C

C DETERMINE ANGLE BROVO BETWEEN X-AXIS AND STA2-STA1

C

BROVO=DARSIN ( (STA (1,2)-STA (2,2) ) /D) C

C DETERMINE X AND Y LENGTH

C

X=STA (2,3) *DCOS (ALPHA +BROVO)

Y = STA (2,3) *DSIN (ALPHA +BROVO) C

C DETERMINE XO AND YO

C

XO = STA(2, 1) +X

YO = STA(2,2) ■^Y

in

RETURN END

SUBROUTINE GPTOXY(SEC LAT, SECLON,XCO, YCO^FEST ,CLAT,CMER)

IMPLICIT REAL*8 (A-H,0-Z)

DATA E2,RK0,A / .00676 8658 DO ,. 99998D0 , 6378206 .UDO/

DATA RKGE0,W1,W2 /O. 0 4848 1 368D0 , 0. 11 422D0, 2 1 . 73607D0/

DATA W3, W 4/5 104. 57 33 8 DO, 63 673 99. 6 3 9D0/

DATA RADSEC /.O 000048 48 13681 1 1D0/

C C

RADLAT = SECLAT * RADSEC SINLAT = DSIN (RADLAT) SIN2LA = SINLAT * SINLAT COSLAT = DCOS (RADLAT) C0S2LA = COSLAT * COSLAT P = (CMER - SECLON) / 10000. ODO V = A / DSQRT(1.0D0 - E2*SIN2LA) TANCON = 1.0D0 - SIN2 LA/C0S2LA

S = W4 * (RADLAT - SI NLAT*C0SLAr/1 0. 0DO**6 * * (W3 -COS2LA*(W2- W1*C0S2LA) ) )

T1 = S * RKO - CLAT T2 = RKGEO * COSLAT * RKO * V T3 = T2 * RKGEO / 2. 0 DO T4 = T3 * SINLAT

T5 = T3 * RKGEO * COS 2LA / 3. ODO T6 = T5 * TANCON

T7 = (4. ODO + TANCON) *T5 *RKGEO * SINLAT / 4, ODO XCO = (T2 + (T6*P**2))*P + ?EST YCO = (T7*p**4) + (T4*P**2) > T1 RETURN END

75

SUBROUTINE XYTOGP(XCO , YCO, SECLAT, SECLON,FEST,CLAT,CMER)

IMPLICIT REAL*8 (A-H,0-Z) C

DATA E2,A,SR /O .00676 86 58D0 ,6378206. UDO , 1 0.0000048U81368D0/

DATA W1,W2,W3 /O. 2468 2D0, 30. 0233 5D0, 5078 .64 97700/ C

D = CLAT ♦ YCO

WO = 0. 15704998 1D0/10.0D0**6 * D

SINWO = DSIN(WO)

COSWO = DCOS (WO)

C0S2W0 = COSWO * COSWO

PHI1 = WO + SINWO*COS WO/1 0.0D0**6 * * (W3-^COS2WO*{W2+W 1*C0S2W0) )

PHI2 = PHI1 / 0.99998D0

PHI3 = PHI2 / SR

Q = (XCO - FEST) / 10.0D0**6

V = A / DSQRT{1.0D0 - E2*DSIN {PHI2) **2)

T = DC0S(PHI2) * SR

C = V * 0.99998D0

T1 = 10.0D0**6 / (T*C)

T2 = (T1*10. 0DO**6) / (2.0D0*C)

T3 = (T2*10.0D0**6) / (3.0D0*C)

T4 = (T3*10.0D0**6) / (4.0D0*C)

DELLON = (T1-Q**2*T3* (2.0D0*DTAN (PHI2) **2+1 .ODO) ) *Q

SECLAT = ( ( (3.0D0*DTAN(PHI2) **2 + 5.0D0) *T4) *Q**2-T2) 1 *Q**2*DSIN (PHI2) + PHI3

SECLON = CMER - DELLON

RETURN

END SENTRY

76

DATA SET EXAMPLE - PROGRAM GPBYLQ.

SHIP'S POSITION OBSERVED LORAN RATES

LATITUDE (D-M-S)	LONGITUDE (D-M-S)	9940-X (fisec)	9940-Y
3 6 36 40.20	121 52 48,62	27508.79	42742.71
36 36 42.41	121 52 48.16	27508.81	42742.93
3 6 36 44.56	121 52 47.52	27508.83	42743.15
3 6 36 46.84	121 52 46.98	27508.76	42743. 26
36 36 49.09	121 52 46.5 9	27508.76	42743.48

77

APPENDIX B PROGRAM LOR AN

C PROGRAM LORAN

C

C PROGRAM COMPOTES LINE OF POSITIONS FOR LORAN-C USING

C THE SECONDARY FACTOR (SF) BASED ON SEAWATER EM MODEL.

C

IMPLICIT REAL*8 (A-H,0-Z)

DIMENSION AXIS( 13) ,RF (13)

DIMENSION XSLAV1 (100 0) ,XSLAV2 (1000)

DATA RHOSEC,PI,UNCOV, RN/2. 06264 8062U71D05, 1 3. 1 4 15 92 6535 89 8D0, 2 9 9.79 245 800,1 .000338DO/

DATA XMEAN1,XMEAN2,VAR1,7AR2/O.OODO,O.OODO, 1 0.0ODO,00.0D0/

DATA XMEAN3,XMEAN4/0. 0ODO,O.00DO/ C CCCCCC* ******************** *************

DATA AXIS/6. 3782064D06, 6. 378388 D06 , 6. 377397 1 55D06 ,

1 6.37816 D06, 6. 37816D06, 6, 378249145006,6. 378165D06,

2 6.378166006,6.378165 D06 , 6 . 378 1 45D06 , 6. 3775634D06,

3 6.378245006,6.3781350006/

DATA RF/6. 3565838 006,2.97 002,2.9915 28 12 85002,

1 2.98 2500 2,2. 98 2 4716 7 4270 02,2.9 3 46 50 02,2.9 8 25002,

2 2.983 002,2.983002,2-9825 002,6.3562569006,

3 2.933 002,2.9826002/ C*****ELLIPSOID OPTION NUMBER

C 1. CLARKE 1866 8. MERCURY

C 2. INTERNATIONAL (HAYFORD) 9. MARSHALL ISLAND

C 3. BESSEL 1841 10. NAVY 8D

C 4. AND (AUSTRALIAN) 11. AIRY

C 5, 1967 REFERENCE 12. KRASSOWSKI 1940

78

C 6. CLARKE 1880 MOD 13. WGS 1972

C 7. SAO

C

cccccc* ************ ******** *************

C CC1-2 = ELLIPSOID NUMBER (K)

C CC3-5 = NUMBER OF POINTS ALONG COAST (IREC)

C

READ (5, 100) K,IREC 100 F0RMAT(lX,l2,ia)

TW0PI=2.*PI

A = AXIS(K)

F=1./RF (K)

IF (F.LT.3.D-3) F=(A-1./F)/A C

C READ MASTER AND SLAVE STATIONS POSITIONS

C THE FIRST RECORD IS THE NUMBER OF MASTER AND SLAVE

C STATIONS FOR THE PARTICULAR CHAIN.

C

WRITE (6,202) 202 FORMAT(IHI)

WRITE (6,201) 201 FORMAT (1H )

READ (5, 105) ILATM,IMINM,RSECM,ILONM,ILMINM,RLSECM

WRITE (6,1 05) ILATM,IMINM,RSECM,ILONM,ILMINM,RLSECM 105 FORMAT (IX, 13, IX, 12, IX, F5. 2, IX, 14, IX, 12, IX, F5. 2)

RMAST = ( (lABS(ILATM) * 60 + IMINM) * 60 > RSECM) / 1 RHOSEC

IF(ILATM .LT. 0) RMAST = -RMAST

RMASTL = ( (TABS (ILONM) * 60 + ILMINM) *60 +RLSECM) / 1 RHOSEC

IF (ILONM .GT. 0) RMASTL = TWOPI - RMASTL C

C READ THE FIRST SLAVE STATION AND CHANGE THE LATITUDE

C AND LONGITUDE INTO RADIANS.

79

READ (5, 101) ILATS,IMINS,RSECS,rLONS,ILMINS,ELSSCS, 1 DELAY1

WRITE (6,101) ILATS,IMINS,RSECSrILONS,ILMINS,RLSBCS, 1 DELAY1 101 FORMAT (IX, 13, IX ,12 , 1 X ,F5. 2, IX, lU , IX, 12, IX, F5 . 2 , F9 . 2) RSLAV1 = ((lABS (ILATS) * 60 4- IMINS) * 60 + RSECS) / 1 RHOSEC IF (ILATS .LT. 0) RSLAV1 = -RSLAV1

RSLAL1 = ((lABS (ILONS) * 60 + ILMINS) * 60 ■»• RLSECS) / 1 RHOSEC IF (ILONS .GT- 0) RSLAL1 = TWOPI - RSLAL1 C

C READ THE SECOND SLAVE STATION AND CHANGE THE LATITUDE

C AND LONGITUDE INTO RADIANS.

C

READ (5, 101) ILATS, IMINS, RSECS, ILONS, ILMINS, RLSECS, 1 DELAY2

WRITE (6,101) ILATS, IMINS, RSECS, ILONS, ILMINS, RLSECS, 1 DELAY2

RSLAV2 = ((TABS (ILATS) * 60 ^ IMINS) * 60 ■•• RSECS) / 1 RHOSEC IF (ILATS .LT. 0) RSLA V2 = -RSLA72

RSLAL2 = ( (IA5S (ILONS) * 60 + ILMINS) * 60 + RLSECS) / 1 RHOSEC IF (ILONS .GT. 0) RSLAL2 = TWOPI - RSLAL2 WRITE (6,201) C

C READ THE RECORDS POSITIONS AND OBSERVED RATES, THEN

C COMPUTE THE TOTAL DISTANCE.

C

DO 550 I=1,IREC,1

READ (5, 104) ILAT,IMIN ,RSEC ,ILON , ILMIN, RLSEC, 1 RATE1,RATS2

30

104 FOEMAT(1X,I3,I3,F6.3, 15,13, F6 . 3 , 3X, 2F1 0 .2)

C

C CONVERT LAT AND LONG TO RADIANS.

