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EVALUATION OF CALIBRATION METHOD FOR
HYDROGRAPHIC ELECTRONIC POSITIONING SYSTEMS

Kenneth Wingo Perrin

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESIS

EVALUATION OF CALIBRATION METHODS
HYDROGRAPHIC ELECTRONIC POSITIONING

FOR
SYSTEMS

Kenneth Wingo Perrin

September 1980

Thesis Advisor: D. E. Nortrup

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Evaluation of Calibration Methods for
Hydrographic Electronic Positioning
Systems

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Master ' s Thesis ;
September 1980

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Kenneth Wingo Perrin

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IE SUPPLEMENTARY NOTES

IS. KEY WORDS (Contlnuo on rowotoo •<<*• II n«c*««<i

Calibration

Accuracy of positioning
Hydrographic positioning
Auto calibration
Least squares

mn* Hontlty or Aloe* WMfJ

Random error
Systematic error
Repeatability
Predictability
Blunders

Survey requirements
Accuracy requirement
Electronic survey
positioning

ABSTRACT (Comllmto on rovoroo oldo II nooooomry onO Homlltr or olomM mtmoot)

The accuracy requirement for hydrographic positioning
systems and the types of systems used are identified. The
nature of the position accuracy and sources of errors in the
determination of a position are defined.

The reasons for calibrating an electronic positioning
system and the accuracy requirements for such a calibration
are presented. An "idealized" calibration procedure for
optimum results is defined.

DO , 9S\% 1473

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Actual methods used to calibrate electronic positioning
systems are delineated and compared to derive the best
application for a given set of survey requirements. The
accuracy of each calibration method is tabulated.

Data used to substantiate this research was derived from
questionnaires sent to operational survey units and equipment
manufacturers.

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Evaluation of Calibration Methods for
Hydrographic Electronic Positioning Systems

Kenneth Wingo Perrin

Lieutenant, NOAA

B.S., Virginia Polytechnic Institute

and State University, 1973

Submitted in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE IN OCEANOGRAPHY (HYDROGRAPHY)

from the

NAVAL POSTGRADUATE SCHOOL
September 1980

ABSTRACT

The reasons for calibrating an electronic positioning
system and the accuracy requirements for such a calibration
are presented. An "idealized" calibration procedure for
optimum results is defined.

Data used to substantiate this research was derived
from questionnaires sent to operational survey units and
equipment manufacturers.

TABLE OF CONTENTS

I. INTRODUCTION - - 8

A. ACCURACY OF POSITIONING --- 8

1. Blunders, Random, and Systematic Errors 8

2. Repeatability and Predictability 12

B. CALIBRATION OF ELECTRONIC POSITIONING

SYSTEMS 14

II. NATURE OF PROBLEM - 16

A. ELECTRONIC POSITIONING SYSTEMS 16

1. Position Accuracy 16

2. Hydrographic Positioning Systems 16

B. ACCURACY REQUIREMENTS AND CALIBRATION

OF POSITIONING SYSTEMS- 17

III. PURPOSE FOR RESEARCH -- 19

IV. RESEARCH PROCEDURE - 20

V. CALIBRATION METHODS - --- 21

A. RANGE- COMPARISON METHODS 21

1. Base-Line Method- 22

a. Base-Line Comparison with
Attenuators 23

b. Base-Line Comparison without
Attenuators - -- 24

2. Electronic Range Finder Method- 26

3. Base-Line and Base-Line Extension

Crossing Method 27

B. POSITION COMPARISON METHODS 2 9

1. Fixed-Point Position-- -- 29

a. Visual Range-Angle Method 30

b. Range Intersection Method 32

c. Static Method - - 34

2. Variable Point Position- 36

a. Sextant Calibration Method 37

b. Electronic Range-Azimuth Method 38

c. Theodolite (Azimuth) Intersection
Method- - 41

d. Three-Range Microwave Method 42

e. Three or Four Signal Calibration
Transfer Method 43

C. AUTO CALIBRATION METHODS 44

1. Raydist Director System-- - 45

2. Alternate Application of Least Squares

to Redundant Observations- - 46

VI. CONCLUSION-- - --- 49

APPENDIX A: Research Questionnaire - 52

APPENDIX B: Base-Line and Base-Line Extension

Crossing Method 58

APPENDIX C: Locating and Establishing Stationary

Objects -- 63

APPENDIX D: Table I, Summary of Calibration Methods 71

LIST OF REFERENCES - - -- 75

INITIAL DISTRIBUTION LIST --- 78

ACKNOWLEDGEMENTS

I would like to express my appreciation to CDR. D. E.
Nortrup, NOAA, and LCDR. D. Leath, USN, as thesis advisor
and second reader, for encouragement and guidance throughout
this project.

I am indebted to those who responded to the research
questionnaire. Their answers provided most of the necessary
information needed to complete this undertaking.

I would also like to thank the Graphics Department for
providing the supplies and materials needed to produce the
illustrations used in this thesis.

Finally, I would like to thank my wife, Leslie, for her
patience and support during this project.

I. INTRODUCTION

A. ACCURACY OF POSITIONING

The accurate positioning of a sounding vessel is a
fundamental element of hydrographic surveying. According to
the International Hydrographic Bureau (IHB) , the required
accuracy for positioning, combined with the allowable plot-
ting error, is one and a half millimeters at the scale of
the survey [Ref. 1]. The minimum plotting error is approxi-
mately two-hundredths of an inch or one-half millimeter
[Ref. 2]; therefore, the position accuracy itself must be
one millimeter or better. For example, at a survey scale
of 1:10000, one millimeter equates to a position accuracy
of ten meters.

1. Blunders, Random, and Systematic Errors

Blunders, random, and systematic errors affect the
accuracy of an electronic positioning system.

Blunders are mistakes which result from misreading
instruments, transposing figures, faulty computations, etc.
They are usually large and easily detected through repeated
measurements and can be eliminated by manual or automatic
data evaluation routines, either on or off line.

Random errors are unpredictable in magnitude and
direction and are governed by the laws of probability. They
may derive from instrument errors, observational errors,

ephemeral propagation anomalies, e.g., anomalies due to
lightning, etc.

The random error of any measurement system can be
evaluated by making repeated measurements of the same quan-
tity, e.g., measurement of a fixed range with a positioning
system. The computed standard deviation of these measure-
ments may be used as an estimate of the random error for that
system. The standard deviation will vary from one position-
ing system to another. For example, as determined by the
manufacturer, Del Norte Transponder has a a of plus or minus
three meters per line-of -position (lop) , while Argo has a a
of plus or minus ten meters per lop (average installation
[Ref. 3]. The random errors of the electronic positioning
system must be statistically quantified to determine if the
system meets the accuracy requirements, that is, whether the
positioning system is of hydrographic quality or not.

Systematic errors follow some law by which they can
be modeled. Accuracy of determining the model depends upon
the accuracy by which the governing law is derived [Ref. 4] .
These errors occur in a predictable direction and induce a
shift or bias into an observation. If, for example, the mean
observed coordinates at a given point differ from the computed
value for that point and the differences remain unaltered
with time, a systematic error exists. The errors may be
caused by built-in instrument bias (fixed error), observer
bias, errors from predicted refraction (variable error),

errors from radio waves, i.e., changes in the velocity over
the propagation path, etc.

The better the systematic errors are identified and
modeled, the better the achievable accuracy of the electronic
positioning system. The errors must be modeled so they can
be removed either by instrument adjustment or by correcting
position data. Unfortunately, all systematic errors cannot
be modeled and removed. A calibration provides a means of
estimating residual systematic errors. A calibration is the
comparison of the positioning system's indicated range or
position and a "known" range or position. From this compar-
ison the total effect of all remaining systematic errors is
estimated. Correctors are then applied to the data or
adjustments are made to the surveying system in order to
compensate for these remaining systematic errors.

Refraction and radio wave velocity are the most dif-
ficult systematic error sources to model. Refraction is
affected by temperature, atmospheric pressure, and humidity.
It is directly related to the frequency of the electronic
positioning system, varying within the light spectrum, but
being almost constant within the radio band except near 60
GHz and around 22 GHz where there is dispersion similar to
that of light emission [Ref. 5].

Propagation velocity of radio waves is affected by
the conductivity of water and ground surfaces. Velocities
may vary from 299,670 kilometers per second over sea water

to 298,800 kilometers per second over rocky mountainous
land.

An example of a systematic error resulting from the
use of an incorrect propagation velocity is that of a radio
wave velocity of 299,670 kilometers per second being utilized
when the actual velocity of propagation is 299,370 kilometers
per second. An error of 300 kilometers per second would
exist in the determination of each line-of-position. Thus,
a range measurement based on a travel time of 10 seconds
would result in a difference of three meters at three kilo-
meters, i.e., one meter per kilometer.

Refraction and radio wave velocity, the major
sources of systematic error, affect the electronic position-
ing system lattice making the actual lattice different from
an ideal lattice of the system (see Figure 1).

MODEL

ACTUAL

Figure 1. Propagation velocity spatial pattern,

A constant value for propagation velocity of radio waves is
used in constructing hyperbolic or circular lattices. These
smooth lops are idealized mathematical models of the actual
lattice. As a result of the spatial and temporal variability
of refraction and propagation velocity, each is an irregular
and undetermined surface as shown in Figure 1.
2. Repeatability and Predictability

The accuracy of an electronic positioning system is
a function of two terms, "repeatability" and "predictability."

