CA1092651A

CA1092651A - Geodetic survey method

Info

Publication number: CA1092651A
Application number: CA292,719A
Authority: CA
Inventors: James R. Huddle
Original assignee: Litton Systems Inc
Current assignee: Northrop Grumman Guidance and Electronics Co Inc
Priority date: 1976-12-10
Filing date: 1977-12-08
Publication date: 1980-12-30

Abstract

ABSTRACT OF THE DISCLOSURE

The present method involves the detection of local variations of the direction of gravity from the vertical with a degree of accuracy not heretofore obtainable. In accordance with the present method an inertial system is mounted in a mobile vehicle which moves along a survey route from a first control point to a second control point, with the locations and the deflection from the vertical being known at the two control points. The vehicle is stopped periodically between the two control points. At selected stopping points (error removal points), accumulated errors in the inertial system are removed. At additional selected stopping points (survey points), the accumulated inertial system errors are removed and, in addition, the indicated position of the stopping points and vertical deflection are recorded. To avoid complex intermingling of errors, the inertial platform is not releveled at each of the stopping points. When the vehicle reaches the second control point, the position indicated by the inertial guidance system is compared with the actual position of the second control point, errors determined, and the position of the various intermediate stopping points are recalculated using the overall error and the time at which each point was surveyed. Similarly, the separate errors in the deflection of the vertical and position are determined corrected. The position and deflection from the vertical of each of the intermediate survey points are then determined, which may then be plotted on a map.

Description

~ 75-21 . ~0~

1 Field of the Invention . ~

2 The present invention relates to a geodetic survey method

3 ¦using an inertial guidance system.

4 aack~round of the Invention It has previously been proposed to use inertial guidance systems for conducting surveys~ One such system is described in 7 an article entitled "The Application of Inertial Navigation Systems to Precision Land Survey", by S. R. Ellms and J. R. Huddle, pages 9 ~3 through 105, Navigation, The Journal o~ the Institute of 10 Navigation, Summer, 1976, Volume 23, No. 2~ In such prior systems, 1~ the emphasis was on position location rather t~an measurement of 12 "deflection of the vertical". As mentioned above, the deflection 13 of the vertical is a phrase used to designate the departure of the 14 gravity vector from the gravity vector which would be expected from 15 a mathematical model of the earth. When a point on the earth's 16 surface is located between two portions of the earth's crust having 1~ signi~icantly different densities, the gravity vector will be 18 shifted slightly toward the more dense material, and this deflectior 19 of the gra~ity vector from the direction which would normally be 20 expected is ~nown as "deflection of the vertical". The deflection 21 f the vertical is normally not very si~niicant and rarely reaches 22 a value above 50 or 100 arc-seconds, where there are 3600 arc-23 seconds in one degree. However, deflections of the vertical are of 24 onsiderable interest to geologists and others who are interested 2~ in the location o~ bodies of ore, or other geological formations 26 hich are indicated by gravitational anomalies.
27 ~eturning to a consideration of prior navigation land 28 urvey methods, the me~hod described in the article cited above 29 ncluded the mounting of an inertial system including a stable latform on a vehicle such às a j~ep, aligning the inertial naviga-31 ion system, and drivi~g it from a first control point to a second

5~

~CD-75-21 3La~9'~:65~

1 control point. Betwcen the two ContrO~ points, the vehicle would 2 be stopped at intermediate points to be surveyed, and at time 3 intervals not in excess of predetermined limits, in order to 4 eliminate accumulated errors. In addition, at each stop the inertial navigation system would determine the direction of