C

RPOST = ((lABS(ILAT) * 60 + IMIN) * 60 + RSEC) / 1 RHOSEC

IF(ILAT .LT. 0) RPOST = -RPOST

RPOSTL = ((lABS(ILON) * 60 + ILMIN) * 60 + RLSEC) / 1 RHOSEC

IF(ILON .GT. 0) RPOSTL = TWOPI - RPOSTL C

C COMPUTE DISTANCES AND AZIMUTHS FROM THE OBSERVED POINT

C

C MASTER

C

CALL INVER1 (A, F, RPOST , RPOSTL, RM AS T, RMASTL, FAZM , BAZM , 1 DISTM)

DDISTM = (RN * DISTM) / UNCOV

CALL SECFAC {UDISTM,SFM) C

C SLAVE1

C

CALL INVER1 (A,F ,RPOST , RPO STL,RSLA V1 , RSLAL1 , F AZ 1 , SAZ 1 , 1 DIST1)

UDIST1 = (RN * DIST1) / UNCOV

CALL SECFAC (UDI ST1, SF 1) C C SLAVE2

C

CALL INVERT (A, F ,R?OSr , RPO STL,RSLAV2, ESLAL2, F AZ2, BAZ 2, 1 DIST2) UDIST2 = (RN * DIST2) / UNCOV CALL SECFAC (UDIST2,SF2)

81

C COMPOTE THE RATES AND COMPARE TO THE OBSERVED RATES

C

TDM1 = UDIST1 - ODISTM + SF1 - SFM ■•■ DELAYl

DIPF1 = TDM1 - EAT El C

TDM2 = UDIST2 - UDIST M + SF2 - SFM + DSLAY2

DIFF2 = TDM2 - RATE2 C

C COMPUTE THE LANE WIDTH IN METERS BASED ON EQUATION

C 4.20 IN ELECTRONIC SURVEYING AND NAVIGATION -

C LAURILA, PAGE 94.

C

BR1 = DABS (FAZ1 - FAZ M)

3R2 = DABS(FAZ2 - FAZ M)

WIDTH1 = (DIFF1 * UNCOV * 0.5) / DSIN (BR1 * 0.5)

WIDTH2 = {DIFF2 * UNCOV * 0.5) / DSIN (BR2 * 0.5) C

C WRITE THE POSITION OF VESSEL, COMPUTED RATE, OBSERV^ID

C RATE, AND THE DIFF BETWEEN THEM.

C

WRITE (6^200) ILAT,IMIN,RSEC,IL0N,ILMIN,RL3EC,RATS1,

DIFF1,RATE2,DIFF2 200 F0RMAT(1X,I3,I3,1X,F6.3,I5,I3,1X^F6.3,F12.2,F8.2, 1 F12.2,F8.2)

WRITE(6,201) C

C XMEAN1 AND XMEAN2 ARE THE MEAN DIFFS BETWEEN THE

C COMPUTED RATS AND THE OBERSEHVED. XSLAV1 AND XSLAV2

C ARE THE STORED DIFFS.

C

XMEAN1 = XMSAN1 + DIFF1

XMEAN2 = XMEAN2 ■•■ DIFF2

XMEAN3 = XMEAN3 * WIDTHi

XMEAN4 = XMEAN4 + WIDTH2

82

XSLAV1 (I) = DIFF1

XSLAV2(I) = DIFF2 550 CONTINUE C

C COMPUTE THE MIAN AND STANDARD DEVIATION C

XMEAN1 = XMEAN1 / IREC

XMEAN2 = XMEAN2 / IREC

XMEAN3 = XMEAN3 / IREC

XMEAN4 = XMEAN4 / IREC C

DO 6 00 I = 1, IREC, 1

VAR1 = 7AR1 + ((XSLA7 1(I) - XMSAN1)**2) 600 7AR2 = VAR2 + ((XSLA72(I) - XMEAN2)**2)

C

VAR1 = VAR1 / (IREC - 1.0)

VAR2 = VAR2 / (IREC - 1.0) C

SD1 = DSQRT(VARI)

SD2 = DSQRT(VAR2) C

WRITE (6,201)

WRITE (6,210) XMEAN1,SD1,XMEAN3

WRITE(6,201)

WRITE(6,211) XMSAN2,S D2,XMEANa

WRITE (6,202)

210 F0RMAT(1X,' SLAVE #1, MEAN = ',?10.3,

1 • STANDARD DEVIATION = • ,

2 F10.3,' DISTANCE IN METERS = ',F10.3)

211 F0RMAT(1X,' SLAVE #2, MEAN = ',F10.3,

1 ' STANDARD DEVIATION = ',

2 F10.3,' DISTANCE IN METERS = •,F10.3) STOP

END

83

C=====: = = == = == == = = = = ======== == = = = = = = ==== = == = = = = = = = = = = == = == =

SUBROUTINE SECFAC (UTDIST, SF) C

c

C THIS ROUTINE WILL COMPUTE THE SEA SECONDARY FACTOR

C OTDIST = TOTAL DISTANCE

C SF = SECONDARY FACTOR

C

IMPLICIT REAL*8 (A-H, 0-Z) C

c

C COEFFICIENTS

C

AO = 129.04323

A1 = -0.40758

A2 = 0.00064576813 C

BO = 2.741282

B1 = -0.011402

B2 = .00032774815 C

IF(UTDIST .GT. 537) 30 TO 10

SF = ( BO / UTDIST) + B1 + ( B2 * UTDIST)

GO TO 20 10 SF = ( AO / UTDIST) •»• A1 + ( A2 * UTDIST)

C 20 CONTINUE

RETURN

END

C== ======================== ================================:

SUBROUTINE INVSR1 (A, ? INV, GLAT1 , GLON 1 , GLAT2 , GL0N2 ,FAZ , 1 BAZ,S) C

c

34

Q 4e«:(c SOLUTION OF THE GEODETIC INVERSE PROBLEM AFTER

C *** T.VINCENTY MODIFIED RAINS FORD'S METHOD WITH HELMERT'S

C *** ELLIPTICAL TERMS. EFFECTIVE IN ANY AZIMUTH AND AT

C *** ANY DISTANCE SHORT OF ANTIPODAL STANDPOINT/FOREPOINT

C *** MUST NOT BE THE GEOGRAPHIC POLE

C

C *** A IS THE SEMI-MAJOR AXIS OF THE REFERENCE ELLIPSOID

C *** FINV IS THE FLATTENING (NOT RECIPROCAL) OF THE

C *** REFERNECE ELLIPSOID LATITUDES AND LONGITUDES IN

C *** RADIANS POSITIVE NORTH AND EAST FORWARD AZIMUTHS AT

C *** BOTH POINTS RETURNED IN RADIANS FROM NORTH GEODESIC

C *** DISTANCE S RETURNED IN UNITS OF SEMI-MAJOR AXIS A

C

C *** PROGRAMMED FOR CDC-66 00 BY LCDR L.PFSIFER NGS

C *** ROCKVILLE MD 18FEB75. MODIFIED FOR IBM SYSTEM 360

C *** BY JOHN G 3ERGEN NGS ROCKVILLE MD 7507.

C

IMPLICIT REAL*8 (A-H,0-Z)

DATA EPS/0. 5D-1 3/, PI/ 3. 14 1 59265 35 89 8D0/

TW0PI=2.*PI

R=1.-FINV

TU1 = R*DSIN(GLAT1) /DCOS (GLATI)

TU2=R*DSIN (GLAT2) /DCOS (GLAT2)

CU1=1 ./D3QRT(TU1*TU1+ 1.)

SD1=CU1*Tai

CU2=1 ./DSQRT(TU2*TU2+ 1.)

S=CU1*CU2

3AZ=S*TU2

FAZ=BAZ*TU1

X=GL0N2-GL0N1 100 SX=DSIN (X)

CX=DC0S (X)

TU1=CU2*SX

TU2=BAZ-SU1*CU2*CX

85

SY=DSQRT(Tai*T0 1+TU2*TU2) CY=S*CX+FAZ Y = DATAN2(SY,CY) SA=S*SX/SY C2A=-SA*SA-H. CZ=FAZ+FAZ

IF(C2A.GT.O.) CZ=-CZ/C2A+CY E=CZ*CZ*2.-1.

C= ((-3.*C2A + 4 .) *FINV4-a.) *C2A*FINV/16 . D = X

X= ((E*CY*C + CZ) *SY*C-«-Y) *SA X= (1 .-C) *X*FINV+GL0N2-GL0N1 IF (DABS (D-X) .GT.EPS) GOTO 100 FAZ=DATAN2(T01,TU2) IF (FAZ.GE.TWOPI) FAZ= FAZ-T WOPI IF (FAZ.LT.O.DO) FA2=F AZ+TWOPI BAZ=DATAN2(CU1*SX,BAZ*CX-S01*Ca2) +PI IF (BAZ.GE.THOPI) B AZ= BAZ-T WOPI IF (BAZ.LT.O.DO) BAZ=B AZ+IWOPI X = DSQRT ( (1./R/R-1.) *C2A+1.) +1. X= (X-2.)/X C=1.-X

C= (X*X/U. + 1.) /c D=(0.375*X*X-1. ) *X X=E*CY S=1.-E-E

S= (( ( (SY*SY*4.-3.) *S*CZ*D/6.-X) *D/4.+CZ) *SY*D + Y) *C*A*R RETURN END SENTRY

86

DATA SET EXAMPLE - PEOGRAM LORAN

SHIP'S POSITION OBSERVED LORAN RATES & ERRORS (E)

LATITUDE LONGITUDE 9940-Y EY 9940-W EW

(D-M-S) (D-M-S) ()1S6C) (;isec) (;isec) (usee)

36 U3 45.800 121 55 27.160 42789.31 -0.49 16294.04 -1.06

36 44 3.400 121 55 32.340 42791.13 -0.38 16293.46 -1.10

36 44 21.180 121 55 37.390 42793.04 -0.38 16292.73 -0.99

36 44 37.490 121 55 46.950 42795.13 -0.58 16292.03 -1.06

36 44 53.260 121 55 57.710 42796.93 -0.51 16291.43 -1.27

87

APPENDIX C PROGRAM LOPLC

C PROGRAM LOPLC

C

C PROGRAM COMPUTES LINE OF POSITIONS FOR LORAN-C USING

C THE SECONDARY FACTOR (SF) AND ADDITIONAL SECONDARY

C FACTOR (ASF) THE SF AND ASF ARE BASED ON

C SEMI-EMPIRICAL TD GRID.

