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
Approved for public release; distribution unlimited
T2C8076
SCCUNtTV CUASSiriCATIOM OF THIS ^A<JC (Whtt Dmtm Btttmr*^)
REPORT DOCUMENTATION PAGE
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
Maen
•• CONTNACT OI» GHAnT NLMSERraj
"*• tSS^VA^^''*'*'^ '•'•OJtCT TASK
AHCA • WOKK UNIT NUMBEHS
12 (lEPOUT OATE
October 1982
*S NUMBER OF PAGES
129
IS. SeCUniTY CLASS, (ot thl» r*>artj
Unclassified
ISa. OeCLASSlFICATION/ OOWNSRAOINC
SCHEDULE
16. OISTRISUTION STATCMCNT (ol tMi R*p»H)
Approved for public release; distribution unlimited
17. OISTKISUTION STATEMENT (ol th» atattmct anlararf In Stack 30, II dlllmrmnt tram Rmport)
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
Live Music Archive
Librivox Free Audio
Metropolitan Museum
Cleveland Museum of Art
Internet Arcade
Console Living Room
Books to Borrow
Open Library
TV News
Understanding 9/11