6 the local vertical, and the stable element of the inertial sys~em ~ is releve]ed. At the end of the survey anothPr control point 8 would be reached, and the position errors for the intermediate 9 points would be recalculated usin~ the overall error in position, together with the time of survPying of the various individual 1~ intermediate points.
12 One of the serious short-comin~s of the prior system 13 involved the relevelin~ of the inertial guidance system at each-14 stopping point. This produced a complex intermingling of errors associated with the inertial system with changes in the deflection 16 of the vertical.
Accordingly, a principaL object of the present invcntion 18 is to avoid complex intermingling of inertial system errors with the chan~e in the deflection of the vertical, in inertial guidance survey methods.
21 Brief Summary of the Invention 22 In accordance with the invention an inertial ~uidance 23 system is moun~ed on a mobile vehicle, and is initially turncd on and aligned with the local geographic coordinates; and it is there-after driven from a ~irst control point reading to a second control 26 point readin~ ~ith periodic stops between the two control point 27 readings. For the second con~rol poin~ reading, the deflection of 28 the vertical indicate~ by ~he i~ertial system is observed and 29 ~ompared with the known de~lection of the vertical, and the ma~nitude and direc~ion of the error is determined for thc ~criod 31 of the survey. At e~ch stoppinq point, the timct t~l~ position and ,., . - .

E;5~

other inertial system sensing unit output signals as required for determinin~ deflection of the vertical, are recorded, without re~eveling the inerti~l system at the intermediate stops. Following completion of the survey, the deflection of the vertical for the intermediate survey points is cal-culated, using the control point deflection of the vertical error determination, the information recorded at each survey point, and the times at which the various stops occurredO
In accordance with a feature of the invention, the continuation from one stopping point to another without releveling of the apparatus prevents complex intermingling of (l) inertial system error and (2) change in the deflec-tion of the vertical and thus facilitate determination of the deflection of the vertical at each stopping point with high accuracy.

,.
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, , , , , , , . . . . . , .. -Other objects, features, and advantages of the invention will become apparent from a consideration of the following detailed description, and from the accompanying drawings.
Brief Description of the Drawings Figure 1 shows diagrammatically a geodetic survey system using an inertial platform mounted in a vehicle;
Figure 2 is a block diagram of the system of Figure 1;
Figure 3 is a typical surveying route for the sur-: veying system shown in Figures 1 and 2;
Figure 4 is a simplified representation of an error model indicating the principles upon which the present invention is based; and Figures 5 and 6 are comparative plots showing the error in the deflection of the vertical plotted against time for a prior art system and for the system of the present invention.
`` Detailed Description Wi~h reference to the drawings, Figure 1 shows a vehicle 12 in which the various units making up the inertial geodetic surveying system are mounted. More specifically, the vehicle 12 carries the power source 14 in the engine compartment, three units including the power supply 16, the inertial guidance unit 18, which includes a stable platform, the gyroscopes, and the accelerometers, and the computer or ` data processing unit 20 all mounted on a table or rack 22.
The input-output controller unit 2~ is mounted at an angle on the floor of the vehicle. The control and display unit is mounted above the dashboard of the vehicle 12 so that it is readily accessible for actuation of switches and the like by the driver or the passenger in the front seat of vehicle 12.

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. I . ~ ' . , `

GCD 75-2~
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1 Figure 2 shows a block diagram of the interconnections 2 of the various units shown in vehicle 12 in Figure 1. In addition, 3 Figure 2 shows the azimuth marker switch 28 which is employed in 4 the control of the system.
The system.as shown in Figures 1 and 2 is known as the 6 "AUTO SU~VEYOR" system and is available from a company having the ~7 following address: Span International, Inc., 733 E. Shoeman Lane, .. ; Scottsdale, Ari~ona 85251; alternate address: P. O. Box 29534, 9 San Antonio, Texas, 78229. .
Figure 3 shows a typical survey route which might be 1~ traversed from first control point 32 to a second control point 34 12 via a number of survey points indicated by circular dots, and a 15 number of additional error removal stopping points indicated by 14 "x's".
In operation, as is described in instruction manuals 16 provided with the purchase of the "AUTO SURVEY~R" system, the 17 system is initi.ally turned on and is ali~ned wit.h the north-south .
18 and east-west axes at the point where the vehicle is located.
19 Thi.s is accomplished in part by the inertial navigation system including.the stable element, the gyroscopes, and three mutually ; 21 orthogonal accelerometers contained in the inertial measurement 22 unit 18. For example,- to accomplish leveling or rebalancing of 23 the system to the local ver~ical, the acceleration of gravity is 24 sensed and the system is oriented so that the east-west and north-sou`th accelerometers indicate zero acceleration. To align the 26 system with the true north-south and east-west at the location 27 where the vehicle is located, the rotation of the earth is sensed 28 by the inertial measurement unlt (IMU).