C

IMPLICIT REAL*8 (A-H,0-Z)

DIMENSION PHI (100) ,ELON (100) ,DISTM (100) ,DIST1 (100) , 1 DIST2(10 0) ,AXIS (13) , RF (13) ,AZ1 (100) , AZ2 (1 00) , AZM (1 00)

DATA RHOSEC,PI, UNCOV/2. 06 264806 2U7 1D05, 1 3.1U15926535898D0,299.693D0/ C cccccc* ****** ******** ****** *************

DATA AXIS/6. 3782064D06, 6. 378388 D06, 6. 377 397 1 55D06 ,

1 6.37816 D06,6. 37816D06^6.3782U91U5D06,6.378165D06,

2 6.378166D06,6. 378165 D06 , 6. 378 1 a5D06 , 6 . 377563UD06,

3 6.378245D06,6. 3781350D06/

DATA RF/6. 3565838 D06,2.97 D 02, 2 . 99 15 28 1285D02 ,

1 2.98 25D0 2,2. 98 247 167 4 27D 02, 2 .93 465D02 , 2 .9825D02 ,

2 2.983 D02,2.983D02,2 .9825 D02, 6 , 3562569D06 ,

3 2.983 D02,2.98 26D02/ C*****ELLIPSOID OPTION NUMBER

8. MERCURY

9. MARSHALL ISLAND

10. NAVY 8D

11. AIRY

12. KRASSOWSKI 19U0

13. WGS 1972

88

C	1.	CLARKE 1866
c	2.	INTERNATIONAL (HAYFORD)
c	3.	BESSEL 1841
c	4.	AND (AUSTRALIAN)
c	5.	1967 REFERENCE
c	6.	CLARKE 1830 MOD

C 7. SAO

C

cccccc* ************ ******** *************

C CC1-2 = ELLIPSOID NUMBER (K)

C CC3-5 = NUMBER OF POINTS ALONG COAST (IREC)

C

READ(5,100) K,IREC,ISTA1,ISTA2

100 FOEMAT(1X,I2,I4 ,213) TW0PI=2.*PI

A = AXIS(K)

F=1./RF (K)

IF (F.LT-3.D-3) F=(A-1./F)/A C

C READ MASTER STATION POSITIONS.

C

READ (5, 105) ILATM,IMINM,RSECM,ILONM,ILMINM,RLSECM 105 FORMAT (1X,I3, 1X,I2,1X,F5.2,1X,I4,1X,I2,1X,F5.2)

RMAST = ( (IA3S (ILATM) * 60 + IMINM) * 60 + RSSCM) / 1 RHOSEC

IF (ILATM .LT. 0) RMAST = -RMAST

RMASTL = ((TABS (ILONM) * 60 + ILMINM) *60 +RLSECM) / 1 RHOSEC

IF(ILONM .GT. 0) RMASTL = TWOPI - RMASTL C

C READ THE FIRST SLAVE STATION AND CHANGS THE LATITUDE

C AND LONGITUDE INTO RA DI ANS . DELAY IS THE CODING DELAY

C AND BIAS IS THE OFFSET IN MICROSECONDS.

C

READ (5, 101) ILATS,IMINS,RSSCS,ILONS,ILMINS,RLSECS, 1 DELAY1,3IAS1

101 FCRMAT(1X,I3, 1X,I2,1X,F5.2, 1X,I4, 1X,I2,1X,F5.2, 1 ?9.2,F7.3)

RSLA71 = ( (lABS (ILATS) * 60 + IMINS) * 60 * RSSCS) / 1 RHOSEC

39

IF(ILATS .LT. 0) RSLAV1 = -RSLAV1

RSLAL1 = ( (lABS (ILONS) * 60 + ILMINS) * 60 + RLSECS) / 1 RHOSEC

IF (ILONS .GT. 0) RSLAL1 = TWOPI - RSLAL1 C

C READ THE SECOND SLAVE STATION AND CHANGE THE LATITUDE

C AND LONGITUDE INTO RADIANS.

C

READ (5, 101) ILATS,IMINS,RSECS, ILONS, ILMINS, RLSECS, 1 DELAY2,BIAS2

RSLAV2 = ((TABS (ILATS) * 60 + IMINS) * 60 + RSECS) / 1 RHOSEC

IF(ILATS .LT. 0) RSLAV2 = -RSLAV2

RSLAL2 = ( (lABS (ILONS) * 60 + ILMINS) * 60 + RLSECS) / 1 RHOSEC

IF (ILONS .GT. 0) RSLAL2 = TWOPI - RSLAL2 C

C READ COAST POINT LAT AND LONG AND CONVERT TO RADIANS.

C STORE LAT IN PHI AND LONG IN ELON.

C

DO 5 00 I=1,IRZC,1

READ (5,102) INUM,ILAT,IMIN,RSSC,ILON,ILMIN, RLSSC 102 FORM AT ( 1 X, 14, 14, 13, F7. 3, 1 5, 13, F 7. 3)

PHI (I) = ((lABS(ILAr) * 60 -<■ I2IIN) * 60 + RSSC) / 1 RHOSEC

IF(ILAT .LT. 0) PHI (I) = -PHI (I)

ELON (I) = ((IABS(IL3N) * 60 + ILMIN) * 60 ^- RLSEC) / 1 RHOSEC

IF(ILON .GT. 0) ELON (I) = TWOPI - ELON (I) C

C COMPUTE DISTANCE FROM COAST POINT TO MASTER AND

C SLAVE STATIONS. SET UP COMPUTATION AND CALL INVER1

C

?1 = ?HI(I)

90

El = ELON(I)

CALL INVER1 (A, F, Pi, SI ,RMAST,R»1ASTL , AZF , AZB , S)

DISTM(I) = S

AZM(I) = AZF

CALL INVER1 (A,F,P1,E1 ,RSLAV 1 , RSLAL1 , AZF, AZB , S)

DIST1 (I) = S

AZ1(I) = AZF

CALL INVER1 (A,F,P1,E1 ,RSLA72, RSLAL2 , AZF , AZB , S)

DIST2 (I) = S

AZ2(I) = AZF

WRITE (6,210) I,INUM,ILAT,IMIN,RSEC,IICN,ILi5IN, RLSEC, 1 AZM (I) ,AZ1 (I) , AZ2 (I) 219 FORM AT (IX, 14, 14, 14, 1 3 ,F7. 3 , 15 , 13 , F7. 3 , 3F10 . 3) 500 CONTINUE C

C READ THE NUMBER OF RECORDS AND THEIR POSITIONS. C COMPUTE THE TOTAL DISTANCE OVER LAND AND SEA. C TDISTM = TOTAL DISTANCE FROJl FASTER TO DATA POINT. C TDISTS = TOTAL DISTANCE FROM SLAVE TO DATA POINT. C

C COMPUTE THE FORWARD AND BACK AZIMUTHS

C FAZM AND FAZS = FORWARD AZIMUTH TO THE MASTER AND C SLAVE STATION.

C EAZM AND 3AZS = BACK AZIMUTH TO THE MASTER AND C SLAVE STATION. C

READ (5, 103) JREC

103 FORM AT (IX, 14) C

DO 550 1=1, JREC, 1

READ (5, 104) ILAT ,IilIN, RS EC , HON, ILMIN , RLSEC , RATS 1 , HAT E2

104 FORM AT (IX, 13,13, F6. 3, 15,13, F6. 3, F 9.3, F9. 3) C

C CONVERT LAT AND LONG TO RADIANS.

91

RPOST = ((lABS(ILAT) * 60 + IMIN) * 60 + RSEC) / 1 RHOSEC

IF(ILAT .LT. 0) RPOSr = -RPOST

BPOSTL = ((lABS(ILON) * 60 + ILMIN) * 60 + RLSEC) / 1 RHOSEC

IF(ILON .GT. 0) RPOSTL = TWOPI - RPOSTL C

C COMPUTE DISTANCES AND AZIMUTHS FROM THE OBSERVED

C POINT TO THE INTERPOLATED SHORE POINT AND WRITE.

C

ISTA = 1

CALL SHORPT (I RE C^RPOS T, RPOSTL, R MAST, RMASTL , UTDISM, 1 USDIST,ULDIST,FAZM,B AZM)

CALL SECFAC(UTDISM,aSDIST,ULDI3T,BAZM,ISTA,SFM) C

CALL SHORPT (I REC,RPOS T, RP0STL,RSLAV1 , RSLAL1 ,UTDIS1, 1 USDIST,ULDIST,FAZ1,B AZ1)

CALL SECFAC (UTDIS 1 ,as DIST , ULDIST, BAZ1 ,ISTA 1 ,SF1) C

CALL SHORPT (I RE C,RPOS T, RPOSTL, RSL A72 , RSLAL2 , UTDIS2, 1 USDIST,ULDIST,FAZ2,B AZ2)

CALL SECFAC (UTDIS2 ,as DIST , ULDIST, BAZ2 ,ISTA2 , SF2) C

C COMPUTE THE RATES AND COMPARE TO THE OBSERVED RATES

C

TDM1 = UTDISI - UTDISM + SF1 - SFM + DELAY1 + BIASI

DIFF1 = TDMl - RATE1 C

TDM2 = UTDIS2 - UTDISM + SF2 - SFM + DELAY2 + EIAS2

DIFF2 = TDM2 - RATE2 C

C COMPUTE THE LANE WIDTH IN METERS BASED ON EQUATION

C 4.20 IN ELECTRONIC SURVEYING AND NAVIGATION - LAUEILA,

92

C PAGE 94.

C

BR1 = DABS (FAZ1 - FAZ M)

IF(BR1 ,GT. PI) BRI = TWOPI - BR1

BR2 = DABS (FAZ2 - FAZ M)

IF(BR2 .GT. PI) BR2 = TWOPI - BR2

WIDTH1 = (DIFF1 * UNCOV * 0.5) / DSIN(BR1 * 0.5)

WIDTH2 = (DIFF2 * UNCOV * 0.5) / DSIN (BR2 * 0.5) C

C WRITE THE POSITION OF VESSEL, OBSERVED RATES,

C AND THE DIFFERENCES BETWEEN THEM.