"Repeatability" is the measure of the relative accu-
racy with which the system is able to return to a specific
point defined in terms of its lattice, i.e., electronic
lines-of-position [Ref. 6], Repeatability is a function of
the random and systematic errors of the system and the angle
at which the lops intersect, i.e., the net geometry of the
system. For a hyperbolic system, the net geometry is also
affected by the expansion factor of the lattice.

Random errors and the net geometry are included in
the root mean square (drms) error measure of repeatability.
Root mean square is a function of the standard deviation in
each measurement (line-of -position) contributing to a posi-
tion determination. Root mean square error can be expressed
by the following equation for ranging systems:

drms = ^o2 ] a2" esc 3

in which, 3 is the angle of intersection of two lines-of-

position, a and a are the standard deviation of each lop
1 2

measurement in distance units [Ref. 7]. The drms equation

assumes that there is a normal distribution of random errors.

Position accuracy can be stated in terms of the computed drms

value since it can be shown that 63.2% to 68.3% of the time

a survey position will fall within a circle with a radius of

one drms. The exact percentage is a function of the angle

3. When B = 90 degrees, the percentage is 63.2%. As the

angle of intersection approaches zero, the computed drms

value converges to a 68.3% interval [Ref. 8]. Usually, the

standard deviation for both lines-of -position is taken as

being the same for a particular positioning system, that is

0=0. Thus, the accuracy of any positioning system is a
i 2

function of the standard deviation and the net geometry.
For example, let

a = a = +3 meters
1 2 —

8 = 90°

Then, drms = /32 + 32 esc 90° =4.2 meters
For $=45°, drms = 6.0 meters.

"Predictability" is the measure of the absolute
accuracy with which the electronic positioning system can
define a point's location in terms of geographic coordinates
rather than the system's electronic coordinates [Ref. 6].

It requires that all systematic errors have been corrected
and only random errors remain. Unfortunately, in hydrographic
surveys, all systematic errors cannot be modeled and removed.
However, through calibration, these errors can be accurately
estimated so that adjustments may be made to the electronic
instruments or the data. The more extensive the calibration,
the better systematic errors will be estimated and, thus, the
more accurate the determination of random errors.

B. CALIBRATION OF ELECTRONIC POSITIONING SYSTEMS

A calibration is a comparison of an electronic position-
ing system's range or position to an independently determined
known range or position. Generally, the calibration data is
applied when the errors are greater than the a of the posi-
tioning system. The navigator unit aboard the vessel may be
adjusted to read the correct rates or correctors may be
applied to all position data.

To obtain optimum results, calibrations should be provided
continuously, obtaining precise information at all ranges, in
all weather, 24 hours a day, for correlation with environ-
mental data acquired concurrently. A continuous calibration
record is needed throughout the entire survey area to estab-
lish a model of all systematic errors in the system's per-
formance over time and distance.

Since such optimum calibration results cannot be obtained,
a compromise must be made as to when, where, and how

to calibrate. Calibrations should be made at such a fre-
quency and over various areas of the survey to ensure the
accuracy of the positioning system. By determining instru
ment bias and modeling, or at least measuring, systematic
errors at various points throughout the survey area, a
calibration relates the electronic positioning system's
actual lattice to the geographic coordinates.

II. NATURE OF PROBLEM

A. ELECTRONIC POSITIONING SYSTEMS

1 . Position Accuracy

The International Hydrographic Bureau's standard for
positioning accuracy, presented in the introduction, is open
to interpretation. The statement, "seldom to exceed one and
a half millimeters at the scale of the survey" [Ref. 1] does
not specify how much of the tolerable error must be reserved
to accommodate plotting inaccuracies. Each survey organiza-
tion must choose a standard measure of error (circular error,
root mean square error, or some other measure) and quantify
the level of acceptability for position accuracy. The
National Ocean Survey of the National Oceanic and Atmospheric
Administration (NOAA) for example, in applying the IHB accur-
acy standard, uses the root mean square error and has estab-
lished one-half millimeter at the scale of the survey as the
allowable inaccuracies inherent in the position measurement
system. Thus, for a survey at a scale of 1:10000, this
standard requires a positioning accuracy of five meters
[Ref. 7].

2. Hydrographic Positioning Systems

The established accuracy requirement is achieved by
the proper use of hydrographic quality survey system.
These systems fall into two primary categories: pulse

signal- elapsed time systems and continuous wave-phase com-
parison systems.

Pulse signal-elapsed time systems measure the transit
time of a radio pulse between a transceiver and a transponder
unit. Time is converted to an accurate distance based on
the velocity of propagation of electromagnetic radiation.
These systems can operate in either a range measurement mode,
where transit time is measured between two stations, or in
the hyperbolic mode where the difference in range from a
vessel to two known points is determined.

Continuous wave-phase comparison systems measure
the difference in phase of the two-path signal. Position
is determined relative to lines of zero-phase difference.
This system can operate in either the range or hyperbolic
measurement mode.

For a comprehensive discussion of these principles,
consult the IHB's Special Publication No. 39 [Ref. 9].

B. ACCURACY REQUIREMENTS AND CALIBRATION
OF POSITIONING SYSTEMS

A survey unit's main objective is to obtain hydrographic
data. Therefore, it is not possible or practical to cali-
brate an electronic positioning system as often and in as
many locations of the survey area as would be necessary to
completely model the systematic errors throughout.

Calibrations are usually performed at the beginning and
end of a survey to determine any correctors and adjustments

to the system. Daily or twice-daily calibration checks are
made on a positioning system in the survey area to monitor
any variations.

A careful calibration must be made since any error in a
calibration will induce an additional systematic error in
survey data until the next calibration is performed. The
accuracy of a calibration is solely a function of the accur-
acy of the determination of the known rates, ranges, or
positions used for comparison. The calibration method used
must be more accurate, preferably an order of magnitude more
accurate, than the accuracy of the electronic positioning
system being checked. Each calibration procedure should
consist of a minimum of two independent observations. The
National Ocean Survey, for example, requires that the cor-
rectors for each successive comparison must agree to within
one-half millimeter or ten meters at the scale of the survey,
whichever is less [Ref. 10].

III. PURPOSE FOR RESEARCH

There are a variety of techniques by which an electronic
positioning system can be calibrated. A particular method
utilized by an individual field unit may be a matter of
habit rather than a knowledgable choice based on the posi-
tioning system and operating circumstances. The methods that
are frequently used are often inefficient and less accurate
than desirable. This is due in part to an absence of appre-
ciation for the wide variety of available calibration methods

The object of this research is to alleviate the above
condition by making available an inventory of methods for
calibration and their associated attributes. Through the
application of appropriate calibration methods, an increased
operating efficiency and product quality should be achieved.

IV. RESEARCH PROCEDURE

In order to supplement published methods of calibration,
a questionnaire was sent to people currently involved in
hydrographic survey work requesting information as to the
various calibration techniques being presently employed.
The questionnaire was also sent to the manufacturers of
hydrographic positioning systems. The questionnaire asked
for the type of positioning system being used, what pro-
cedure (s) was employed to calibrate the system, and the
estimated accuracy of each calibration method [Appendix A] .

The response was very good. Of the 30 questionnaires
sent, there were 21 acknowledgements, equating a 70% response
rate. All those answering requested copies of this report,
indicating a desire for this type of information.

V. CALIBRATION METHODS

Calibration methods can be grouped into three general
categories: range-comparison, position comparison, and
auto-calibration. The nature of range-comparison is to
compare a known distance to the range as measured by a
positioning system (stationary calibration). The position-
comparison involves comparing the lattice coordinates of a
known position to the rate indicated by the positioning
system at that location (stationary or dynamic calibration) .
The nature of auto-calibration is to calibrate an electronic
positioning system by the use of redundant lop information
(dynamic calibration).

A. RANGE- COMPARISON METHODS

The range-comparison method is based on the comparison
of a known distance to an electronic positioning system's
range measurement between the same end points. This pro-
cedure is applicable to either pulse-time or phase-comparison
systems operating in the range measurement mode. For micro-
wave systems, calibration measurements can be made over
either land or sater since the propagation velocity is un-
affected by surface conductivity. With lower frequency
systems, the calibration should be made over water since the
propagation velocity of radio waves is affected by conduc-
tivity of the surface over which it travels.

When calibrating positioning systems that operate in
the microwave frequency range, special care must be taken
to avoid errors due to multipath and grazing angle effects
[Ref. 11].

The range-comparison method requires a clear line-of-
sight so as to avoid interference of the transmitted signal.
Direct comparisons are made between the electronic position-
ing system's range readings and the actual distance. This
procedure can be done ashore, which allows redundant obser-
vations, or at sea. Several readings should be made to obtain
a mean value, i.e., reduce the effects of random errors, be-
fore determining if any adjustments to the positioning system
or corrections, to be applied to previous positions, are
necessary

Each range measurement of the positioning system, when
compared to a known distance, provides an estimate of the
systematic errors affecting the system. These errors will
show up as differences between the positioning system range
and the known distance for that particular propagation path.

1. Base-Line Method

The base-line method involves the comparison of an
electronic positioning system's range measurement of a known
precomputed or measured distance. This "known" range can be
either an inverse distance (precomputed) between two hori-
zontal control stations of at least third-order accuracy, or
a length measured, with a surveying quality electronic

distance measuring (EDM) instrument (measured) , between two
points. The base line is the known distance in this context
and the term "base- line" should not be confused with that
line connecting two control stations in a hydrographic survey-
net.