`~ 30 32 `

.

Following alignment to the local north-south and east-west coordinates, if this does not take place at the first control point 32, shown in Figure 3, the vehicle is moved to such a point 32 where the latitude, longitude, elevation and deflection of the vertical are known precisely.
~he AUTO SURVEYOR unit is provided with entry arrangements so that the precise value of the latitude and longitude, as well as the elevation may be entered into the geodetic surveying system. In addition, readings of the outputs of the acceler-ometers may be taken at the first control point from which theorientation of the platform relative to the local vertical may be determined; or alternatively, the stable element in the inertial platform unit may be releveled to the local vertical or to the yeodetic vertical. In addition to the other entries which are recorded at the first control point 32 of Figure 3, the time for recording is also noted. As will be mentioned later, the errors due to drift and the like of the inertial system accumulate with time, and it is only through the recording :of the time of the recording of data at each of the survey and control points that the accumulated errors may be properly removed through a recalculation process.
;From the first control point 32, the vehicle 12 pro-ceeds along the route indicated in Figure 3 toward the survey points 34, 36, 38, etc. In an inertial navigation system, however, the accelerations in three mutually orthogonal direc-tions, east-west, north-south, and vertically, are sensed; these accelerations are integrated to give velocities, and the veloc-cities are integrated to provide distance calculations. Clearly, if there is an error which creeps into the system, the multiple integration will result in significantly increasing the error as long as it is not removed from the system. Accordingly, on a _ 7 _ ~ GCD-75-21 periodic basis and at time intervals from 3 up to perhaps 15 minutes, depending on the accuracy of the survey, the vehicle 12 together with its equipment, of coursel is stopped. A
switch on the zero update control 42 shown as part of the control unit in Figure 2, is actuated. This gives a zero velocity measurement of reference, and by use of these periodic zero velocity references the system is allowed to correct velocity and position error as well as other system error sources. The entire update procedure is accomplished auto-matically in 20 seconds of time.
In Fig. 3 the maximum time allowed between "zero up-dates" had elapsed by the time the vehicle reached the first point "X" which is also designated as point 44. Following the update procedure, the vehicle continues to the survey point 34 where an additional zero update sequence is performed. In add-ition, of ^ourse, the indicated position of the survey point 34 in accordance with the IMU measurements, is recorded along with the time r and other output information as needed to determine the deflection of the vertical at the survey point.
As mentioned above, in accordance with the present invention, no releveling of the stable element of the IMU occurs at the stopping points.
As the vehicle proceeds from control point 32 to con-trol point 39, additional stops take place at the error removalstopping points 46 and 48 as well as the additional survey points 52, 54, 56 and 68 on route to the final control point 39. At ; the control point 39 the exact position readings of the system are recorded, as well as the other IMU output readings necessary to determine the IMU system's indicated deflection of the vertical.

By comparing the indicated position and deflection of the vertical at the second control point with the actual known values of position and deflection of the vertical at this control point, tlle errors which have been buildi~g up overtime, despite the periodic stops which eliminate certain errors, can be determined. Thereafter, in a post mission smoothing technique, the position of the various survey points as well as the deflection of the vertical at each of these survey points may be redetermined with ; greatly increased accuracy.
Figure 4 is a simplified representation in block diagram form of the dynamic error model upon which the post mission smoothing of the error in the real time estimate of the change in the deflection of the vertical is based. In Figure 4 the three inputs at .
points 82, 74, and 78 are the drift rates bE, bz, and : bN, relating to the east drift rate, the azimuth drift rate and the north drift rate, respectively. At the right-hand side of Figure 4 the errors in the deflection of the vertical measurements in the east and the north -directions appear at output points 68 and 70, respectively, ~:
and the change in azimuth error appears at output point 71. Other blocks which appear in Figure 4 include the coupling factors or coupling coefficients "omega", where "omega" (~) represents the earth rate. More specifically, the two coupling coefficients omega `~
represent the earth rate about the vertical and in the north-south direction, in each case with "z" identifying the factors relating to the vertical, and the factor "N" representing the north-south factor. Returning to Figure 4, the block 72 connected ;~