C

WRITE (6,200) ILAT,IMIN,RSEC,IL0N,ILMIN,P.LSEC,RATS1, 1 DIFF1,RATE2, DIFF2 200 F0RMAT(1X,I2,I3,F7.3, Iit,l3,F7.3,?10.2,F6.2,F10.2,F6.2) C

C XMEAN1 AND XMEAN2 ARE THE MEAN DIFFS BETWEEN THE

C COMPUTED RATE AND THE OBERSERVED. XSLAV1 AND XSLAV2

C ARE THE STORED DIFFS,

C

XM2AN1 = XMEAN1 + DIFF1

XMEAN2 = XMEAN2 + DIFF2

XMEAN3 = XMEAN3 + WIDTH 1

XMEANU = XMEANU + WIDTH2

XSLAV1 (I) = DIFF1

XSLAV2(I) = DIFF2 550 CONTINUE C C COMPUTE THE MEAN AND STANDARD DEVIATION

C

XMEAN1 = XMEAN1 / JREC

XMSAN2 = XMEAN2 / JREC

XMEAN3 = XMEAN3 / JREC

XMEAN4 = XMEANU / JREC

93

c

DO 600 I = 1, JREC, 1

VAR1 = VAR1 + ((XSLA7 1(I) - XMEAN1)**2) 600 VAR2 = VAR2 + ((XSLAV2(I) - XMEAN2)**2) C

7AR1 = VAR1 / (JREC - 1.0)

VAR2 = VAR2 / {JREC - 1.0) C

SD1 = DSQRT (VAR 1)

SD2 = DSQRT (VAR2) C

WRITE(6,201)

WRITE (6,210) XMEAN1,SD1,XMEAN3

WRITE (6,201)

WRITE (6,211) XMEAN2,SD2,XMEANa

WRITE (6,202)

210 F0RMAT(1X,' SLAVE #1, MEAN = •,F10.3,

1 • STANDARD DEVIATION = •,

2 F10.3,' DISTANCE IN METERS = »,F10.3)

211 F0RMAT(1X,' SLAVE #2, MEAN = «,F10.3,

1 ' STANDARD DEVIATION = •,

2 F10.3,' DISTANCE IN METERS = •,?10.3) WRITE(6,201)

201 FORMAT (ia )

202 FORMAT(IHI) STOP

END C==== ====================== ======= === = ==== ===== = ==== = ========

SUBROUTINE SHORPT (IRE C, RPOST , RPOSTL, RCOUT, RCONTL , UDIST ,

1 USD,ULD,FA,3A) Q

C

C SUBROUTINE SHORPT WILL SELECT A POINT ALONG THE SHORE

C WHICH IS OUTLINED FROM NORTH BY SELECTED POINTS WITH

9a

C KNOWN LATITUDES AND LONGITUDES. THE SHORE POINT IS

C INTERPOLATED BETWEEN TWO KNOWN POINTS USING THE TOTAL

C DISTANCE BETWEEN THE POSITION AND THE CONTROL STATION

C AND THE AZIMUTH BETWEEN THE SHORE POINTS AND THE

C RECEIVERS POSITION.

C

IMPLICIT REAL*8 (A-H,0-Z)

DIMENSION FAZM(IOO)

COMMON/SHORE/PHI (100) , ELON (100) , UNCOV,RN, A , F

DATA PI/3, 1U159 26535398D0/ C

TWOPI = 2.0 * PI C

CALL INVER1 (A,F ,RPOST ,RP0STL,R30NT, RCONTL, FA , B A, RDISTT)

UDIST = (RN * RDISTT) / UNCOV C

RCOMP = 99999.99 C

DO 10 J=1,IREC, 1

P1 = PHI (J)

El = ELON (J)

CALL INVER1 (A, F, PI, El ,RCONT, 3C3NTL , AZF, A23, RDISTL)

CALL INVER1 (A,F ,RPOST ,RP0STL,P1 ,E1 , FAZ, BAZ , RDISTS)

USD = (RN * RDISTS) / UNCOV

ULD = (RN * RDISTL) / UNCOV

FAZM (J) = AZF C

C COMPUTE THE DIFFERENCE BETWEEN THE TOTAL DISTANCE C (UDIST) AND THE SUMMATION OF THE DISTANCE OVER THE WATER C (USD) AND THE DISTANCE OVER THE LAND (ULD) . IT THE C DISTANCE IS LESS THAN RCOMP, UPDAT RCOMP AND JSTA. C JSTA IS THE CLOSEST POINT ALONG THE SHORELINE WHICH IS C NEAR THE EM PROPAGATION PATH. C

95

FDIFP = DABS(UDIST - (USD + ULD) )

IF(FDIFF .GT. RCOMP) GO TO 10

RCOMP = FDIFF

JSTA = J 10 CONTINUE C

C NOW DETERMINE THE INTERPOLATED LATITUDE AND LONGITUDE C SHORE POINT USING AZIMUTH PERCENTAGE.

C

TOPPER = JSTA - 1

ILOWER = JSTA ■«■ 1

AZMU = FAZM(IUPPER)

AZML = FA ZM (ILOWER)

IF (AZMU .GT. FA -AND. FA .GE. FAZM(JSTA)) ICH = lUPPER

IF (FAZM (JSTA) . GE. FA .AND. FA .GT. AZML) ICH = ILOWER

RADJ = 1.00 - DABS ((FAZM(ICH) - FA) / (FAZM (ICH) - 1 FAZM (JSTA) ) )

RNWPHI = PHI (JSTA) ^ ( (PHI (ICH) - PHI (JSTA) ) * RADJ)

IF (ELON (JSTA) . LE. ELON(ICH)) RADJ = 1.0 - RADJ

RNWELN = ELON (JSTA) + ((ELON (ICH) - ELON (JSTA)) * RADJ)

CALL TODMS (RNWPHI, IDG ,MIN, SEC)

RHOLD = TWOPI - RNWELN

CALL TODMS (RHOLD, IDGL,MINL,SSCL)

CALL INVER1 (A,F ,RNWPH I, RNWELN, RCONT, RCONTL , AZ, BZ , RDISTL )

CALL INVER1 (A,F,RPOST , RPOSTL,RN WPHI, RNWELN , AZ, 3Z, RDISTS )

USD = (RN * RDISTS) / UNCOV

ULD = (RN * RDISTL) / UNCOV

RETURN

END

96

SUBROUTINE SECF AC(UTD 1ST, USDIST , ULDIST, AZI , I STA , SF) C

c

C THIS ROUTINE WILL COMPUTE THE LAND/SEA SECONDARY FACTOR

C UTDIST = TOTAL DISTANCE

C USDIST = DISTANCE OVER THE SEA WATER PATH

C ULDIST = DISTANCE OVER THE LAND PATH

C AZI = AZIMUTH FROM NORTH.

C

C MASTER = 1 (ISTA)

C W =2

C X =3

C Y =4

C

IMPLICIT REAL*8 (A-H,0-Z)

51 = (.795 / USDIST) + 0.439 + (.00245 * USDIST) C

IF (UTDIST .GT. 540) GO TO 10

52 = (3.188 / UTDIST) - 0.594 + (.000329 * UTDIST) GO TO 20

10 52 = (128.8 / UTDIST) + 0.187 + (.000652 - UTDIST)

C

20 IF(USDIST .GT. 540) GO TO 30

53 = (3.188 / USDIST) - 0.594 + (.000329 * USDIST) GO TO 40

30 S3 = (128.8 / USDIST) + 0.187 + (.000652 * USDIST)

C

40 IF (ULDIST .GT. 540) GO TO 50

54 = (3.188 / ULDIST) - 0.594 + (.000329 * ULDIST) GO TO 60

50 S4 = (128.8 / ULDIST) + 0.187 *■ (.000652 * ULDIST)

C

60 S5 = 1.428 + (.00158 * UTDIST)

S6 = 1.428 -•• (.00158 * ULDIST)

97

TAZI = 2-0 * AZI

GOTO (70,80,90,100) , ISTA 70 RHOLD = (1.010*DSIN (AZI) ) - ( . 1 96*DCOS (AZI) )

1 - (.893*DSIN(TAZI) ) - ( . 355*DCOS (TAZI) )

GO TO 200 80 RHOLD = (.323*DCOS (AZI) ) - (. 711 *DSIN (TAZI) )

GO TO 200 90 RHOLD = (.9a2*DCOS (TAZI) )

GO TO 200 100 RHOLD = (.588*DSIN (TAZI) )

C 200 S5 = S5 + RHOLD

S6 = S6 + RHOLD

SF = 0.5 * (S5 ^ S6 - SI + S2 + S3 - SU)

WRITZ (6,5 00) S1 ,S2,S3 ,SU,S4,S5,S6 ,S? 500 FORMAT(1X,7F15. 5)

RETURN

END C== ============================================== ==========^

SUBROUTINE INVERT ( A, ? INV, GLAT1 , GLON 1 ,GLAT2 , GL0N2 ,FAZ,

1 3AZ,S) C

See Appendix B for subroutine INVSR1.

98

short points around Monterey Bay, California. The point are used to interpolate geodetic point for computation

of the distance over land and the distance ov^r sea.

NO. LATITUDE LONGITUDE

1 36 57 18.606 122 05 37.525

2 36 56 59.264 122 03 01.817

3 36 57 05.076 122 01 31.701 U 36 57 49.538 122 01 07.857

5 36 57 17.949 121 58 19.830

6 36 58 08.589 121 57 07.288

7 36 58 32.140 121 55 10. 083

8 36 58 01.498 121 53 57.390

9 36 56 46.115 121 52 22.313

10 36 55 38.140 121 51 24.399

11 36 53 13.806 121 49 46.743

12 36 49 38.384 121 47 48.395

13 36 47 39.241 121 47 10.818

14 36 46 27.554 121 47 39.637

15 36 44 56.717 121 47 52.416

16 36 41 14.439 121 48 32.642"

17 36 39 17.211 121 49 28.533

18 36 37 31.128 121 50 31.723

19 36 36 23.446 121 51 34.833

20 36 36 03.628 121 52 50.879

21 36 36 24.782 121 53 48.453

22 36 37 18.151 121 54 11.628

23 36 38 00.300 121 55 57.538

99

DATA SET EXAMPLE - PROGRAM LOPLC

SHIP'S POSITION OBSERVED LORAN RATES & ERRORS (E)

LATITUDE LONGITUDE 9940-Y EY 9940-W EM

(D-M-S) (D-M-S) (;isec) (;isec) (jjusec) (jasec)

36 43 45-800 121 55 27.160 42789.34 1.14 16294.04 1.32

36 44 3.400 121 55 32.340 42791.13 1.25 16293.46 1.29

36 44 21.180 121 55 37.390 42793.04 1.25 16292.73 1.40

36 44 37.490 121 55 46.950 42795.13 1.05 16292.03 1.33

36 44 53.260 121 55 57.710 42796.93 1.12 16291.43 1.11

100

APPENDIX D PROGRAM LORTAB

C PROGRAM LORTAB

C

C PROGRAM COMPUTES LINE OF POSITION FOR LORAN-C USING

C SF SALT WATER CORRECTION FACTOR AND DMAHTC CALCULATED

C OR FIELD OBSERVED ASF CORRECTIONS.