The remote antenna unit of the positioning system is
centered over the established point at one end of the base
line and a master antenna unit and navigator at the other end;
observations and comparisons are made. With this basic set-up
no temporal or spatial variations are considered. In order
to account for the spatial variations, two approaches may be
taken: (1) use of in-line audio attenuators, or (2) set up
different length base lines.

a. Base-Line Comparison with Attenuators

Variable ranges may be simulated by utilizing a
variable in-line audio attenuator on a positioning system.
Since signal strength decreases with increasing range, cali-
bration of the positioning system over a variety of ranges
(simulated) can be accomplished by using different size dB
attenuators such that the signal strength is reduced. This
allows the limiting signal strength values for maximum ranges
to be determined. Calibration can be completed on a single
set-up, with no need to establish different base-line dis-
tances.

b. Base-Line Comparison without Attenuators

Base-line distances should be approximately
equal to the maximum range over which the positioning system
will be used. Comparisons should be made at different ranges
between the minimum and maximum survey distances in order to
determine spatial variations over the total range. This pro-
cedure requires separate set-ups for each range comparison.

When performing these comparisons, with or without
attenuators, signal strength should be monitored to determine
the maximum distance for which accurate range information can
be received.

The temporal variation of the positioning system can
be estimated by performing the comparisons over a long period
of time and at different times during the day (morning and
evening) . The a of the observations may be determined if a
large enough data set is collected.

The expected accuracy of the base-line method, if
the known distance is determined by using two geodetic con-
trol points of at least third-order accuracy, is on the order
of one part in 10,000. Measuring the base line several times
with an electronic distance measuring instrument should pro-
vide an accuracy of plus or minus one millimeter to plus or
minus five centimeters, depending on the make and model of
the EDM instrument used [Ref. 12]. The repeatability of
calibrating a positioning system using these techniques is

a function of the stability of the positioning system being
used and the condition of its electronics. According to
questionnaire respondents, a repeatability of plus or minus
one meter to plus or minus five meters is achieved with this
procedure. The base-line method is least susceptible to
errors. The accuracy of this technique makes it a very good
means of calibration.

Usually due to logistical demands, this method is
used only at the beginning and end of a survey or when equip-
ment or component changes are made in the positioning system.
This method was at times employed periodically throughout the
survey, e.g., monthly. The base-line method was not used for
daily calibrations.

Twelve of the 21 questionnaire respondents calibrate
using the base-line method. Six of the 12 users employ only
this technique to calibrate the Mini Ranger III. The National
Ocean Survey, for example, has determined this method to be
the only acceptable procedure to calibrate Mini Ranger III
[Ref. 13].

An advantage to the base-line method is that it is
not restricted by reduced visibility once the distance has
been established. Disadvantages include the requirement for
a suitable location and a considerable amount of time in the
complete removal of the positioning system from the vessel
and shore stations. This approach is relatively inflexible
in its use over various areas of the survey. The procedure

needs to be supplemented with daily calibration checks for
the purpose of confirming the validity of base line deter-
mined correctors.

2 . Electronic Range Finder Method

The electronic range finder method is a variation
of the base-line technique. The known distance (vessel to
known point) is determined at the time of calibration. This
procedure consists of using a hand-held electromagnetic or
electro-optical distance measuring device to determine the
known distance.

Calibrations are performed from a ship or launch by
holding the range finder beside the master receiving antenna
and measuring the slant range to a prism or receiving unit
located on the shore station antenna. The reverse of this
set-up can be done with the range finder being used on the
beach and sighting at a prism or receiving unit located on
the master receiving antenna. This technique requires shore
party support. However, if performed in a range-azimuth
survey, this approach can be used effectively, eliminating
additional logistic concerns to support calibration.

The vessel can stop and make a calibration at any
time during the survey as long as the distance to the shore
station is within the limited range of the distance measuring
device. This combination probably provides the best calibra-
tion data possible when used in conjunction with the base-
line method. This technique would provide excellent overall

system calibration data. Unfortunately, due to the limited
range of some of the more versatile distance measuring de-
vices, some other technique would likely have to be employed
to calibrate the positioning system over the maximum range
of its intended use. Weather may be an influential factor
in that it limits the optical range finder to times of clear
visibility. Additionally, there may be a need for someone
at the shore site to aim the prism towards the ship or launch
unless multiple prisms or reflectors are employed.

The expected accuracy for one optical range finder
is plus or minus one-half meter or one-tenth percent of the
total range, according to the manufacturer's specifications
[Ref . 14] . None of the questionnaire respondents had used
this technique, thus comparative accuracy results are not
available. One questionnaire respondent suggested this as
an alternative method of calibration, although he had no
personal experience with it other than having seen it demon-
strated [Ref. 15] .

3. Base-Line and Base-Line Extension Crossing Method

This method of calibration should not be confused
with the base-line calibration procedure. Instead, it in-
volves the calibration of a positioning system when crossing
the base-line or base-line extension produced by the geometry
of the control stations for each rate. At the time of cross-
ing the base-line, the observed readings of both shore
stations are added and compared to the computed base-line

distance between the two known locations. By crossing the
base-line extension, the differences in observed range read-
ings of the two shore stations are compared with the known
base-line distance.

There are equations [Ref. 16] that can be employed
to determine the appropriate corrections for each shore sta-
tion. These formulas utilize the combination of both read-
ings at the -base line and base line extension crossing to
resolve any error. The base-line extension crossing method
can also be used to calibrate hyperbolic systems. For a
complete description, see Appendix B.

These methods are not really true forms of calibra-
tion as defined by this paper since the positioning system
is being compared against itself, thereby not achieving the
accuracy that could be obtained by calibrating against an
independent measurement or observation. The techniques do
provide a validity check on the positioning system and assist
the user in determining if the system is operating within its
required accuracy limits as well as to reestablish a lane
count.

The base-line crossing procedure has been employed
by two of the questionnaire respondents. One of the user's
procedure required the calibration of at least one shore
station rate by an accepted calibration method prior to mak-
ing crossing comparisons. This results in the determination
of which shore station needs to be adjusted if there is a

difference in the comparison.

B. POSITION COMPARISON METHODS

The second method of calibration consists of comparing
a known position with the observed value obtained from the
positioning system at the same location. The method is
universal in its application, with either a ranging or
hyperbolic positioning system. The known position can be
determined by a variety of independent methods.

Position comparison is performed over water, thereby
providing the best estimate of all systematic errors at a
specific point and time. Multiple comparisons are needed
at as many points in the survey area as possible to measure
spatial variations.

The position comparison method can be broken down into
two types of positions: fixed-point and variable-point
positions. A fixed-point position has predetermined lattice
coordinates. Direct comparisons can be made with the posi-
tioning system's rates at the time of calibration. A
variable-point position is a known location that is deter-
mined independently at the time of calibration. The variable
point coordinates must be computed before a comparison can
be made with the positioning system's rates.

1. Fixed-Point Position

The fixed-point position utilizes precomputed elec-
tronic lattice coordinates of the known position in comparison
with the electronic positioning system's observed values.
The fixed-point position is spatially inflexible resulting

in calibrations being performed in only a limited area of
the survey. Repeated observations are necessary to obtain
a good comparison.

There are three general methods of establishing a
fixed-point position: visual range-angle method, range-
intersection method, and static method.

a. Visual Range-Angle Method

The vessel is maneuvering such that the receiv-
ing antenna is placed on a range formed by two control sta-
tions of at least third-order accuracy. A predetermined
angle is observed with a sextant from the range to a third-
order control station to the left or right of the range.
The vessel moves at a slow speed, steering so the antenna
is on range until the predetermined sextant angle is reached
At that instant, electronic position data are observed and
compared with the values precomputed from the sextant angle
and range. Several electronic values and positions from
predetermined sextant angles along the range can be computed
beforehand to allow for calibration at different locations
on the range (see Fig. 2) .

This method is a variation of the three-point
sextant fix with one angle equal to zero. The visual range-
angle technique avoids weak fixes which can result from the
three-point sextant method due to small observed angles and
poor geometry.

4^a

*i/^

V fv

\ «(-•

P2
P3

Figure 2. A, B, and C are stations of at least
third-order accuracy. The angles a have
been predetermined for each point on the
range. Positions and electronic values
for P1...P4 have been computed beforehand

[Ref. 17].

To gain the most accuracy on steering the range,
the distance between the range objects should be larger than
the distance between the vessel and the closest object. One
user employing this technique stated: "The ratio of the dis-
tance between the range objects (aid to navigation lights)
to the distance from the ship to the closest object in the
range was approximately seven to one. This high ratio was
favorable to acceptable repeatability and accuracy in the
method" [Ref. 18]. In all, three of the questionnaire
respondents used this method. Their estimated repeatability
was on the order of four to six meters, the majority being

within two meters.

The accuracy of this procedure is basically the
same as that of a three-point sextant fix. Potential sources
of error include the ability of the sextant observer, instru-
ment error, geometry of the control, and the ability of the
helmsman in keeping the vessel on range at the time of cal-
ibration. This latter source probably results in a more
significant error than that of the angle measurement. For
a sextant observation, the standard deviation is approximately
one minute and the expected accuracy of a sextant fix is
about one meter per kilometer from the station [Ref. 19].

Using a theodolite (T-2) observer ashore to mark
the vessel as it passes the predetermined angles may provide
better calibration data than sextant observed angles. How-
ever, overall accuracy might not improve since steering the
range is potentially the major source of error.