:

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~ mb/ ~ "
, ~CD~75-21 1 between output 68 and summing point 74 represen~s the north earth 2 rate factor omega north; the block 76 connected between outputs 3 68 and summing point 78 represents the negative of ome~a-z or the 4 azimuth earth rate factor; and block 80 connected between output 70 and summing point 82 involves the omega-z factor or the 6 azimuthal earth rate. Block 83 between output point 71 and summing

7 point 82 represents the negative of the north earth rate factor.

8 The integrator blocks 84, 86 and 88 which appear in the block diagxam of Figure 4 es~entially represent the build-up of the errors over time.
1~ Figures 5 and 6 represent the error in the deflection 12 of the vertical, in arc~seconds plotted against time for a prior 13 art system (Figure 5) and for the system in accordance with the 14 present invention. In Figure S note that the characteristic 92 has a value o~ -16.0 or more arc-seconds at its farthest departure 16 rom zero error. In contrast, nol~e that the maximum error 17 indicated in the system in accordance with the present invention 18 shown by characteris~ic ~4 in Figure 6, is less than-0.~0 or 1/5 19 of an arc-second. Incidentally, in passing, it is noted that the indicated error in Figure 5 is actually the approximate change in 22 the deflection of the vertical over the test course used for both Figure 5 and ~igure 6. This result arises, of course, from the 23 ~act that in accordance with the prior art system the stable element of the platform was releveled at each stop. In summary, now that the system and its mode of operation and advanta~es have 26 been briefly described, a table o the method steps included in 2q the operation of the system will be set forth:

, -, . - -- - . ,, . - . . . -~ - GCD-75-21 . ~ .

~BLE NO. 1 2 1. Turn on~
3 2. Inertial Sy~tem North-South 6 East-West Orientation.
3. Inertial Guidance System Biasing.
4. Initial Cvntrol Point Positioning Readings.
5. Ori~ntation of Inertial System to Local V~rtical.
. Initial Control Point "Deflection of the Vehicle" Readin~s -8 7. Vehicle Movement~
8. Periodic Stops to Eliminate Inertial SYStem~ errors.

9. Vehicle Movement.
~X 10. Stop at Points to be Surveyed.
12 11. Determine Indicated Position o~ Inertial System.
~3 12. Record Inertial System Parametexs for Vetermining 1~ Deflection of Vertical, Without Reorienting Platfo~m to Local Vertical.
16 13. ~ehicle Movement.
1~ 14. Repea~ S~ops 7-13 for Survey Route.
18 15. Second Control Point Positioning Readings.
19 16. Second Control Point Deflection of the Vertical Re~dings.
17. Determine Position Errors Between First and Second 21 Control Point Readin~s.
18. Correct Interm~diate Survey Point Position Readings.
23 1~. Determine Errors in Deflcction of the Vertical Betwecn 2~ First and Second Control Point Readings.
20. Calculate Deflcction of ~he Vertical at Intermediate 26 Survey Points.

` 1~- .

~ GCD-75-21 ~216~

1 Now that the drawings and the method of operation of 2 the system have been descri~ed, it is useful to provide additional 3 technical background and an outline of the mathematical approach employed to implement the post-mission smoothing of the deflection of the vertical data which was taken at each of "n'l stopping 6 points, for both north-south and east-west deflection at successive 7 times t1, t2~ t3 ~ tn, 8 Before going on with the mathematical analysis, a series 9 of articles will be cited to present related background information

10 both with regard to the mathematical approach and concerning .

12 previous proposals for using inertial guidance systems for determining the deflection of the vertical.
13 1. Kalman, R. E,,"New Methods and Results in Linear ; 14 Prediction and Filtering Theory", Rias Technical Report 61-1, Bal~i.more, 1961.