C

C

IMPLICIT REAL*8 (A-H, 0-Z)

DIMENSION AXIS (13) ,RF (13)

DIMENSION XSLAV1 (1000) ,XSLAV2 (1000)

DATA RHOSEC,PI, UNCOV, RN/2 . 06264 8062471 DOS , 1 3. 14 15 926535 89 800,29 9. 79 24 58D0 ,1 .00 03 3 8 DO/

DATA XMEAN1,XMEAN2,VAR1//AR2/0. OODO, O.OODO, 1 O.OODO,OO.ODO/

DATA XMEAN3,XMEAN4/0. OODO,O.OODO/ C CCCCCC* ************ ******** ♦***********:*

DATA AXIS/6. 3782064006,6. 373338 006,6.377397155006,

1 6.37816 006,6.37816006,6.378249145006,6.373165006,

2 6,378166006,6.378165 006,6.37814 5006,6.3775634006,

3 6.378245006,6,3781350006/

DATA RF/6. 3565838 006,2.97 002,2.99152312 35002,

1 2.9 8 2500 2,2.98 24716 7 4 270 02,2.9 3 46 5002,2.9 8 2500 2,

2 2.983 002,2.983002,2.9825 002,6.3562569006,

3 2,983 002,2.9826002/ C*****ELLI?SOID OPTION NUMBER

C 1. CLARKE 1866 8. MERCURY

C 2. INTERNATIONAL (HAIFORD) 9. MARSHALL ISLAND

C 3. BESSEL 1841 10. NAVY 80

101

c	4. AND (AUSTRALIAN) 11. AIRY
c	5. 1967 REFERENCE 12. KRASSOWSKI 1940
c	6. CLARKE 1880 MOD 13. WGS 1972
c	7. SAO
c
cccccc* ************ ******** *************
1 c	CC1-2 = ELLIPSOID NUMBER (K)
c	CC3-5 = NUMBER OF POINTS ALONG COAST (IREC)
c

READ(5,100) K,IREC,ID1,ID2 100 F0RMAT(1X,I2,I4,2I3)

TW0PI=2.*PI

A=AXIS(K)

F=1./RF (K)

IF (F.LT.3.D-3) F=(A-1./F)/A C

C READ MASTER AND SLAVE STATIONS POSITIONS

C THE FIRST RECORD IS THE NUMBER OF MASTER AND SLAVS

C STATIONS FOR THE PARTICULAR CHAIN.

C

WRITS (6,202) 202 FORMAT(IHI)

WRITE(6,201). 201 F0RMAT(1H )

READ (5, 105) ILATM,IMINM,RSSCM,ILONM,ILMINM,RLSECM

WRITE (6,105) ILATM,IMINM,RSSCM,ILONM,ILMINM,HLSECM 105 F0RMAT(1X,I3, 1X,I2,1X,F5. 2, 1X,I4, 1X,I2,1X,F5.2)

RMAST = ( (lABS(ILATM) * 60 + IMINM) * 60 + RSECM) / 1 RHOSEC

IF(ILATM .LT. 0) RMAST = -RMAST

RMASTL = ((TABS (ILONM) * 60 + ILMINM) *60 +RLSSCM) / 1 RHOSEC

IF (ILONM .GT. 0) RMASTL = TWOPI - RMASTL

102

C READ THE FIRST SLAVE STATION AND CHANGE THE LATITUDE

C AND LONGITUDE INTO RADIANS.

C

READ (5, 101) IIATS,IMINS,ESECS,ILONS,ILMINS,RLSECS, 1 DELAY1

WRITE (6,1 01) IIATS,IMINS,RSECS,ILONS,ILMINS,RLSECS, 1 DELAY1 101 FORMAT (IX, 13, IX ,12 , 1 X ,F5. 2, IX, I 4 , 1 X,I2, IX, F5 . 2 , F9 . 2) RSLA71 = ( (lABS (ILATS) * 60 + IHINS) * 60 + 5SECS) / 1 RHOSEC IF(ILATS .LT. 0) RSLAV1 = -PSLAV1

RSLAL1 = ((lABS (ILONS) * 60 + ILMINS) * 60 + RLSECS) / 1 RHOSEC IF (ILONS .GT. 0) RSLAL1 = TWOPI - R3LAL1 C

C READ THE SECOND SLAVE STATION AND CHANGE THE LATITUDE

C AND LONGITUDE INTO RADIANS.

C -

READ (5, 101) ILATS,IMINS,RSECS, ILONS, ILMINS, RLSECS, 1 DELAY2

WRITE (6,101) ILATS, iaiNS,RSECS, ILONS, ILMINS, RLSECS, 1 DELAY2

RSLAV2 = ((lABS (ILATS) * 60 + IMINS) * 60 + RSECS) / 1 RHOSEC IF (ILATS .LT. 0) RSLAV2 = -RSLAV2

RSLAL2 = ((IA3S (ILONS) * 60 + ILMINS) * 60 + RLSECS) / 1 RHOSEC IF (ILONS .GT. 0) RSLAL2 = TWOPI - RSLAL2 WRITE (6,201) C

C READ THE RECORDS POSITIONS AND OBSERVED RATES, THEN

C COMPUTE THE TOTAL DISTANCE.

C

DO 5 50 I=1,IREC,1

103

READ (5, 10U) ILATrlMIN ,RSEC, ILOM , ILMIN, RLSEC , 1 RATE1,RATE2 10U FORM AT ( IX, 13, 13, F6. 3, 15 ,1 3 ,F6 . 3 , 3X, 2F10 . 2) C

C CONVERT LAT AND LONG TO RADIANS.

C

RPOST = ((lABS(ILAT) * 60 + IMIN) * 60 + RSEC) / 1 RHOSEC

IF(ILAT .LT. 0) RPOST = -RPOST

RPOSTL = ((IA3S(IL0N) * 60 + ILMIN) * 60 + RLSSC) / 1 RHOSEC

IF(ILON .GT. 0) RPOSTL = TWOPI - RPOSTL C

C COMPUTE DISTANCES AND AZIMUTHS FROM THE OBSERVED POINT

C

C MASTER

C

CALL INVER1 (A ,F , RPOST , RPOSTL, RM AST, RMASTL, FAZM ,BAZM, 1 DISTM)

UDISTM = (RN * DISTM) / UNCOV

CALL SECF AC (UDISTM, SFM) C

C SLAVE1

C

CALL INVER1 (A,r , RPOST , RPO STL,RSLA V1 , RSLALI , FAZ 1 , BAZ 1 , 1 DIST1)

UDIST1 = (RN * DIST1) / UNCOV

CALL SECFAC (UDIST1,SF 1) C C SLAVE2

C

CALL INVER1 (A, F , RPOST , RPO STL, RS LA V2, RSLAL2 , F AZ2 , 3A22, 1 DIST2) UDIST2 = (RN * DIST2) / iJNCOV

104

CALL SSCFAC{0DIST2,SF2) C

C DETERMINE THE ADDITIONAL SECONDARY CORRECTORS FROM THE

C LORAN-C CORRECTION TABLE FOR THE WEST COAST CHAIN 99U0

C

CALL TABLE(RPOST,RPOSTL,ID1,ASF1)

CALL TABLE(RPOST,RP0STL,ID2,ASF2) C

C COMPUTE THE HATES AND COMPARE TO THE OBSERVED RATES

C

TDM1 = UDIST1 - UDI3TM + SF1 - SFM + ASF1 + DELAY1

DIFF1 = TDM1 - RATE1 C

TDM2 = UDIST2 - UDISTM + SF2 - SFM + ASF2 -»• DELAY2

DIFF2 = TDM2 - RATE2 C C

C COMPUTE THE LANE WIDTH IN METERS BASED ON EQUATION

C 4.20 IN ELECTRONIC SURVEYING AND NAVIGATION -

C LAURILA, PAGE 94.

C

BR1 = DABS (FAZ1 - FAZ M)

BR2 = DABS(FA22 - FAZ M)

WIDTH1 = (DIFF1 * UNCOV * 0.5) / DSIN(BR1 * 0.5)

WIDTH2 = (DIFF2 * UNCOV * 0.5) / DSIN(BR2 * 0.5) C

C WRITE THE POSITION OF VESSEL, COMPUTED RATE, OBSERVED

C RATE, AND THE DIFF BETWEEN THEM.

C

WRITE (6,200) ILAT,IMIN,RSEC,IL0N,ILMIN,RLSEC,RATE1,

DIFF1,RATE2,DIFF2 200 F0RMAT(1X,I3,I3,1X,F6 . 3,1 5,13, 1 X, F6. 3 ,F 12. 2 , F8 . 2, 1 F12.2,F8.2)

WRITE (6,201)

105

c c

c c c

550

c

c c

XMEAN1 AND XMEAN2 ARE THE MEAN DIFFS BETWEEN THE

COMPUTED RATE AND THE OBEHSERVED. XSLAVI AND XSLAV2 ARE THE STORED DIFFS.