One user reported that maneuvering the vessel
on range and observing the angle with a sextant from the
receiving antenna can sometimes be a problem. This is
especially true if there are strong currents, winds, rough
sea conditions, or poor visibility.

b. Range Intersection Method

With the range intersection method, the known
position is defined by the intersection of two sets of visual
ranges. The vessel steers so that its receiving antenna is
on one range while closing the second range at slow speed.
When the vessel crosses the second range, electronic position

rates are observed and compared with the precomputed lattice
coordinates for that point Csee Fig- 3).

Figure 3. A, B, C, and D are stations of at
least third-order accuracy. The position
and electronic values for the intersec-
tion point P have been precomputed.

Intersection of ranges that are defined by
horizontal control stations will have a predictable lattice
coordinate value. Ranges can be defined by unpositioned
objects, giving flexibility to the location of the calibra-
tion, but the position of the intersection of the two ranges
must be determined. This can be done by performing a the-
odolite (T-2) intersection of the ranges' intersection from
two third-order control points when the vessel is in position,
i.e., in line with both ranges simultaneously. Once the in-
tersection has been determined, the ranges can be used just

as if they were defined hy positioned objects. The lattice
coordinates can also be established by "carrying the rates"
to the point based on some other form of calibration.

The accuracy of the technique depends upon the
geometry of the azimuth configuration, the means of determin-
ing the azimuth of the ranges as well as the position of the
intersection point, and the ability of the helmsman to steer
the range. The distance ratio for acceptable accuracy in
steering the range is the same as with the visual range-
angle method. A position determined from the azimuth in-
tersection of two ranges having at least third-order control
will have a much higher accuracy than a point determined by
theodolite intersection for noncontrolled ranges,
c. Static Method

There are two techniques of calibration employing
the static method: (1) coming alongside the object, (2)
circling the object (Mcircle-buoyM method). Both approaches
can be utilized to reestablish whole lane count for phase-
comparison systems. See Appendix B for methods on locating
and establishing stationary objects (includes "circle-buoy"
method) .

For the first technique, the static known posi-
tion is defined by the use of a stationary structure such as
a piling, beacon, dolphin, or any other accessible object
located in the survey area. The vessel, a launch or a small
boat, comes alongside the established object, and is

positioned such that the receiving antenna is as close as
possible to the object (a major weakness of this method).
If at all possible the receiving antenna unit should be
removed from the vessel and positioned on the object itself
in order to increase the achievable accuracy though any off-
sets may be computed. Comparisons are made between electronic
position rates and the predetermined values for that known
position.

There are times when the calibration object may
modify the positional values that are being checked. One
correspondent wrote that, MHFP Launch 1257 has ceased using
the fixed point calibration because it was apparent that the
fixed point calibration structure was modifying the Raydist
signal" [Ref. 20].

From the results of the questionnaire, it is
apparent that the static method is the most preferred cali-
bration technique (13 correspondents) , especially for compar-
ison checks performed during the survey. It is also probably
the most abused method since many times calibrations are made
when not on station, with offsets being ignored. One
respondent wrote that this procedure was always used unless
impracticable or impossible since it yields the most accurate
and cost effective results when available [Ref. 21]. This
technique may be the fastest one to employ if the distance
to the work area is reasonable and the least susceptible to
errors. Its superior accuracy makes it worth the additional

time and effort to position the stationary object with third-
order control methods. A minimum accuracy of one part in
10,000 can be achieved with third-order methods. Fixed
points in the survey area allow for calibration at any time
it is necessary providing much more repeatability than that
obtained from the three-point sextant method [Ref . 22] . The
user's repeatability was on the order of one to four meters.
Not being able to position the receiving antenna on the
object, as well as sea conditions when trying to maneuver
into position, are some of the factors that would affect the
repeatability of the positioning system during calibration.

Finally, this method is not restricted by re-
duced visibility; however, it requires a suitable object or
location which may present logistic difficulties. Also,
maneuvering a launch in heavy seas or high currents when
coming alongside the object can be hazardous. In most cases
it is too cumbersome and dangerous for larger vessels.
2. Variable-Point Position

With the variable-point position scheme, the known
control point is determined by an independent method at the
time of calibration. The procedure requires computer capa-
bilities or graphics to determine the lattice coordinates
of the known point for comparison with the observed values
of the position system. The variable-point position approach
is spatially flexible, providing calibrations in an unlimited
number of locations in the survey area. To obtain the best

accuracy, geodetic control points of at least third-order
accuracy should be used for determining the known position,
a. Sextant Calibration Method

The method involves the use of three sextant
observers and redundant observation. While the vessel is
close enough to shore to enable the observation of visual
horizontal control signals, a three-point horizontal sextant
fix and check angle are observed simultaneously to obtain
the position of the receiving antenna. This technique pro-
vides a self -checking feature since each angle is independent
of the others. The known position is in effect determined
by two sets of angles simultaneously, thus providing a check
on itself. Electronic rates of the positioning system are
observed simultaneously, recorded and compared to the equiv-
alent values of the fix obtained from the observed angles.

The control stations should have a good geomet-
rical configuration for the best results. Strong fixes will
depend upon the choice of proper signal geometry. Angles of
less than 30 degrees should be avoided whenever possible.
This method requires the angle observers to be as close
together as possible and as close as possible to the receiv-
ing antenna when obtaining a fix.

The accuracy and repeatability achieved with
this method of calibration varies from one to ten meters.
This technique is very susceptible to errors. A main source
of error is the human factor such as eccentricity due to the

three sextant observers not all standing where the receiving
antenna is located when obtaining a fix (a physical impossi-
bility) . Other human factors that result in errors are due
to observers not observing the angle simultaneously, observer
and objects not lying in the same plane, and misidentif ication
of a signal. Other sources of error result from adjustable
and nonadjustable errors (instrument error) inherent in the
sextant [Ref . 23] .

The sextant method is restricted by reduced
visibility, a limited range of approximately five kilometers,
and the amount of proper control available. The manpower
requirement is high, but a minimum investment in equipment
is required.

Thirteen correspondents indicated using sextant
calibration. One respondent ranked it as the most preferred
procedure, since it has been used for so many years. Despite
its inherent inaccuracies it provides a good system to fall
back on when other methods are not available, and, under some
specialized circumstances, may be the most desirable approach
[Ref. 18] . The sextant method for calibrating microwave
systems was not recommended by one correspondent based on
his conviction that Mini Ranger is inherently more accurate
[Ref. 21].

b. Electronic Range-Azimuth Method

The electronic range-azimuth method involves the
determination of the known position by observation of an

azimuth, with a theodolite, and an electronic range to the
receiving antenna on the vessel. A theodolite and ranging
instrument are positioned over the same geodetic control
station. The theodolite uses another control station of
equivalent or better accuracy for its initial azimuth. A
prism or receiving unit is mounted (or held as close as pos-
sible) to the master antenna on the vessel to transmit back
the pulse light or signal received from the ranging instru-
ment. When calibrating, the receiving antenna on the vessel
is simultaneously sighted on by the theodolite, a range
reading made, and the positioning system's rates observed
and recorded.

The procedure requires the use of a surveying
theodolite (T-2) and a surveying ranging instrument such as
the Electronic Range Finder [Ref. 14] or the Tellurometer
CA1000-D EDM [Ref. 24]. An electronic (infra-red) theodolite
which combines the angle and the electronic distance measur-
ing capabilities into a single compact unit would provide an
ideal approach [Ref. 25].

The accuracy of a ranging instrument, providing
the target is stationary, is on the order of plus or minus
one-half meter or one-tenth percent of the total range for
the Electronic Range Finder, and plus or minus two feet at
a range up to 10 miles for the dynamic use of the CA1000-D.
An accuracy of plus or minus five millimeters plus five milli-
meters/kilometer is obtainable for an electronic theodolite

ranging component. The accuracy of a theodolite azimuth
observation, taken as one-half minute of arc, results in
approximately seven-tenths of a meter displacement of the
vessel at five kilometers.

Sources of error that affect the accuracy are
the ability of the theodolite observer, proper leveling and
adjustment of the theodolite, having both the theodolite and
range finder centered over the control station, and the
misidentif ication of the control stations both occupied and
observed.

This technique is very effective in areas of
limited control. When a range-azimuth survey is being per-
formed using a microwave positioning system and a theodolite,
for example, this means of calibration may be utilized most
effectively. A calibration, employing one of the previously
mentioned EDM instruments, can be obtained at any time during
the survey, such as at the end of a survey line, resulting
in little time lost between breaking the survey operations,
calibrating, and returning to the survey work.

The method may be limited by the maximum effective
range of the distance measuring unit being used. The range
for the electronic theodolite is five kilometers, for the
Electronic Range Finder up to seven kilometers, and up to 30
kilometers for the CA1000-D. Note also that with increasing
range the azimuth of the theodolite degrades rapidly.

None of the questionnaire respondents indicated
using this type of calibration, although one respondent did
suggest it as an alternative method.

c. Theodolite (Azimuth) Intersection Method

When using this technique, the known position is
determined by the intersecting azimuth of two surveying theo-
dolites (T-2), both of which are positioned over horizontal
control stations. The control stations need not be inter-
visible, but the azimuth or initial used from each station
must be of equivalent or better accuracy. The receiving
antenna on the vessel is positioned by the intersection of
the two azimuths from the theodolites while simultaneously
obtaining the positioning system's rates.