1~ 2. Huddle, J. R., "~pplication of Kalman Filtering Theory to ~ugmented Inertial Navigation Systems", ; 18 Chapter 11, NAT0-AGARDograph 139, Editor C. T.
.~ Leondes, ~ebruary 1970.
3. Rose, R. C. and Nash, R. A., "Direct Recovery of Deflections of the Vertical Using an Inertial 22 Navigator", IEEE Transactions on Geoscience 23 Electronics, GE-10 No. 2, April 1~72.

4. Huddle, J. R. and Maughmer, R. W., "The Application .~ of Error Control Techniques in the Design of an 26 ~dvanced Augmented Inertial Surveying System", 27 23th ~nnual Meeting of the Insti~ute of NavigatiOn, West Point, June, 1972.
. 2~

31 . .
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1 S. "The Position and Azimuth Determining System", Kitchens, C. W. Sr., American Congress on 3 Survaying and Mapping in Orlando, Florida, 4 October, 1973.
6. "The Prototype Jeep-Mounted Position and Azimuth 6 Determining System (P~DS)", Perrin, J. L., Proceedings of the 8th Data Exchange Conference 8 ~or Inertial Systems at MIT, August, 1974, pp.
9 214-236.
7. "Gravimetric and Position Determinat.ions Using .
1~ Land-Based Inertial Systems", Huddle, J. R. and 12 Mancini, A., Proceedings of the 35th Annual Meeting 13 of the American Congress on Surveying and Mapping 14 in Washington, D. C., March 1975, pp. 93-106.
8... "Testing an Airborne Inertial Survey System or 16 Buxeau of Land Management Cadastral Survey Applicatio s 1~ in Alaska", Ball, h. E., Proc~edings of the 35th 18 ~nnual Meeting of th~ American Congress on Surveying 19 and Mapping in Washington, D.C., March, 1975, pp.
~O 107-137.
21 9. "Inertial Instrumentation at the Geodetic Survey of Canada", Gregerson, L. F., Commonwealth Survey 23 Officers Conference at Cambridge, England, August 1975, and the General Assembly of the IUGGIAG in G.renoble, August and September, 1975.
26 10. "The Application o Inertial Navigation Systems to 27 Precision Land Survey'l, Ellms, S. R. and lluddle, J.R.
28 31st Annual Meeting of the In~titute of Navigation 29 at Washington, D.C., Julle, 1975.

31 . ` .

52 .

, ' , ~ . . . , .' 65i1 ~ 7 ~ .L

1 11. "Inertial Geodesy in Canada", Gregerson, L. F., 2 American Geophysical Union Conference, San Francisco , 3 California, December, 1975.
12. "A Second-Order Markov Gravity Anomaly Model", Rasper, J. F., Journal of Geophysical Research 6 Vol. 76, No. 32, Nov. 10, 1971, pp. 7844-7849.
7 13. "Inertial Surveys in Private Practice", Barr, J. R., 8 Alaska Surveying and Mapping Convention, January, 9 1~76.
In passing, it may be noted that some of the foregoing 1~ articles are authored by the present inventor or his associates.
12 Also, with regard to prior inertial guidance systems employed or 13 proposed to determine the deflection of the vertical, none of 14 them is capable of accuracies approaching that of the present syste n in which errors are held to less than two arc-seconds.
16 In the following analysis, an off-line, post-mission ~7 mathematical smoothing procedure or program is defined. The 18 function of the analysis is to:
19 1. Employ the difference between:
An arbitrary number of reference measurements o~
the change in the components of the deflection of the vertical, relative to the mission initiation point 2~ and:
The real-time estimates of the deflection com-26 ponent changes as obtained in real-time by the 27 surveying systems along the survey course 2~ rela~ive to the mission initiation point 29 to:
Estimate the components of platform drift rate S2 about the east, north and vertical axes during the mission.
.
~ - 14 -,, ~ .