XMEAN1 = XMEAN1 + DIFF1

XMEAN2 = XMEAN2 ••- DIFF2

XMEAN3 = XMEAN3 + MIDTH1

XMEAN4 = XMEANU + WIDTH2 XSLAV1 (I) = DIFF1 XSLAV2(I) = DIFF2 CONTINUE

COMPUTE THE MEAN AND STANDARD DEVIATION

XMEAN1 = XMEAN1 / IREC

XMEAN2 =-XMEAN2 / IREC

XMEAN3 = XMEAN3 / IREC

XMEAN4 = XMEANa / IREC

600 C

DO 6 00 I = 1, IREC, 1

VAR1 = VAR1 + ((XSLA7 1(I) - XMEAN1)**2)

VAR2 = VAR2 ■•• ((XSLA72(I) - XMEAN2)**2)

VAR1 = VAR1 / (IREC - 1.0) VAR2 = VAR2 / (IREC - 1.0)

SD1 = DSQRT (VAR 1) SD2 = DSQRT (VAR2)

WRITE (6,201)

WRITE(6,210) XMEAN1,SD1,XMEAN3

WRITE (6,201)

WRITS(6,211) XMEAN2,SD2,XMEAN4

106

WRIT2(6,202)

210 F0RMAT(1X,» SLAVE #1, MEAN = SFIO.S,

1 • STANDARD DEVIATION = «,

2 P10.3,' DISTANCE IN METERS = »,F10.3)

211 F0RMAT(1X,' SLAVE #2, MEAN = ',F10.3,

1 • STANDARD DEVIATION = »,

2 F10.3,' DISTANCE IN METERS = •,F10.3) STOP

C========= = ========== ====== ==== === === = = === ====== = = = = = = ===

SUBROUTINE SECF AC(UTD 1ST, SF) C

C

C THIS ROUTINE WILL COMPUTE THE SEA SECONDARY FACTOR

C OTDIST = TOTAL DISTANCE

C SF = SECONDARY FACTOR

C

IMPLICIT REAL*8 (A-H,0-Z) C C

C COEFFICIENTS C

AO = 129.0U323

A1 = -0.U0758

A2 = 0.00064576813 C

BO = 2.741282

B1 = -0.011402

B2 = .000327748 15 C

IF(UTDIST .GT. 537) GO TO 10

SF = ( BO / UTDIST) + B1 + ( 32 * UTDIST)

GO TO 20 10 SF = ( AO / UTDIST) + A1 + ( A2 * UTDIST)

C

107

20 CONTINUE

BETURN END

C=="= = = == == = ==== = = ==:====== ===== = = = == = = = =:==:== = = = = = = = = = = = ==== =

SUBROUTINE TABLE(RLAT ,RLON,ID, ASF)

Q

C

C SUBROUTINE TABLE SELECTS THE PROPER ASF CORRECTOR FROM

C THE LORAN-C CORRECTION TABLE PUBLISHED BY THE DEFENSE

C MAPPING AGENCY.

C RLAT = POSITION LATITUDE IN SECONDS

C RLON = POSITION LONGITUDE IN SECONDS

C ID = LORAN-C CHAIN IDENTIFIER

C W = 1

C X = 2

C Y = 3

C ASF = ADDITIONAL SECONDARY FACTORS

C

C THE FOLLOWING TABLES OF ASF CORRECTORS ARE FOR

C MONTEREY BAY, CALIFORNIA - 9940 -W, -X, -Y,

C

IilPLICIT REAL*8 (A-H, 0-Z)

DIMENSION TA3LEW(3,5) ,TAB LEX (3 , 5) ,TABLEY (3 , 5) C

DATA TABLSW/ 1. 6D0, 1 - 6D0 , 0. ODO ,

1 1. 6D0,1. 5D0,1.4D0,

2 1. 5D0,1, 4D0,1 .6D0,

3 1. 4D0,1. 3D0,1 .5D0,

4 1. 3D0,0. ODO, O.ODO/ C

DATA TABLEX/ -0 . 9D0, - 0. 9D0 , O.ODO,

1 -0.9D0,- 0.9D0,-0.3D0,

2 -1 ,0D0,- 1.0DO,-1.0DO,

3 -1 .ODO,- 1.2D0,-1 .1D0,

108

a -1.1D0, O.ODO, O.ODO/

c

DATA TABLEY/ 0. 2D0 , 0. 2D0,0 - ODO,

1 0. 3D0,0. 3D0,0.3D0,

2 0. 3D0,0. 2D0,0.4D0,

3 0. 4D0,0. 3D0,0.6D0,

4 0. 5D0,0. ODO, O.ODO/

DATA RHOSEC,PI/2,0626 4306 2a71DD5,3.1U159 26 5 358 98D0/ C

TWOPI = PI * 2. 0 C

C CONVEE RLAT AND RLON TO SECONDS

C

HLAT = ELAT * RHOSEC

HLON = TWOPI - RLON

HLON = HLON * RHOSEC C

C STARTING LAT AND LONG FOR SEARCH

C LAT = 37/00/00.0 LONG = 122/05/00.0

C

c

C DETERMINE THE AS? CORRECTOR FOR THE LORAN-C COMBINATION

C

C LATITUDE

C

SLAT = 133200.0 SLON = 439500.0 RMID = 300.0 RDIFF = 150.0

DO 10 J=1,5, 1 SLAT = SLAT - RMID ULAT = SLAT + RDIFF VLAT = SLAT - RDIF?

109

10 IF (hLAT .LT. DLAT .AND. hLAT .3E. VLAT) GO TO 15

15 CONTINUE

C

C LONGITUDE

C

DO 30 1=1,3,1

SLON = SLON - RMID

ULON = SLON + RDIFF

VLON = SLON - RDIFF 30 IF (hLON .LT. ULON .iND. h LON .3T. VLON) GO TO 35 35 CONTINUE C C DETERMINE ASF CORRECTOR

C

ASF =0.0

IF (ID .EQ. 1) ASF = rABLEW(I,J) IF (ID .SQ. 2) ASF = TABLEX(I,J) IF (ID .EQ. 3) ASF = TABLEY(I,J)

RETURN END

SUBROUTINE INVER1 ( A, F INV, GLAT1 , GL0N1 ,GLAT2 , GL0N2 ,FAZ, 1 BAZ,S)

See Appendix B for subroutine IN7ER1

110

DATA SET EXAMPLE - PROGRAM LORTAB

SHIP'S POSITION OBSERVED LORAN RATES & ERRORS (E)

LATITUDE LONGITODE 9940-Y EY 9940-W EW

(D-M-S) (D-M-S) (psec) (fisec) {fisec) (usee)

36 U3 45.800 121 55 27. 160

36 44 3.400 121 55 32.340

36 44 21. 130 121 55 37.390

36 44 37.490 121 55 46. 950

36 44 53. 260 121 55 57.710

42789.	.34	-0.	29	16294,	.04	0.	34
42791.	13	-0.	18	16293	.46	0.	30
42793,	04	-0,	18	16292,	.73	0.	41
42795.	13	-0.	38	16292,	.03	0.	34
42796.	93	-0.	31	16291,	.43	0.	13

111

APPENDIX E PROGRAM ASFSEL

C PROGRAM ASFSEL

C

C PROGRAM DETERMINES OBSERVED ASF CORRECTORS BY SCANNING

C DATA AT 1 DEGREE LATITODE AND LONGITODE INTERVALS. THE

C ASF CORRECTORS ARE DETERMINED 3Y SUBTRACTING THE

C CALCULATED TD USING THE SEAWATER SECONDARY FACTOR FROM

C THE OBSERVED TD RATES.

C

IMPLICIT REAL*8 (A-H,0-Z)

DIMENSION AXIS ( 13) ,RF (13)

DIMENSION ASFCR 1 (16,2 6) ,ASFCR2(16 ,2 6) , 1 IN01 (16,26) ,IN02(16, 26)

DATA RHOSEC,PI, UNCOV, RN/2, 06264 3062471D05, 1 3. 1 4 15 9265 35 89 8D0, 29 9.79 245800,1 .00 03 38D0/

DATA XMEAN1,XMEAN2,VAR1 //AR2/0. 0 0D0,0.00D0, 1 0.00D0,00.0D0/

DATA XMEAN3,XMEAN4/0. 00D0,0.00D0/ C cccccc* ******************** *************

DATA AXIS/6. 3782064DO 6,6. 378383 D06 , 6. 3773971 55D06 ,

1 6.37816 D06, 6. 37816D06, 6. 378249145006,6. 378165D06,

2 6.373166006,6.378165 D06 , 6 . 378 1 45D06 ,6 . 3775634006 ,

3 6.378245006,6.3781350006/

DATA RF/6. 3565838 006,2.97 D 02 , 2 .99 152312 85D02 ,

1 2. 9 8 2500 2, 2. 98 247 16 7 4270 02,2.9 3 465002,2.9 8 2500 2,

2 2.983 002,2.983002,2.9825 002,6.3562569006,

3 2.983 002,2.9326002/ C*****ELLI?SOID OPTION NUMBER

C 1. CLARKE 1866 8. MERCURY

112

C 2. INTERNATIONAL (HAYFORD) 9. MARSHALL ISLAND

C 3. BESSEL 1841 10. NAVY 8D

C 4. AND (AUSTRALIAN) 11. AIRY

C 5. 1967 REFERENCE 12. KRASSCWSKI 194 0

C 6. CLARKE 1880 MOD 13. WGS 1972

C 7. SAO

C

cccccc* ****** ******** ****** *************

C CCl-2 = ELLIPSOID NUMBER (K)

C CC3-5 = NUMBER OF POINTS ALONG COAST (IREC)

C

READ(5,100) K,IREC,ID1,ID2 100 F0RMAT(1X,I2,I4,2I3)

TW0PI=2.*PI

A = AXIS(K)

F=1./RF (K)

IF (F.LT.3.D-3) F=(A-1./F)/A C

C READ MASTER AND SLAVE STATIONS POSITIONS

C THE FIRST RECORD IS THE NUMBER OF MASTER AND SLAVE

C STATIONS FOR THE PARTICULAR CHAIN.

C

WRITE (6,202) 202 F0RMAT(1H1)

WRITE (6,201) 201 FORMAT (1H )

READ (5, 105) ILATM,IMINM,RSECM,ILONM, ILMINM, RLSSCM

WRITE (6,105) ILATM,IMINM,RSSCM,ILONM,ILMINM,RLSECM 105 FCRMAT(1X,I3, 1X,I2,1X ,F5. 2, 1X,I4, 1X,I2, 1X,?5.2)

RMAST = ( (lABS(ILATM) * 6 0 > IMINM) * 60 + RSECM) / 1 RHOSEC

IF (ILATM .LT. 0) RMAST = -RMAST

RMASTL = ( (TABS (ILONM) * 60 + ILMINM) *60 +RLSECM) / 1 RHOSEC

113

IF(ILONM .GT- 0) RMASTL = TWOPI - RMASTL C

C READ THE FIRST SLAVE STATION AND CHANGE THE LATITUDE

C AND LONGITUDE INTO RADIANS.

C

READ (5, 101) ILATS,IMINS,RSECS,ILONS,ILMINS,RLSECS, 1 DELAY1

WRITE (6,101) ILATS,IMINS,RSECS,ILONS,ILMINS,RLSECS, 1 DELAY1 101 FORM AT (IX, 13, IX, 12, IX, F5. 2, IX, 14, IX, 12, IX, F5. 2, F9. 2) RSLAV1 = ((lABS (ILATS) * 60 + IMINS) * 60 + RSECS) / 1 RHOSEC IF(ILATS .LT. 0) RSLAV1 = -RSLAV1

RSLAL1 = ((lABS (ILONS) * 60 + ILMINS) * 60 + RLSECS) / 1 RHOSEC IF (ILONS .GT. 0) RSLAL1 = TWOPI - RSLAL1 C

C READ THE SECOND SLAVS STATION AND CHANGE THE LATITUDE

C AND LONGITUDE INTO RADIANS.