The accuracy of this technique depends upon the
geometry of the azimuth configuration; the same conditions
that affect the three-point sextant method. A one-half
minute angular error in the theodolite observation equates
to a position error of approximately one-and-a-half meters
at ten kilometers from the stations.

This method is both fast and accurate once
shore sites have been established. The calibration accuracy
obtainable is better than the accuracy of the three-point
sextant procedure. Nine questionnaire respondents indicated
that they used this technique for calibrating. These cali-
brations can be quickly computed with small calculators
having geodetic programs.

d. Three-Range Microwave Method

With this approach the known position for com-
parison is determined by the observation of three range rates
from a microwave positioning system while simultaneously
observing the rates of the system being calibrated. With
three ranges, the known position is in effect determined by
three pairs of ranges simultaneously. This also provides a
check on the microwave system itself.

This technique is used to calibrate medium range
phase comparison systems only. A convenient means of on-site
comparison is to calibrate both positioning systems simul-
taneously by using the theodolite intersection method. To
provide the best accuracy, the microwave system should be
calibrated by the base-line method. In general, the accu-
racy of this method depends on the repeatability of the micro-
wave system and the technique used to calibrate it.

The main advantage to this method is that a
phase comparison system can be calibrated at any time and
in any weather. The major disadvantage is the requirement
for expensive equipment and extensive logistic support for
maintaining the microwave system.

Five questionnaire respondents use this as a
means for calibrating phase comparison systems. It was found
that on the average, weekly calibrations of the microwave
system are sufficient. This was determined from watching
the inverse between fix and the check fix [Ref . 26] . Due to

the accuracy and versatility of this procedure, having to
calibrate a medium range phase-comparison system with the
three-point sextant or theodolite intersection method would
be eliminated in most circumstances [Ref. 21].

e. Three or Four-Signal Calibration Transfer Method
An electronic positioning system that can receive
and display rates from three or four stations simultaneously
is employed. The pair of shore stations that is used for
position control initially are calibrated in the best avail-
able manner. When the vessel reaches the area where all
four signals are received without interference, and just
before leaving the usable work area of the initial pair that
have been calibrated, the vessel will determine the exact
position rates of the second pair. The second pair will be
corrected at this time and can then be used for position
control. This pair will be calibrated using the best avail-
able method when the vessel reaches a suitable area to verify
the position values and provide correctors as required. When
only three signals are received simultaneously, the vessel
calibrates the third rate before switching from one of the
initial pair of stations in order to change the control.

The approach outlined is not a true form of cal-
ibration as defined by this paper. Just as in the base-line
crossing technique, the positioning system is being compared
against itself.

The accuracy of this method depends upon the
accuracy of the technique used to calibrate the initial pair
of shore stations. Repeatability of the positioning system
also affects the accuracy.

If the vessel is able to receive all four rates
simultaneously, all can be calibrated at one time. With
redundant observations, if the reliability of any fix ob-
tained from the two stations being used is in question, an
inverse distance from the position obtained can be computed
and any problem identified.

This method eliminates the need of transit time,
from the survey area and back, to recalibrate when switching
from one positioning net configuration to another. It is a
useful alternative when there is limited control for cali-
brating certain net configurations in the survey area.

Only two questionnaire respondents indicated
using this technique and then only with a phase comparison
system that could receive at least three position rates
simultaneously.

C. AUTO CALIBRATION METHODS

The auto calibration technique calibrates the electronic
positioning system against itself by using redundant lop
information which in turn is adjusted to obtain the most
likely position. Utilizing redundant lops, a determination
as to whether or not there are systematic (fixed or variable)

errors in the positioning system can be made at any time.
Variations in the system, both spatially and temporally,
can be determined. This capability must be designed into
the system, requiring special and costly equipment. It can
be used with either ranging or hyperbolic systems and permits
great flexibility throughout the survey area.
1. Raydist Director System

The Raydist Director System incorporates the princi-
ples of auto calibration by interrogating simultaneously and
continuously four independent ranges (shore stations). The
vessel passes in any direction in the area of the survey,
collecting position data from all control stations. A com-
plex set of equations dealing with changes in range to the
base station is used to derive only one fit for all four
position rates. The system performs a statistical analysis,
i.e., adjust rates for best fit by least squares for each
station, thus providing automatic error detection and
correction [Ref. 27].

Complete and unambiguous lane identification, in-
cluding fractional values, are provided. This allows for
reestablishment of the exact position within minutes after
losing lane count due to a power failure, equipment failure,
atmospheric phenomena, or other causes, by processing redun-
dant data supplied by the four shore stations using the
mathematical model in the system.

This system results in reduced operating time and
costs, as well as increased accuracy. Positioning systems
of this type improve the absolute accuracy (predictability)
of an operation to a standard deviation of one-and-a-half
meters [Ref . 27] .

None of the questionnaire respondents indicated

using this system. "The Yugoslavian Naval Hydrographic

Office bought the first marine model" of the Raydist Director

System [Ref. 28].

2 . Alternative Application of Least Squares
to Redundant Observations

In general, the least squares method provides a
mathematical procedure by which the most probable values of
acquired quantities are obtained from a set of observations.
The most probable value is the value of an observed quantity
that has the highest probability. The observed quantities
are said to be adjusted after this technique and the neces-
sary corrections have been applied. For a set of observa-
tions, the fundamental condition in the least squares method
is that the sum of the square of the residuals is minimized,
a residual being the difference between an observed value of
a quantity and the arithmetic mean value of that quantity
obtained from a number of observations. In order to use this
procedure redundant observations are required. This pro-
cedure can be applied to other methods where redundant in-
formation is available: (1) the three-range microwave method,
or (2) the three or four-signal calibration transfer method.

In the least squares adjustment method, the observed
quantities are related to the desired unknown quantities
through mathematical functions called observation equations.
For each measurement, there is one observation equation
written. The observations are assumed to be independent of
each other. When obtaining a unique position solution there
would normally be two equations and two unknowns. By obtain-
ing redundant observations there will be more observation
equations than unknowns. The most probable values of the
unknowns can be determined, thus providing a means of cali-
bration. The observation equations can be either linear or
higher-order functions. For an in-depth discussion on this
application and the mathematics of least squares, see Kaplan,
1980 [Ref. 29].

By using an electronic positioning system that can
receive at least three position rates continuously and simul-
taneously, the least squares adjustment method can be used
to compute the coordinates at any particular position in the
survey area. Position rates from three shore stations are
obtained while the vessel is performing normal survey oper-
ations. The observation equation can be employed, using
matrix notation and successive observation information, for
a best fit of each position as well as the detection of errors
in any of the position rates. The technique could reduce
operating time and costs, as well as increase accuracy, as
compared with other methods of offshore calibration.

Least squares applies the same procedure as built
into the Raydist Director System with processing done on
line. Using least squares to calibrate, computer software
is needed to make the comparisons off line.

VI, CONCLUSION

The calibration of electronic positioning systems consists
of a variety of methods which in most cases are time consuming
and expensive, but necessary to ensure the accuracy of the
hydrographic data. By calibrating these types of systems
over various regions of the survey, and at different times,
the systematic (fixed and variable) errors can be estimated
and compensated for in the positioning data.

When deciding on the best possible calibration technique,
several considerations must be taken into account. The method
selected will depend on the type of positioning system being
used, the accuracy requirements for the scale of the survey,
and the ability to establish an appropriate calibration site
(availability of adequate control, logistics, location
requirements) .

Ideally, two types of calibration should be performed:
(1) stationary calibration using the base-line or static
method where redundant observations can be made,
and (2) dynamic calibration throughout the survey area.

The most accurate stationary technique for calibrating
any range measurement system, whether pulse-time or phase-
comparison, is the base-line method; unfortunately, it is
also the most time consuming and inflexible in its applica-
tion over the survey area. It is important to note that

microwave ranging systems can use this procedure over either
a land or water path. Systems using radio frequencies must
be calibrated over water due to the extreme variability of
propagation velocity between a land and water path. When
calibrating the ranging system in the survey area, the static
method (a stationary comparison), electronic range finder,
azimuth (T-2) intersection, and electronic range-azimuth
methods provide the best accuracy. The latter three tech-
niques (dynamic comparisons) are, within their range limita-
tions, the most flexible.

Hyperbolic positioning systems can not be calibrated by
the base-line technique or any other method where a single
range is being employed for the comparison. The static
method provides the most accurate stationary calibration and
is one of the least time consuming techniques for this type
of system. It is not flexible in providing calibrations over
various areas of the survey. The techniques providing the
most flexibility over the survey area and at the same time
having very good accuracy for a hyperbolic system are the
azimuth (T-2) intersection and the electronic range-azimuth
methods (dynamic calibrations) .

When a phase-comparison system is being utilized, cali-
bration serves two purposes: (1) check or reestablish whole
lane count, (2) estimate systematic errors. Crossing a base
line or rate transfers are good for the first but not for
the second purpose.

An auto calibration system, such as Raydist Director
System, which includes the necessary hardware and software
features, provides the best accuracy and versatility in its
use throughout the survey area for a positioning system.
The principles of this system could be incorporated into any
type of electronic positioning system, but the cost/benefit
concerns would be a major consideration in its implementation.

By being able to obtain redundant observations, the
application of the method of least square adjustments can be
used to calibrate any type of positioning system, both spa-
tially and temporally, during the survey. In most cases of
particular concern, the appropriate observation equations
and redundant data can be entered into a ship or launch-board
minicomputer, the best fit for a position can be made, and
appropriate corrections determined. It would be advantageous
to have this method of calibration developed further since it
offers the possibility of calibrating a system in real time.
The main limitation is the need of redundant observations.