2. Employ the estimates of the three platform drift rates so obtained, to improve the real-: time estimates of the change in the components of the deflection of the vertical.
Since:
The number of reference deflection change component measurements is arbitrary, and The platform drift rate components to be estimated are assumed constant, a recursive mechanization based upon Kalman filter theory has been selected for the implementation of the platform drift rate estimation function in the post-mission smoother. Once these 3 drift rate estimates [bE, bN, bz] are obtained, the estimates of the errors [~(t), ~(t)]s induced in the real-time deflection change estimates [~(t), Qn(t)]R are obtained by a linear time-variant transformation, H(t):
~(t) ~E
= [H(t)] SN ( 1) ~ n ( t) s bzand used to obtain the improved, real-time or smoothed estimates .; 20 of the deflection changes ~(t), ~n(t)]S relative to thê mission initiation point as follows:

[~(t~ [~(t~ (t~

n(t n(t ~n(t s . ~ R _ s Definition of the Post-Mission Smoothin~_Pro~ram Initially, the analytical model for the propagation of error in the real-time estimates of the deflection change compon-` ents due to constant platform drift rate may be represented as ' 5 follows:

: ` :

, . .

1 ~t~ t) 2 where:

3 ~(t)l are the induccd errors in the csti~natcs of the _ North-South (~5) ~nd the E~5t-W~st (~11) . ~ t~ de~lcc~ion change s .
6 b- .
'7 b - _bE_ are She constarlt platform dri~t rates abc7ut the 8 . bz ea~t, north and vertical axes 1~:) . . .' 1~: H(t) ~ ~ ) hl2(t) hl3(t)1 ~ hl(t)l 12 lh21~t) h22(t) 23( J l' h21t~J
13 .

hll(t) = IQ 1 sin [Ql:~ (5) 16 hl2(e) _ ~Q 1 sin ~ [1 - cos [Qt~]] (6) lq hl3(t) = [S~ cos [~ tl - cos [Qt]~ (7) 19 h21(t) = hl2(t) (8) h22(t) = ~t- cos ~3 - sin [~] h~l(t)] (9) 22 h23~t) = tsin [~ ~ C05 1~] ~1. t hll(t)]] (10) ~3 . :
2~ Or~ani2ation of Data for.Platform Drift Rate Estimation After a mission has been performed t real-time estimates 2G of th~ change in the componen~s of the deflection of ~he ~ertic~l 27 relative to the mission initiation point will be available 28 at the end of each "marked" vehicle stopping point. ~hese data 29 will be assllmed available as 2,n-dimensional vectors:

71 . ' . .
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~ (tl) ~R- vector of North-South deflection change estimates at the times, ti; i =1, ~(t ) ; i~l ~ti (11) ~n (tl) . vector of East-West deflection change _ . estimates at the times, ti.
' (12) an (tn) R
Depending on the (permitted) availability of reference measurements of the change on the deflection components, 2m-dimensional sub-vectors (m > n) of the differences between the real-time estimates of the deflection changes and the reference - changes can be-formed:
~ (til) V[Q~; (ti ) - ~; (ti ) ]-~^' ~ Q~ = (13) ~(tim) R [~(tim) ~(tim)]

~n(ti~ n(t ) -~(t 1]1 25~nR = _[ anR - ~nl = (14) (ti ) R [~n(ti ) ~n( im) .~
.. ., ,. ~ ~ ~., , - - - . - -.
, . : : ;: : ~ - . :

Assuming the validity of the mathematical model defined a~ove, the differences can be related to the platform drift rate vector as:
R - Hib (15) ~ H'b (16) where:
. -<hl ( til ) -Hi_ . (17) .
<h2 ( ti ) ~h2 ( til~
. ., H2 - . (18) : . .
;~ <h2(tim) ., - b is the unknown (assumed constant) platform drift rate vector.
Recovery of the platform drift rate vector can be obtained ~ 20 by processing the individual differences defined above in a re-:l cursive manner using the Kalma~fil~er .algorithm. No order of .~` processing is preferred but for convenience assume the 2m-dimen-~ sional sequence: [~(til),~ n(tim)~.
I This sequence of individual observations can then be re-denoted as:
: ~j j = 1,........... ,2m (19) ; with corresponding rows:
. h. j = 1,........... ,2m (20) ~`, ', - ` ~ ' ' - , .' :- ' . ' ' ' - I GCD~ 21 .
~ Z~S9.