C

READ (5, 101) ILATS, IMINS, RSECS, ILONS, ILMINS, RLSECS, 1 DELAY2

WRITE (6,101) ILATS, I ^ INS, RSECS, ILONS, ILMINS, RLSECS, 1 DELAI2

RSLAV2 = ( (TABS (ILATS) * 60 + IMINS) * 60 + RSECS) / 1 RHOSEC IF (ILATS .LT. 0) RSLAV2 = -RSLAV2

RSLAL2 = ( (lABS (ILONS) * 60 + ILMINS) * 60 + RLSECS) / 1 RHOSEC IF (ILONS .GT. 0) RSLAL2 = TWOPI - RSLAL2 WRITE(6,201) C

C READ THE RECORDS POSITIONS AND OBSERVED RATES, THEN

C COMPUTE THE TOTAL DISTANCE.

11U

DO 55 0 I=1,IREC,1

READ (5, 104) ILAT,IMIN ,RSEC,ILON , ILMIN , RLSEC, 1 RATE1,RATE2 104 FOEMAT(1X,I3,I3,F6.3, 15,13 ,F6. 3 , 3X, 2F1 0. 2) C

C CONVERT LAT AND LONG TO RADIANS.

C

RPOST = ((IA3S(ILAT) * 60 + IMIN) * 60 + RSEC) / 1 RHOSEC

IF(ILAT .LT. 0) RPOST = -RPOST

RPOSTL = ((IABS{ILON) * 6 0 -»• ILMIN) * 60 + RLSEC) / 1 RHOSEC

IF(ILON .GT. 0) RPOSTL = TMOPI - RPOSTL C

C COMPUTE DISTANCES AND AZIMUTHS FROM THE OBSERVED POINT

C

C MASTER

C

CALL INVER1 (A ,F , RPOST , RPOSTL, RM AST ,RMASTL, FAZM , BAZM , 1 DISTM)

UDISTM = (RN * DISTM) / UNCOV

CALL SECFAC (UDISTM,SFM) C

C SLA7E1

C

CALL INVER1 (A,F ,RPOST ,RPO STL,RSLA71 , RSLAL1 , FAZ1 , 3AZ 1 , 1 DIST1)

UDIST1 = (RN * DIST1) / UNCOV

CALL SECFAC (UDIST1,SF 1) C C SLAVE2

C

CALL INVER1 ( A, F, RPOST ,RPO STL,RS LAV2, RSLAL2, F AZ2, 3AZ2,

115

1 DIST2) 0DIST2 = (RN * DIST2) / UNCOV CALL SECFAC (UDIST2,SF2) C

C DETERMINE WHICH LAT AND LONG THE ASF CORRECTOR

C IS ASSIGNED TO.

C

CALL ASSIGN (RPOST, RPO STL, JN1, JN2) C

C COMPUTE THE RATES AND COMPARE TO THE OBSERVED RATES

C

TDM1 = DDIST1 - UDISTM + SFI - SFM + DELAYI

DIFF1 = TDM1 - RATS1 C

TDM2 = UDIST2 - UDISTM + SF2 - SFK + DELAY2

DIFF2 = TDM2 - RATS2 C

C SUM THE DIFFERENCES TO THE MATRIX AND COUNT THE NUMBER

C OF ASF CORRECTORS FOR EACH BLOCK TO LATTER DETERMINE

C THE MEAN.

C

ASFCR1 (JN1, JN2) = ASFCR 1 ( JN 1, JN 2) + DIFFI

ASFCR2(JN1,JN2) = ASFCR2 ( JN1, JN2) + DIFF2

IN01 (JN1,JN2) = IN01 ( JN1, JN2) + 1 550 IN02 (JN1,JN2) = IN02 ( JN1, JN2) + 1 C

C DETERMINE THE MEAN ASF CORRECTOR FOR EACH LAT AND LONG

C

DO 650 1=1, 16,1

WRITE(6,201)

DO 600 J=1,26,1

IF(IN01(I,J) .EQ. 0) GO TO 580

ASFCR1(I,J) = ASFCR1(I,J) / IN01(I,J) 580 IF(IN02(I,J) .EQ. 0) GO TO 590

116

aSFCR2(I,J) = ASFCR2(I,J) / IN02(I,J) 590 IF(ASFCR1 (I,J) .EQ. 0.0) ASFCR1(I,J) = 9.99 600 IF(ASFCR2 (I,J) .EQ. 0.0) ASFCR2(I,J) = 9.99 650 CONTINUE C

C WRITE THE CORRECTORS IN MATRIX FORMAT

C C

IF(ID1 .EQ. 1) WRITE (6,1000)

IF(ID1 .EQ. 2) WRITE(6,1001)

IF(ID1 .EQ. 3) WRITE(6, 1002)

WRITE(6,201) C

WRITE (6,300) ( (ASFCR1 (I,J) ,1 = 1 , 1 6) , J=1 , 26)

DO 700 L=1,5, 1

WRITE(6,201) 201 FORMAT (1H )

700 CONTINUE C

IF(ID2 .EQ. 1) WRITE (6,1000)

IF(ID2 .EQ. 2) WRITE (6,100 1)

IF(ID2 .EQ. 3) WRITE(6,1002)

WRITE (6,201)

WRITE (6,300) ( (ASFCR2 (I,J) ,1 = 1,16) ,J = 1,26) 300 F0RMAT(16F6.2)

1000 FORMATC TABLE FOR 99U0-W »)

1001 FORMATC TABLE FOR 99 UO-X ')

1002 FORMATC TABLE FOR 9940-1 •) STOP

END C"== ===== = ================ == ======= = = === ====== =

SUBROUTINE SECF AC( UTD 1ST, SF) C

C

117

C THIS ROUTINE WILL COMPUTE THE SEA SECONDARY FACTOR

C UTDIST = TOTAL DISTANCE

C SF = SECONDARY FACTOR

C

IMPLICIT REAL*8 (A-H, 0-Z) C C

C COEFFICIENTS

C

AO = 129.04323

A1 = -0,40758

A2 = 0.00064576813 C

BO = 2,741282

B1 = -0.011402

32 = .00032774815 C

IF (UTDIST .GT. 537) GO TO 10

SF = ( 30 / UTDIST) + 31 + ( 32 * UTDIST)

GO TO 20 10 SF = ( AO / UTDIST) + A1 + ( A2 * UTDIST) C 20 CONTINUE

RETURN

END C== =============== = ================== = = === === = === = === = = =

SUBROUTINE ASSIGN (RLA T, RLON, I, J) C

c

C SUBROUTINE ASSIGN SELECTS THE COLUMN AND ROW FOR

C THE LATITUDE AND LONGITUDE OF THE RECORD. C RLAT = POSITION LATITUDE IN SECONDS C RLON = POSITION LONGITUDE IN SECONDS C I = COLUMN

118

C J = ROW

C

IMPLICIT REAL*8 (A-H, 0-Z)

DATA RHOSEC,PI/2.0 62 6a806 2U71D0 5, 3 . 1 U 1 59265 35898D0/ C

TWOPI = PI * 2. 0 C CONVER RLAT AND RLON TO SECONDS

C

HLAT = RLAT * PHOSEC

HLON = TWOPI - RLON

HLON = HLON * RHOSEC C

C STARTING LAT AND LONG FOR SEARCH

C LAT = 37/05/00.0 LONG = 122/05/00.0

C

SLAT = 133200,0 SLGN = 439500.0

c
c	LATITUDE
c
	J = 0
	DO 10 IC = 1,26,1
	SLAT = SLAT - 6 0.0
	RULAT = SLAT + 30.0
	RLLAT = SLAT - 30.0
10	IF (HLAT .LT. RULAT -AND
15	J = IC
C
C	LONGITUDE

HLAT .GE. RLLAT) GO TO 15

1 = 0

DO 20 IC = 1,16,1 SLON = SLON - 60.0 RLLON = SLON + 30.0

119

RRLON = SLON - 30.0 20 IF(HLON .LT. RLLON .AND. HLON .GE. HRLON) GO TO 25

25 I = IC

RETURN

END

C== ======================== ================================:

SUBROUTINE INV2R1 ( A, F INV, GLAT1 , GLON 1 ,GLAT2,GLON2 ,FAZ,

1 BAZ,S) C

See Appendix B for subrcu-ine INVER1.

120

DATA SET EXAMPLE - PROGRAM ASFSEL

TABLE FOR 9940-Y

50»

1220 / 00*

US*

0.56 -0.51 -0.39

-0.41

-0.53 -0.44

-0.46 -0.40

-0.54 -0.39 -0.55 -0.45

-0. 63 -0.57 -0.49

-0.54 -0.50

-0.62

40'

35'

360

121

TABLE FOR 9940-Y 1210 / 55*

1210 / 50'

50"

-0.45 -G.U7 -0.41 -0.37

45* -0.51 -0.50

-0.38 -0.49 -0.50 -0.46

-0.54 -0.51 -0.49

-0.54 -0.57 -0.49

-0.55 -0.55 -0.50

40* -0.67 -0.61 -0.50

-0.64 -0.65

-0.60

-0.43 -0. 44 -0.47 -0.44

-0.52 -0.46

35'

122

BIBLIOGRAPHY

Admiralty Manual of H ydrographic Surve^in^, First Edi-icn, 7 . T7 Hy^rograpEer oT ^he Navy, ronton, England, 1965.

!!as^ers TEesis JTz Frep araTionj". " School, Monterey, California, 1982,

Backus, Alexandra, "HK121, LOEAN-C R^al-Time Hydroplot," Language PAL 8, NOAA, Rockville, Maryland, December 10, 1980.

Bigelow, Henry W. , "Elecrronic Surveying: Accuracy of Electronic Positioning System," Journal of the Siirve^in^ and Mapping Division, October 1'9E3,

Dansford, Ed, Electronics Division, DMAHTC, Washington, D.C., private communications, 9 September 1982.

Defense Mapping Agency. M-^-can Practical N§.'^-3^l0£/ DMA Publication Number "'57 DE'K JTy^rograpHIc"* Cen-er, Washington, D.C, v. 1, 1977.