Depending on the particular situation and an operator's
ingenuity, other methods can be devised to calibrate or
check the positioning system.

APPENDIX A
RESEARCH QUESTIONNAIRE

The following questionnaire was sent to various users
and manufacturers of electronic positioning systems:

I am in the process of working on a research project
in the Oceanography/Hydrography Curriculum at the Naval Post-
graduate School, Monterey, California. The research will
involve the evaluation of calibration methods for Hydrographic
Control Systems.

Since there are probably as many calibration methods as
there are Hydrographic Control Systems, an effort is being
made to catalogue the various calibration methods that are
being used for each type of system available. In addition,
an evaluation will be made as to which method may be best
suited for certain conditions and accuracy requirements.

To help me obtain the information needed to accomplish
this project, I would appreciate it if you could answer the
questions on the following page with respect to your par-
ticular systems.

In order to get the data and use it for this research,
your immediate attention to this matter is appreciated. I
would like to have this information no later than January 1,
1980.

Please provide your name and telephone number so I may
contact you if any questions regarding your answers should
arise.

If you would like a copy of the research results, I

would be glad to send you one. YES No

Please submit answers to:

Lt. Kenneth W. Perrin, NOAA
SMC Box 1710 NPS
Monterey, CA 93940
Telephone: 408-646-3131
Thank you.

1) What type of Hydrographic Control System(s) do you use'

2) What method of calibration do you use for each system?
Describe. (If more than one method is used for the
same system, please explain what the conditions are
for using a particular method) .

3) What type of repeatability (accuracy error) do you get
from one calibration to the next?

The questionnaire was sent to the following users and
manufacturers of electronic position systems:

USERS:

Pacific Marine Center, NOAA
1801 Fairview Ave. , East
Seattle, Washington 98102

The following at the above address:

The Commanding Officer of the NOAA Ships:

*Fairweather

*Rainier

*Davidson

*McArthur

*Surveyor

*Miller Freeman
*LCDR. David MacFarland, CPM 130
*LCDR. Pamela Chelgren, CPM 3
*LCDR. Dirk Taylor, Chief, Pacific Hydrographic Party

Atlantic Marine Center, NOAA
439 W. York St.
Norfolk, Virginia 23510

The following at the above address:

The Commanding Officer of the NOAA Ships:

*Mt. Mitchell

Whiting

Peirce

Rude $ Heck

Ferrel

*George B. Kelez

*LCDR. Thomas Richards, Chief, Hydrographic Surveys
Branch

*LCDR. David Yeager, CAM 1

*Mr. Jim Shea, CAM 102

*Chief, Electronic Engineering Department, CAM 6

*Canadian Hydrographic Service
615 Booth Street
Ottawa, Ontario K1A 0E6

*Atlantic Region
Bedford Institute of Oceanography
P.O. Box 1006
Dartmouth, Nova Scotia B2Y 4A2

Laurentean Region

Ocean £j Aquatic Sciences

P.O. Box 75500

Cap Diamant

Quebec, Quebec G1K 7X7

*Central Region
Canada Centre for Inland Waters
P.O. Box 5050
867 Lakeshore Road
Burlington, Ontario L7R 4A6

*The Commanding Officer
USNS Chauvenet
OCUNIT
FPO, San Francisco, California 99601

*U.S. Army Engineers District
Hydrographic Surveys Division
P.O. Box 1027
Detroit, Michigan 48231

MANUFACTURERS :

*Decca Survey Systems, Inc.
Houston, Texas

Del Norte Technology , Inc.
P.O. Box 696
Euless, Texas 76039

Motorola Government Electronic Division
8201 E. McDowell Road
Scottsdale, Arizona 85252

Teledyne Hastings-Raydist

P.O. Box 1275

Hampton, Virginia 23661

*Cubic Western Data
P.O. Box 80787
San Diego, California 92138

*Aster.isk indicates response received.

QUESTIONNAIRE RESPONSE

Number of questionnaires sent: 30
Number of responses received: 21
Response rate: 7 0%

Number of responses for each calibration method:

BASE-LINE METHOD - - - 12

ELECTRONIC RANGE FINDER METHOD - 1

SEXTANT CALIBRATION METHOD - 13

ELECTRONIC RANGE-AZIMUTH METHOD 1

VISUAL RANGE-ANGLE METHOD 3

THEODOLITE (AZIMUTH) INTERSECTION METHOD 9

RANGE INTERSECTION METHOD- - 1

THREE- RANGE MICROWAVE METHOD - - 5

THREE OR FOUR-SIGNAL CALIBRATION TRANSFER METHOD 2

BASE-LINE AND BASE-LINE EXTENSION CROSSING METHOD- 2

STATIC METHOD---- 13

Request rate from responses for copies

of the research results-- 100!

APPENDIX B
BASE-LINE AND BASE-LINE EXTENSION CROSSING METHOD

For positioning systems which operate in the range meas-
urement mode, the following procedure and equations can be
used to determine corrections for each control station.

B ■ base-line length

RC ■ required correction (red)

GC = required correction (green)

CASE I : Indicators calibrated by cutting base line and the
red extension (Fig. B-l) [Ref. 16]

Figure B-l

At point A, read indicators upon crossing red base-line
extension to obtain R and G.

At point C, read indicators upon crossing base line to
obtain R' and G' .

RC = (G - G') - (R + R')
• 2

GC 3 (R - RT) - CG + G') + 2B
2

CASE II: Indicators calibrated by cutting base line and the
green extension (Fig. B-2) [Ref. 16]

Figure B-2

At point A, read indicators upon crossing base line to
obtain R* and G' .

At point C, read indicators upon crossing green base-line
extension to obtain R and G.

RC = CG - G') - CR * R') * 2B

GC s CR - R') - CG + G')

For positioning systems which operate in the hyperbolic
measurement mode, the base-line extension crossing procedure
can be used to determine corrections for each control station
(see Fig. B-3) [Ref. 16].

• SLAVE

MASTER

SLAVE \

Figure B-3

When a base line or a base-line extension (dash lines)
is crossed by a vessel, one set of dials will reverse direc
tion. When crossing one of the inner base-line extensions
(the base line extensions joining the center station), the
minimum value of the net (zero) will be received. When a

vessel crosses one of the outer base-line extensions (the
base-line extension joining either the red or green station),
the maximum red or green value of the net (Br or Bg) will be
received.

Calibration of the red or green station may be obtained
by either crossing the inner or outer base-line extension.
When the dial reverses, it should be reading either zero or
the maximum value (Br or Bg) of the system. If the above do
not hold true, correct the red dial to the desired value.

The base-line extension should be crossed at approxi-
mately the same point in both directions, obtaining two
minimum readings. Best results in calibration on base-line
extension should be experienced at distances of five to ten
nautical miles from the near antenna. When using a helicopter
to calibrate the system, at a distance of five miles from the
antenna, it is desirable that 100 feet be considered maximum
altitude. Heights up to 500 feet are permissible at a distance
of 10 miles with 100 feet altitude being minimum.

Other guidelines to follow to ensure better accuracy of
calibration are:* (1) the crossing point should not be within
1000 feet of a land-water boundary, (2) the crossing point
should not be within 1000 feet of buildings, power lines,
railroads, or other structures which may produce local in-
duction and re-radiation effects, and (3) there should be no
obstacles between the near antenna and aircraft of sufficient
height so as to block the direct signal.

Base line and base-line extensions totally over water
provide the best calibration accuracy, while all-land paths
produce the largest errors. Water-land path combinations
result in varying accuracies, with the following serving as
a guide: (1) with the base line over water and base-line
extension over land, the accuracy of calibration should
approach that for all-water paths, (2) with the base line
over land and the base-line extension over water, the accu-
racy should be slightly better than for all-land propagation
paths, also (3) with broken land and broken water paths, the
accuracy can range from that of an all-water path to that of
an all-land path depending upon the ratio of the water path
to that of the land path and the order of arrangement. It
may be generally stated that for a one-to-one water-to-land
ratio, the resulting accuracy will vary from the average of
water-land accuracy to that of all land [Ref. 16].

APPENDIX C
LOCATING AND ESTABLISHING STATIONARY OBJECTS

If there are no objects with known positions in the survey
area already available, several procedures can be used to
either locate an existing object or to establish a calibration
fix point. The ' techniques used are the same as in some of
the various calibration methods. The object can be located
either by theodolite (T-2) intersection cuts, a three-point
horizontal sextant fix with a check angle, or by electronic
range-azimuth positioning. Various existing objects that
can be located for calibration purposes by these methods are
the end of piers, a designated point along a dock, breakwater,
or bulkhead, an exposed rock in the survey area, or a buoy.

When a vessel is using a medium range phase-comparison
system in a survey area that is a considerable distance off-
shore, a buoy in that survey area should be established for
a check on the whole lane count of the system. In order to
locate this buoy, the vessel must first obtain a good cali-
bration near shore by the best available method. On the way
back to the survey area careful watch on the positioning
system must be maintained to be assured of no lane losses.
Once in the survey area, the vessel can then position the
buoy by coming alongside of it and obtaining several obser-
vations, averaging the ones in good agreement, and computing

the position and lane values for the buoy. The vessel can
then use the buoy for redetermining and checking the whole
lane count if necessary.