2 ~ ~er2 for cxample:
3 ~ ~?~til)R . ~ 21~

4 1 ~2m Y ~II(t~ 3 R ~22) ~ ¦ h3, ~ (ti ) j (23) 8 ¦ 2m z(ti ) (24 ) 10 ¦ Notc that it may occur tl-at only onc of thc dc~lcction cha.n~e dilfcrcnccs is ¦ Iormablc at one o the timc points. ~évicw o~ the proccssin~ schcmc dcfinc(3 12 ¦ h~rc indicatcs that this cvcnt poscs no s~ecial problems.
13 ¦ E:stim;~tion o~ thc Platform l~rift Ratc Vcctor ~ia a ICalman Mcchanization 1~ ¦ Thc ~unctions to be implcmcntcd in cstimatin~ thc platform drift r~tc 15 ¦ Yector from thc obscrvation scqucnce dcfincd above arc:

17 1 63 . Initialization (Onc Time E~rcnt~
I o Kalman Gain Computation ~Itcrative) 18 1~ ~ Drift Ratc Estimate Update ~Itcrative) 20 ¦ ~ Covariance Matri~c Decremcnt (Itcrative~
21 ¦ Thesc l~urlctions arc dcfincd belo~.
22 l Initi ali ~ati on 2~ ~ _ ~. a b 25 ¦ ~ a ~ _ bN ~ 2 S) 26 ~ . _ . _ . I

~, 2~1 ~ 29 . .
31 1 . . .
~: 32!

, ~ GCD-75-21 ~2~

where:
~ bE 7 ~ (o oo '/hr) l ¦ ab I =~ (0,00 '/hr) ¦ (26) , abz ~ (0.002-/hr)2 are the initial variances for the platform drift rate components.
Set:
.;, . bE
b = bN = (27) bz Kalman Gain_Computation c~ hT]j , a 3 by 1 column vector (23) d = Chjcjt rl , a scaler (29) r = [1 sec] (30) kj= [c/d~j , a 3 by 1 column vector (31) Drift Rate Estimate Upaate ~ bj = kj~j (32) :~ bj = bj_l + ~bj (33) Convariance Matrix Decrement ~j= [k c~; , a 3 by 3 matrix(34) j = j _ 1- Qj (35) .. .
:.

~.0926S1 GCD-75-21 where the 3 sets of equations defined immediately above are solved iteratively for j = 1, ..., 2m.
Estimation of the Error in the Real-Time Estimates of the Deflection Changes Due to Drift Rates and Formation of the Smoothed Estimates . _ .
Once all 2m available deflection change differences defined above have been processed to yield the platform drift A ~ ~
rate estimate b, (where b = b2m) the errors in each of the 2n real--time deflection change estimates is computed as:

A ~ ; ( t l ) ~

= A = Hlb (36) ~ (tn) s ~n (tl) s = . = H2b (37) ~n ( tn) ~' _ S
where . <hl ( tl ) Hl = (3~) .-<hl ( tn) 'h2 (tl) 2 . (39) .
~h2 (tn) ~1 ] A ~ ~ ~

6~
GCD-75~21 The smoothed estimates of the 2n deflection change com--ponents are then formed as:

_ ~ a~ (tl) .

~s . [ ^ ~ ^

`. ~ ~ ( tn ) s lo ~n ( tl) : .
~ns= . = ~nR ~r~s~ (41) .
~n s .
It is again noted that the foregoing analysis assumes that there have baen "n" stops, and that at each stop there have been a determination both of the north-south deflection of the vertical. and also of the east-west deflection of the vertical, making a total of 2n deflection oE the vertical preliminary determinations which are respectively corrected by the 2n de~lection change components determined in the manner set forth above.
Together with the information set forth in the articles cited above, the foregoing mathematical presentation will il permit those skilled in the art to implement the method :; described in the present specification utilizing any suitably mechanized inertial surveying system having capabilities ~ comparahle to the AUTOSURVEYOR system mentioned hereinabove.