Defense Mappina Agency Hydr ographic/Topographic Center, Washington, 6.C., DMA Stock No. LCPU322 1 2100-C, LORAN-C Correction Table, West Coast, USA 99a0, 1981.

du Plessis, Roaer M. , Poor Man's Explanation of Kalman

Eaton, R.M,, Mortimer, A.R., and Gray, D.H., "Accurate Chart Latticing for LORAN-C," International

H ydrographic Review, Monaco, LV1 (1), January T^T^".

Funakoshi, Larry, Private Communication Forwarding Codv of FORTRAN Program TD3HID, DMAHTC, Coda:' N^rlE, Washington, D.C, 26 February 1982.

General Electric Co., TEMPO division, Santa Barbara,

California, Report Number CG-D-U-80, LORAN-C Signal Analysis Final Report, by Nelson, Larry W. and iJam^iTTT Hur^, TJecemBer TT75.

Heinzen, Morris Rudy, H^dro^raghic Surve_ys: Geodetic

Ccntrcl Criteria, Hasher or science Thesis, Cornell [rniversiry,"TTEaca, New York, 1977.

Ingham, Alan, Sea Surveying , Volume 1, John Wiley and Sons, 1 9TS7

123

Laurila/ Sinio H. , Electronic Surveying and Navigation, Wiley-Interscience PuETIcation, T975'. ""

Leath, Dudley W., FORTRAN Program LSQR, by Paul R. Wolf, Naval Postgraduate School, Monterey, California, 1981.

Mortimer, A. R. , Eaton, R. M. , and Gray, D. K.,

"CaliiDration of the West Canadian LORAN-C Chain." Canadian Aeronautics and Space Journal, v. 24, No. 3, Hay73une T^TBT

National Oceanic and Atmospheric Administration, NOAA, Marine Chart Division, OA/C321, UNCLASSIFIED Letter to Chief Radionavigat ion Division, U.S. Coas- Guard, G-NRN-3. Washington, D. C, , Subject: ASF Corrections, 3 May 19 8 2.

National Oceanic and Atmospheric Administration, National Ocean Survey, Descriptive 3§2^£i (Hydrographic) ,

Registry Number: H-?H22 , AlasRl, Guir of IlasTca, S"ou^east of~Kcfiak Island, Chief of Party: Capt J. G. Grunwell, Capt B. I. Williams, 1979.

National Oceanic and Atmosoheric Administration, National Ocean Survey, Descriotive Report (Hydrographic) ,

Registry Numoer: TF^HII . AlasSa, GuTT o? liaslca, " ■ -. • - £ p^^^y. c^pt J. G.

National Oceanic and Atmospheric Administration, National Ocean Survey, Descriptive Report, Registry Number SiJS902-WH-82, Texas'; nuII"of "Mexico, rTeaIa~and ^"Sine FanTcs, Cn^sr of Party: Cdr. Roy K. Matsushige, 1982.

Nav L

igation Department, Defense Mapping Agency, UNCLASSIFIED etter to: LCDR Jerry Mills, Naval Postgraduate School, Monterey, California, Subject: Definition of a Lane on a Baseline of the LORAN-C Radionavigat ion System in tEe gygergglic 32l£/ August 9, HE2, ~

NOAA Ship Surveyor SI 32, Cruise Report 3U-aO-7-82. Ridges

and Fractures Tectonics Experiment 2, by Alexander

!!aTahcrf, TTEz-et ^lentist leg T~aQ3 Dr. Rcber Embley, Chief Scientist Leg II., 1982.

Pfaifer, L., LCDR., Subroutine INVER1 , National Geodetic Survey, Rockville, Maryland, 18 February 1975.

Pfsifer, L., private communications. National Geodetic Survey, RocKville, Maryland, 10 September 1982.

Poppe, Martin Carl, Jr., "The LORAN-C Receiver A Functional Description," Navigation, v. 29, No.1, Spring 1982.

124

Frsssey, B- G.- Ashwee, G.E., and Fowler, C.5., "Char.ga of Phase with Distance of a Low Frequency Sroundwavs Propagated Across a Coastline," Proceedinqs I.E.S., Paper No. 2082R, July 195 6.

Racal-DECCA Survey, Inc., Brochure. Titled 5U0 Digital Distance Measuring Unit, Racal-DECCA Survey, Inc., TU^TJT~¥est T5IJIcelirZT Houston, Texas, 1931.

Riordan, R., National Ocean Survey, Code C64X2, Rockville, Maryland, private communication Program LORAN, 24 May 197 9.

1979.

Samaddar, S. N., "The Theory of LORAN-C Ground Wave

Propagation - A Review," Navigation, 7. 26, No. 3, Fall, 1979.

Samaddar S. N., "Weather Effect on LORAN-C Propagation," Navigation, v. 27, No. 1, Spring 19 80.

Schne t ? 1979;

Smith-Rose, R.L., D.Sc, Ph.D., "Electric Measurements on Soil with Alternating Currents," Proceedings I.E.E. V. 75, August 1934. ~

Speight, John J., "DMAHTC Support to National Ocean Survey LORAN-C Charting," Navisation, Spring 1982.

The Analytic Science Corporation, Reading, Massachusetts, Ap2lication of Semi-Empirical TD Grid Calibration to the~¥es^ ^oas^ Lg!?ITP"C Cliai.n, by Ra3Ea R. ^uota, July

4, 1976.

U.S. Coast Guard, CF-462, LORAN-C User Handbook, Department of Transportation Coasx Suar^, August T^T^T.

U.S. Naval Oceanographic Office^ Marine Science Department, Washington, Q.C. , Unpublished Manuscript, The

Preparation of Secondary Phase Correction Charts, rcr ID'RO-r. , Transmi^t e^~75' FeSf uary~T7B"77

125

Wallace, J. L., HYDRO PL0T/HYD30L0G System Manual, National Ocean Survey Technical Manual No. 2, September 1971.

Wallace, J. L., "HYDROPLOT/HYDROLOG Systems Manual," U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, NOS Technical Manual No. 2, v. 1, Section 3, Sept 1972 (Revised 21 May 1974).

Wallace, J.L. , National Oceanic and Atmospheric

Administration, private communications, July 15, 1982.

Wolf, Paul R. , Solution Manual to Accompany Elements of P hotoqra metrvT Hc(?r aw-!IiIT~Soolc Company, 1977.

Wonnacott, Thomas H. and Wonnacott, Ronald J., Introductiory Statistics, 3rd ed. , John Wiley and Sons., 1915.

125

INITIAL DISTRIBUTION LIST

4. Chairman (Code 63 RD) Department of Mereoi Naval Postqraduat € Schoo

Department of Meteorology Naval Postgraduate School Mcn-erev, CA 939a 0

5. Director

Naval Oceanography Division (OP952) Naval Observatory 34th and Massachusetts Avenue NW Washington, D.C. 20390

6. Commander

Naval Oceanography Command

NSTL Station

Bay St. Louis, MS 39522

7. Commanding Officer

Naval Ocaanoaraphic Office

NSTL Station"

Bay St. Louis, MS 39522

8. Commanding Officer

Fleet Numerical Oceanography Cen^iar Monterey, CA 93940

9. Commanding Officer

Naval Ocean Research and Development

Ac-tiivity NSTL S-ation Bay St. Louis, MS 39522

10. Commanding Officer

Naval Environmental Prediction Research

Facility Monterey, CA 939 40

11. Chairman, Oceanography Department 0.3. Naval Academy

Annapokis, MD 21402

12. Chief of Naval Research 800 N. Quincv Street Arling-on, VA 22217

127

No. Copies

1. Defense Technical Information Center 2 Cameron Station

Alexandria, VA 22314

2. Library, Code 014 2 2 Naval postgraduate School

Monterey, CA 93940

3. Chairman (Code 68Mr) 1 Depar-^ment of Oceanography

Naval Postgraduate School Monterey, CA 9394 0

13. Office of Naval Research (Coda U20) Naval Ocean Research and Development

Activity NSTL Station Bay St. Loais, MS 39522

14. Director (Code PPH) Defense Mapping Agency

Bldg. 56, U.S. Naval Observatory Washington, D.C. 20305

15. Director (Code HO)

Defense Mapping Avency Hydcrgraphic Topographic Canter 6500 Brookes Lane Washing-con, D.C. 20315

16. Director (Co4e PSD-MC) Defense Mapping School Ft. Belvoir, VA 22060

17. Director

National Ocean Survey (OA/C) National Oceanic and Atmosoheric

Administration Roclcville, MD 20 852

18.

Chief, Program Planning and Liaison (NC2) Na-ional Oceanic and Atmospheric

Administration Rockville, MD 20852

19. Associate Director, Marine Surveys and

Maps (OA/C 3). National Oceanic and Atmospheric

Administration Rockville, MD 20 852

20. Chief, Hydrcgraphic Surveys Division (OA/C35) National Ocenaic and Atmospheric

Administration Rockville, MD 20 852

21. Director

Pacific Marine Center - NOAA 1801 Fairview Avenue East Seattle, WA 9810 2

22. Director

Atlantic Marine Center - NOAA 439 W. York Street Norfolk, 7A 23510

23. Commanding Officer NOAA Ship RAINIER Pacific Marine Center, NOAA 1801 Fairview Avenue 2 ast Seattle, WA 98102

128

24. Ccmmanding Officer NOAA Ship FAIRWEATHER Pacific Marine Center, NOAA 1801 Fairview Avenue Sast Seattle, WA 98102

25. Ccmmanding Officer NOAA Ship DAVIDSON Pacific Marine Cen-cer, NOAA 1801 Fairview Avenue East Seattle, WA 98102

26. Commandina Officer NOAA Ship^MT. MITCHELL Atlantic Marine Center, NOAA 439 West York Street Norfolk, Virginia 23510

27. Commanding Officer NOAA Ship WHITING Atlantic Marine Center , NOAA 439 Wesx York Street Norfolk, Virginia 23510

28. Commanding Officer NOAA Ship PSIRCE

Atlantic Marine Center, NOAA 439 West York Srreet Norfolk, Virginia 23510

29. Chief, Hydrographic Surveys Branch Arilantic Marine Center , NOAA

439 WesT York S-ree:: Norfolk, Virginia 23510

129

1 0 O r> r- p

factors 1 f^^-^Mary

aesls 19^^P58

W4844 Wheaton

c.l Application of

additional secondary factors to LORAN-C positions for hydro- graphic operations.

Application of additional secondary fact

3 2768 001 95034 8

DUDLEY KNOX LIBRARY