In the circumstance that the vessel is unable to come
alongside the buoy, the "circle-buoy" method can be used if
the line-of -position arcs are of larger radius. A position
on the buoy can be determined by passing close to the buoy
while holding one rate steady with the other rate changing.
The electronic position values are observed and recorded when
the buoy is abeam. The procedure is repeated while the sec-
ond rate is held steady with the first rate changing. This
should continue until the buoy has been circled completely.
The entire procedure should be done several times, maintain-
ing the same distance from the buoy each time. An average
of the position values will give the position of the buoy.

By computing or scaling azimuths for the line-of -position
where the buoy is located, the vessel can check the whole
lane count at any time. While the vessel circles the buoy,
the bearing of the buoy is continuously observed with a
pelorus. At the time that the bearing of the buoy is the
same as the azimuth of a line-of -position for a particular
arc, the lane count for that arc on the vessel is the same
as that of the buoy (see Fig. C-l). In circling the buoy in
such a manner, the vessel will cross each arc twice. This
procedure is repeated until there is a satisfactory agreement
of the correctors. Once the correctors are applied, another

circle of the buoy should be made for verification. "If the
vessel is not equipped with a gyroscope repeater and pelorus
from which accurate bearings can be observed, whole lane
values may be determined by estimating the bearing from the
vessel to the buoy and by obtaining the distance by a range
finder or depression angle from the horizon" [Ref. 17].

Figure C-l. When the observed bearing of the buoy
from the vessel is 268 degrees, the whale lane
value for the line-of -position P~ is 335 lanes

[Ref. 17].

If there is a lighthouse tower or an offshore rig in the
survey area, the position of which is accurately known, then
an exact lane count can be determined by the same circling
method. Since the structure is stationary, the partial lane
count may be obtained if the procedure is repeated enough
times to get a satisfactory agreement among the correctors.

For circling offshore rigs there are two methods, depend-
ing on the location of the known position on the rig. If the
point has been located in the center of the rig, then an
eight-point fix can be made on the rig by circling at an equal
distance and fixing the position, i.e., reading the position
rates (see Fig. C-2). A four-point run is made when the known
coordinate for the rig is on one of the four corners. Four
rate readings are made while circling at an equal distance
around the known position on the rig (see Fig. C-3). By-
computing the mean of the readings, the rate reading for the
control position on the rig can be determined and compared
to the actual rates [Ref . 30] .

Figure C-2. Eight-point
calibration run
[Ref. 30]

Figure C-3. Four-point

calibration run

[Ref. 30]

A three-point mooring system can be used to establish a
buoy so as to ensure little drift from its determined posi-
tion. The material used for the construction of this mooring
consists of one-inch diameter Manila line, three 100-pound
danfort anchors, a metal tie-ring, and a small buoy. The
Manila line is used because it will shrink four to five per-
cent when wet, thus tightening up the mooring once in place.
The ratio between the depth of water in which the buoy will
be moored and the length of line between the anchors' tie
point should be approximately one to ten to ensure a good
stable mooring. For example, a buoy moored in 30 feet of
water will require 300 feet of Manila line for each anchor
line (see Fig. C-4a). The angle between the anchor lines
should be approximately 120 degrees to provide an equal dis-
tribution around the buoy (see Fig. C-4b) . A tagline is tied
to the metal tie-ring and the buoy is attached to the other
end. The length of the tagline is not important but it
should be long enough to prevent the buoy from being sub-
merged at the highest tidal level. The three-point buoy
mooring system is fairly stable with only about a one-and-
a-half to two meter displacement in a three-knot current
[Ref. 31].

Once the buoy is properly moored, a position on the buoy
is determined by one of the previously mentioned techniques.
Whenever a calibration is needed the vessel can come along-
side, pick up the buoy putting tension on the tagline to

ensure that the vessel is over the buoy mooring, and perform
a static calibration. This mooring may be stable enough to
provide partial lane determination when calibrating a phase
comparison system using the "circle-buoy" method.

Figure C-4a. Three-point buoy
mooring system (side view)

Figure C-4b. Three-point buoy
mooring system (top view)

Another buoy mooring technique, though not as good as a
three-point mooring, is to use railroad wheels as the anchor
and a single one- inch diameter Manila line of minimum scope
to secure the buoy to the anchor so that the buoy floats just
at the surface during the lowest tide. Attached to the top
of the buoy will be another line with a series of small floats
(plastic bottles) attached along the line. This line should
be long enough to account for the highest tidal level (see
Fig. C-5). Once the buoy is moored, the vessel can come
alongside, pick up the series of small floats, thus applying
tension on the line to ensure that the vessel is over the
mooring, and then determine the position of the mooring by
the best available method.

FLOATS

BUOY

A RAILROAD

"1 WHEEL

Figure C-5. Buoy mooring, low tide

Another approach is to come alongside the buoy on the up
current side and perpendicular to the string of floats, mak-
ing observations when the antenna is lined up with the string
of floats. The buoy can then be used to calibrate the posi-
tioning system at any time that it is necessary.

In both cases, the buoys should be painted international
orange to increase the chance of being seen by other vessels.
If possible, a radar reflector should also be attached to the
buoy to aid its detection, especially at night.

A variation of the static method of calibration, as men-
tioned by one of the questionnaire respondents, is the bridle
method [Ref . 18] . With this method the launch positions it-
self by attachment to a bridle which in turn is attached to
a stationary object such as a bulkhead, pier, or dock. While
the launch is backing down, keeping equal tension on both
sides of the bridle, a calibration of the positioning system
can be performed once that position has been determined by a
method such as a theodolite (T-2) intersection.

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KEY AND NOTES FOR TABLE I

Key for Positioning Systems:

PT -- Pulse Signal-Time Elapsed System.

CP -- Continuous Wave-Phase Comparison System.

R/R -- Range-Range Measurement.

H -- Hyperbolic Measurement.

Notes :

1. Precomputation of geodetic inverse distance.

2. Position and rates precomputed.

3. Geodetic inverse distance 1 part in 10,000, third-order
control. EDM measurement, ±.1 millimeter to ±5 centimeters
[Ref. 12].

4. For a specific instrument [Ref. 14].

5. From Ingham [Ref. 19].

6. For ranges consisting of third-order geodetic accuracy.
Non-controlled ranges -- intersection point determined
by Azimuth (T-2) intersection method 1 to 2 meters.

7. For points located by geodetic third-order accuracy
methods. Accuracy variable depending on method used
to locate point.

8. Accuracy dependent on accuracy of instrument used.

9. Degree of accuracy dependent on geometrical configuration,
distance between stations, distance from station and
angular resolution of instrument observation.

10. Depends on accuracy of microwave system.

11. Depends on accuracy of positioning system being used.

12. For a specific positioning system [Ref. 27].

13. Depends on range of ranging instrument as to maximum
offshore observation.

14. Calibration in only a particular part of survey area.

15. Sextant observation up to 5 kilometers from stations
(Ref. 32].

16. Depends on the number of iterations performed. Accurate
to within the resolution of the system being used.

LIST OF REFERENCES

1. International Hydrographic Bureau, Special Publication
44, Accuracy Standards Recommended for Hydrographic
Surveys , Monaco, January 1968.

2. USAF Aeronautical Chart and Information Center, ACIC
Reference Publication No. 28, User's Guide to Under-
standing Chart and Geodetic Accuracies, St. Louis,
Missouri, September 1971.

3. XV International Congress of Surveying, Report on the
Work of WG 414b, Positioning Systems, Rear Admiral
Robert C. Munson, Chairman, U.S. Department of Commerce,
NOAA, NOS, p. 13 and 24, June 1977.

• 4. Bowditch, N. , American Practical Navigator, Publication
No. 9, Vol. I, p. 1205-1207, Defense Mapping Agency
Hydrographic Center, 1977.

5. Laurila, S. H. , Electronic Surveying and Navigation,
p. 125-133, John Wiley and Sons, 1976.

6. Heinsen, M. R. , Hydrographic Surveys: Geodetic Control
Criteria, Masters Thesis, Cornell University, p. 48 ,
December 1977.

7. U.S. Department of Commerce, National Oceanic and Atmos-
pheric Administration, National Ocean Survey, Hydrographic
Manual, Fourth Edition, by M. J. Umbach, p. 4-22 - 4-23,

4 July 1976.

8. Bowditch, op . cit . , p. 1231.

9. International Hydrographic Bureau, Special Publication
No. 39, Radio Aids to Maritime Navigation and Hydrography,
Monaco, 1965.

10. Umbach, op. cit., p. 4-27.

11. Kolitz, B.L., A Field Guidance Manual for Mini Ranger
III Electronic Positioning Systems, p. 4-5 - 4-14.
Systems Test and Evaluation Branch, Test and Evaluation
Laboratory, NOAA, National Ocean Survey, 15 November
1977.

12. Laurila, op. cit . , chapter 20.

13. NOAA, National Ocean Survey, Pacific Marine Center:
OPORDER, "Appendix A" Calibration Procedure for Mini-
Ranger Surveys Systems," 11 April 1974.

14. Vyner CSurveying Equipment) Limited, The New RF2K
Electronic Range Finder, distributed by Laser Systems
Electronic Co., Telahoma, Tennessee, 1979.

15. Shea, J., National Ocean Survey, Atlantic Marine Center,
CAM 102, Norfolk, Virginia, 30 January 1980, private
communication.

16. U.S. Naval Oceanographic Office, Special Publication 143,
Hydrographic Survey Procedures, p. 46-56, March 1970.

17. Umbach, op. cit . , p. 4-28.

18. Lt. Mezger, B. K. , Field Operations Officer, NOAA Ship
Davidson, National Ocean Survey, Pacific Marine Center,
Seattle, Washington, 29 November 1979, private communi-
cation.