; Further, suitable programs for use with the AUTOSURVEYOR

- 22 - :

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GCD-75-ll 5~

system may be purchased from the Guidance and Control Division, Litton Systems, Inc., 5500 Canoga Avenue, Woodland Hills, CaliEornia, 91364.
In conclusion it is to be understood that the foregoing description is of an illustrative method of implementing the present invention, and that other implementations, including the use of different types of vehicles, or of different mathematical approaches for performing equivalent operations, are within the scope of the present invention.
More specifically, the deflection of the vertical of a series of survey points of accurately known position could also be accomplished by the present method, and the position deter-mining steps could then be eliminated.

: - 23 , , . : . , . . : . ,. :

Claims

1. A geodetic survey method using an inertial sur-veying system mounted in a vehicle which may be periodi-cally stopped or brought to a substantially fixed position relative to the earth, comprising the steps of:
calibrating the system while the vehicle is in a fixed position including biasing the inertial system plat-form gyros and aligning the system accelerometers with the local coordinates;
at a first control point having a known location and a known deflection of the vertical, recording the surveying system indicated position, and recording the output from the inertial system sensing units, as required for determining the deflection of the vertical;
moving the vehicle along the terrain to be surveyed;
stopping the vehicle, at points which are to be sur-veyed, and at time intervals not to exceed the survey limit time interval, and eliminating accumulated errors from said system;
at the survey points recording position including lat-itude, longitude, elevation, and the output from inertial system sensing units as required for determining the deflec-tion of vertical, without releveling the inertial platform;
proceeding to a control point having a known location and known deflection of the vertical to take a second control point indication reading, and recording the inertial surveying system indicated position with regard to latitude, longitude elevation, and recording the output from the inertial system sensing units as required for determining the deflection of the vertical;

determining the position errors in latitude, longi-tude and elevation between the first and second control point indication readings;
recalculating the position of the intermediate survey points, utilizing the position errors between the two control point readings;
determining the error in the deflection of the vertical between the first and second control point indication readings; and calculating the deflection of the vertical at the intermediate survey points, utilizing the error in the change in the deflection of the vertical between the two control point readings.

2. A geodetic survey method as defined in claim 1 further including the step of leveling said inertial system to the local gravitational vertical at the first control point.

3. A geodetic survey method as defined in claim 1 further including the step of plotting the results of the survey on a map.

4. A geodetic survey method as defined in claim 1 including the additional step of recording the time of each stop, and wherein the recalculation of the location of the intermediate survey points, and the calculation of the deflection of the vertical of the intermediate points, utilize the times of surveying the intermediate points as inputs.

5. A geodetic survey method using an inertial sur-veying system mounted in a vehicle which may be periodically stopped or brought to a substantially fixed position relative to the earth, comprising the steps of:
initially calibrating and aligning the inertial sur-veying system while the vehicle is in a fixed position;
at a first control point having a known location and a known deflection of the vertical, recording the outputs from the inertial system including outputs required for determining the deflection of the vertical;
moving the vehicle along the terrain to be surveyed;
stopping the vehicle, at points which are to be sur-veyed, and at time intervals not to exceed the survey limit time interval, and eliminating accumulated errors from said system;
at the survey points recording the outputs from the inertial system required for determining the deflection of the vertical, without releveling the inertial platform;
proceeding to a control point having a known location and a known deflection of the vertical to take a second control point indication reading, and recording the outputs from the inertial system required for determining the deflec-tion of the vertical;
determining the error in the deflection of the vertical between the first and second control point indication read-ings; and calculating the deflection of the vertical at the inter-mediate survey points, utilizing the error in the deflection of the vertical between the two control point readings.

6. A geodetic survey method as defined in claim 5 further comprising the steps of:
determining the position errors between the first and second control point indication readings; and calculating the position of the intermediate survey points, utilizing the position errors between the two control point readings.

7. A geodetic survey method as defined in claim 5 further including the steps of:
recording the time of each of the stops; and calculating the deflection of the vertical at the survey points as a function of the time of stopping at each of said stops.