19. Ingham, A. E. , Ed., Sea Surveying, (Text), p. 71, John
Wiley and Sons, 1975.

20. Lt. Cdr. Richards, T. W. , Chief, Hydrographic Surveys
Branch, National Ocean Survey, Atlantic Marine Center,
Norfolk, Virginia, 5 November 1979, private communication.

21. Lt. Cdr. Schiro, R. A., NOAA Ship Fairweather, National
Ocean Survey, Pacific Marine Center, Seattle, Washington,
28 January 1980, private communication.

22. Lt. Cdr. MacFarland, D. B. , National Ocean Survey, Pacific
Marine Center, CPM 130, Seattle, Washington, 28 January
1980, private communication.

23. Bowditch, op. cit . , p. 406-411.

24. Tellurometer , CA1000-D Electronic Distance Measuring
System, distributed by Tellurometer, Hauppauge, New York,
1975.

25. Hewlett-Packard, Civil Engineering Products, HP 38 2 0A
Electronic Total Station, Hewlett-Packard, 1979";

26. Lt. Cdr. Chelgren, P. R. , National Ocean Survey, Pacific
Marine Center, CPM 3, Seattle, Washington, 1 February
1980, private communication.

27. Teledyne Hastings-Raydist , Raydist Director System, dis-
tributed by Teledyne Hastings-Raydist, Hampton, Virginia,
July 1979.

28. Bender, E. , "Director System Aids Marine Surveys,"
Sea Technology, September 1979.

29. Lt. (JG) Kaplan, A. , Error Analysis of Hydrographic
Positioning and the Application of Least Squares,
Masters Thesis, Naval Postgraduate School, Monterey,
California, September 1980.

30. Yennie, J. V., Surveyor, Decca Survey Systems, Inc.,
Houston, Texas, 6 December 1979, private communication

31. Lt. Cdr. Thomas, L. K. , NOAA, Space Environmental
Laboratory, Radio Boulder, Colorado, private commun-
ication.

32. Ingham, A. E. , "Aspects of Modern Land Surveying,"
Hydrography for the Surveyor and Engineer, p. 18,
John Wiley and Sons, 1974.

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Alexandria, Virginia 22314

2. Library, Code 0142 2
Naval Postgraduate School

Monterey, California 93940

3. Chairman, Code 68 1
Department of Oceanography

Naval Postgraduate School
Monterey, California 93940

4. Chairman, Code 63 1
Department of Meteorology

Naval Postgraduate School
Monterey, California 93940

5. CDR. Donald E. Nortrup 1
NOAA SHIP PIERCE

439 W. York St.
Norfolk, Virginia 23510

6. LCDR. Dudley Leath (Code 62 Lf) 1
Naval Postgraduate School

Monterey, California 93940

7. Director 1
Naval Oceanography Division

Navy Observatory

34th and Massachusetts Avenue NW

Washington, D.C. 20390

8. Commander 1
Naval Oceanography Command

NSTL Station

Bay St. Louis, MS 39529

9. Commanding Officer 1
Naval Oceanographic Office

NSTL Station

Bay St. Louis, MS 39529

10. Commanding Officer

Naval Ocean Research and Development

Activity
NSTL Station
Bay St. Louis, MS 39529

11. Director (Code PPH)
Defense Mapping Agency

Bldg. 56, U.S. Naval Observatory
Washington, D.C. 20305

12. Director (Code HO)

Defense Mapping Agency Hydrographic

Topographic Center
6500 Brookes Lane
Washington, D.C. 20315

13. Director (Code PSD-MC)
Defense Mapping School

Ft. Belvoir, Virginia 22060

14. Director

National Ocean Survey (C)
National Oceanic and Atmospheric

Administration
Rockville, Maryland 20852

15. Chief, Program Planning and Liaison (NC-2)
National Oceanic and Atmospheric

Administration
Rockville, Maryland 20852

16. Chief, Marine Surveys and Maps (C3)
National Oceanic and Atmospheric

Administration
Rockville, Maryland 20852

17. Director

Pacific Marine Center - NOAA
1801 Fairview Avenue East
Seattle, Washington 98102

18. Director

Atlantic Marine Center - NOAA
439 West York Street
Norfolk, Virginia 23510

19. Commanding Officer
Oceanographic Unit Four
USNS CHAUVENET (T-AGS29)
FPO San Francisco, CA 96601

20. Commanding Officer
NOAA SHIP FAIRWEATHER
Pacific Marine Center
1801 Fairview Avenue, East
Seattle, Washington 98102

21. Commanding Officer
NOAA SHIP RAINIER
Pacific Marine Center
1801 Fairview Avenue, East
Seattle, Washington 98102

22. Commanding Officer
NOAA SHIP DAVIDSON
Pacific Marine Center
1801 Fairview Avenue, East
Seattle, Washington 98102

23. Commanding Officer
NOAA SHIP MCARTHUR
Pacific Marine Center
1801 Fairview Avenue, East
Seattle, Washington 98102

24. Commanding Officer
NOAA SHIP SURVEYOR
Pacific Marine Center
1801 Fairview Avenue, East
Seattle, Washington 98102

25. Commanding Officer

NOAA SHIP MILLER FREEMAN
Pacific Marine Center
1801 Fairview Avenue, East
Seattle, Washington 98102

26. LCDR. David MacFarland, CPM 130
Pacific Marine Center, NOAA
1801 Fairview Avenue, East
Seattle, Washington 98102

27. LCDR. Pamela Chelgren, CPM 3
Pacific Marine Center, NOAA
1801 Fairview Avenue, East
Seattle, Washington 98102

28. LCDR. Dirk Taylor

Chief, Pacific Hydrographic Party
Pacific Marine Center, NOAA
1801 Fairview Avenue, East
Seattle, Washington 98102

29. Commanding Officer

NOAA SHIP GEORGE B. KELEZ
Atlantic Marine Center
439 West York Street
Norfolk, Virginia 23510

30. Commanding Officer
NOAA SHIP MT. MITCHELL
Atlantic Marine Center
439 West York Street
Norfolk, Virginia 23510

31. Commanding Officer
NOAA SHIP WHITING
Atlantic Marine Center
439 West York Street
Norfolk, Virginia 23510

32. Commanding Officer
NOAA SHIP RUDE § HECK
Atlantic Marine Center
439 West York Street
Norfolk, Virginia 23510

33. LCDR. Thomas Richards, CAM 11
Atlantic Marine Center, NOAA
439 West York Street
Norfolk, Virginia 23510

34. LCDR. David Yeager, CAM 1
Atlantic Marine Center, NOAA
439 West York Street
Norfolk, Virginia 23510

35. Mr. Jim Shea, CAM 102
Atlantic Marine Center, NOAA
439 West York Street
Norfolk, Virginia 23510

36. Chief, Electronic Engineering Department,

CAM 6

Atlantic Marine Center, NOAA

439 West York Street

Norfolk, Virginia 23510

37. Canadian Hydrographic Service
615 Booth Street

Ottawa, Ontario K1A OE6

38. Atlantic Region 1
Bedford Institute of Oceanography

P.O. Box 1006

Dartmouth, Nova Scotia B2Y 4A2

39. Central Region 1
Canada Centre for Inland Waters

P.O. Box 5050

867 Lakeshore Road

Burlington, Ontario L7R 4A6

40. U.S. Army Engineers District 1
Hydrographic Surveys Division

P.O. Box 1027

Detroit, Michigan 48231

41. Decca Survey Systems, Inc. 1
Houston, Texas 77002

42. Cubic Western Data 1
P.O. Box 80787

San Diego, California 92138

43. Mr. John Murdock (Code 8412) 1
U.S. Naval Oceanographic Office

NSTL Station

Bay St. Louis, MS 39522

44. Mr. Martin Mandelberg, P.E. 1
United States Coast Guard

Research and Development Center
Avery Point, Groton, CT 06340

45. Mr. John Rees (Code NVE) 1
Defense Mapping Agency-

Hydrographic/Topographic Center
6500 Brookes Lane
Washington, D.C. 20315

46. LCDR. Gerald B. Mills (Code 68 Mi) 1
Naval Postgraduate School

Monterey, California 93940

47. Ms. Penny D. Dunn 1
P.O. Box 158

Long Beach, MS 39560

48. LCDR. Donald Winter 1
SMC Box 1745

Naval Postgraduate School
Monterey, California 93940

49. LCDR. Francisco Abreu

Av. Salvador Allende, 30, R/C
2780 - OEIRAS, Portugal

50. LT. Luis Faria

R. Arriaga N° 10 - 1°
1200 - LISBOA, Portugal

51. Ms. Pat Eaton
SMC Box 2181

Naval Postgraduate School
Monterey, California 93940

52. LT. Donald Dreves
NOAA SHIP DAVIDSON
FPO

Seattle, Washington 98102

53. LT. Ali Kaplan
Boslonci Koyu
Gonen-Balikesir , Turkey

1 q n »0755

Thesis 1 7U / 5

P33965 Perrin ,|i-

c.l Evaluation of Calibra«)r

tion methods for hydro-:ron_

graphic electronic , -si terns

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Thesis i9c;

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c.l Evaluation of Calibra-
tion methods for hydro-
graphic electronic
positioning systems.

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Evaluation of calibra

tion methoda for hy

3 2768 001 97987 5

DUDLEY KNOX LIBRARY

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