CA1149201A - Method and apparatus for calibrating gyroscopically-stabilized, magnetically- slaved heading reference system - Google Patents

Abstract

Abstract of the Disclosure A heading reference system mounted in a vehicle, e.g. an aircraft or a tank, includes a magnetic compass and a gyroscope. The magnetic compass is subject to deviation in the magnetic field, hence the system must be calibrated. If the vehicle is oriented in a starting direction, and the output of the magnetic compass compared to the output of the gyroscope, an error signal is developed. This error signal is filtered to reduce noise, then stored. The vehicle is then re-oriented and the procedure repeated until sufficient information is available to calibrate the system. A micro-processor may be used for the computations and filtering of noise.

Description

Broad]y speaking, this invention relates to gyroscopically-stabili-zed, ma~netically-slaved heading reference systems. ~lore particularly, in a preferred embodiment, this invention relates to methods and apparatus for calibrating the magn~tic sensor used therein.
Most modern military vehicles utilize a heading reference system for navigation and fire control purposes. Typically, such systems are gyro-scopically-stabilized and magnetically-slaved, that is they employ a flux valve or magnetic compass. Unfortunately, the magnetic compass in a vehicle is subject to headin8 errors caused by magnetic deviation. Therefore, the compass must periodically be calibrated so that the known error can be added to or subtracted from the indicated heading to obtain the true magnetic heading ..
Existing techniques for calibrating a magnetic compass take several hours and require from 2 to 3 persons. Essentially, they involve swinging the vehicle either manually or electronically, and hence the compass, and comparing the readings obtained against a known standard compass free from deviation error.
It is accordingly an object of this invention to provide methods and apparatus for calibrating a magnetic compass that significantly reduce the amount of time required for the calibration, which are fully automatic in operation, and which can be performed by the pilot alone, without the use of external aids.
The above and other objects have been attained by a method of cali-brating a gyroscopically-stabilized, magnetically~slaved heading reference system, the system being mounted in a vehicle and including a flux valve magnetic sensor and a gyroscopic compass, both of which generate on output signal which is a function of the heading of the vehicle.
The method comprises the steps of:
(a) orienting the vehicle in a first direction;
(b) comparing the output signal from the flux valve magnetic sensor with the output signal from the gyroscopic compass, to ge,nerate an error signal;
(c) storing the error signal; and then (d) re-iterating steps (a) through (c) until sufficient error signals have been stored to calibrate the heading reference system.
The invention and its mode of operation will be more fully compre-hended from the following detailed description when taken with the appended drawings, in which Figure 1 is a block schematic drawing of an illustrative compass connecting apparatus according to the invention; and J Figure 2 is a flow chart illustrating the operation of the circuit shown in Figure 1.
Figure 1 depicts an illustrative embodiment of the invention~ As shown, the analog output of a gyroscopic compass 10 is applied to a first analog-to-digital converter 11, thence, to a first input port 12 of a computer 13. In like manner, the analog output of a flux valve, or magnetic sensor, 16 is applied to a second input port 17 of the computer, via a second analog-to-digital converter 18.
Computer 13 may be of any known type, for example, a microcomputer using the Intel 8080 or Motorola MC6800 microprocessor. The progranl to run the computer is shown in flowchart form in Figure 2 and may be stored in ROM
or EPROM. The program may also be loaded into RAM from magnetic tape or disc.
The computer is entirely conventional and includes a CPU 19, a clock 21, memory 22 and an output port 23.
In operation, the gyroscopic compass 10 and flux valve 16 (magnetic sensor) independently transmit analog heading information to the two analog-to-digital converters. The converters transform the analog heading information to a digital format which is compatible with the microprocessor.
As shown in Figure 2, the computer periodically samples and stores in memory~ digital heading angles 1' and 2' from the gyroscopic compass and flux valve, respectively. The frequency of this sampling is a function of computer speed, filter design, and the characteristics of the magnetic sensor, gyroscopic compass, and noise. When a magnetic sensor calibration is requested, the computer enters the calibration routine shown in the flow-chart. The calibration routine computes and smoothes the difference angle or error (1'-2') 2CJ ~
as shown in block 33. Tlle type of smoothing or filtering performed on this difference angle may change from application to application. The computer will remain in a loop consisting of blocks 33 and 34 until enough data has been gathered to obtain a good estimate of the error at heading 2'.
It should be noted that a simple averaging filter, or its recursive implementation, :.
= 1 N
_ N n n = O
Where N --9 ~umber of samples =~ ~verage error L, ~ => Error samples (which include random noise) can be used to reduce the noise if the calibratorlpilot positions the vehicle `on the ground during the data gathering and filtering period. In general, as the filtering time increases and the gyro drift characteristics are improved, the confidence level of the estimated error increases. The use of a more complex filter, as discussed below, would minimize the operational L
constraints during calibration.

When a good estimate of heading error has been obtained, the program proceeds to block 35 requesting a new heading. The above processing, in blocks 33 and 34, will begin again when the vehicle has settled on a new heading. The computer will continue to accept raw data, compute the heading error, filtering the error signal, and commanding a move to a new heading until enough information has been collected to allow an accurate determination of the flux valve calibration/compensation constants. The computer will then, in block 37, process the error data and obtain the compensation constants~
These constants are then stored in non-volatile memory or read-out of port 23 for future reference and study.

Whenever power is applied to the heading reference system, the compensation constants stored in non-volatile memory are used to produce corrected magnetic heading.

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Other embodiments of the invention, such as the use of a strapdown magnetic sensor, or use of a different filtering algorithm may allow contin-ued vehicle rotation (instead of periodic stopping) and reduce the total calibration time.
The basic methodology used in this invention is to record the heading angle difference (error) between the gyroscope, in an unconstrained or free mode, and the magnetic sensor (flu~ valve), in either raw or filtered form, while the vehicle is rotated continuously or stopped at various headings through an angle of 360 degrees or less. The difference angle between the gyroscope and the magnetic sensor represents, in the short term, errors caused by magnetic field perturbations including index, one cycle, and two cycle errors. At a single heading, the static difference angle is given as:
DAi = I ~ A Cos (~) + B Sin (~) + C Cos (2~) ~ D Sin (2~) t W + H
where DAi = angle difference at one heading I = index error A,B = magnitudes of one-cycle error C,D = magnitudes of two-cycle error ~ = heading W = error due to gyro drift H = higher order terms The heading angle differences are used to compute the value of the constants A, B, C, D and thereby to compensate for the one and two cycle errors. Pre-indexed flux valves or external updates (positional or angular) may be used to eliminate index error. The additional error introduced by the gyro drift is time dependent and can be effectively neglected if the total calibration time of vehicle rotation is short compared to the drift characteristic. In addition, ~he drift error can be removed from the total error curve if the gyro drift rate can be determined during the calibration.
30`

2~

The operation of the invention can best be described by considering a typical calibration scenario. A calibration request is initiated by the operator while the vehicle is in a stationary position. The difference angle between the gyroscope and the magnetic sensor is sampled and averaged to reduce noise content. The averaged or smoothed difference angle is then stored and the pilot is requested to rotate and position the vehicle to a new heading, illustratively 45 - 5 degrees from the previous heading. The -process is repeated at the new heading. The entire process is continued until a sufficient number of smoothed difference angles (errors) is obtainedO
The difference angles can be used to estimate the coefficients A, Bg C, D which characterize the one and two cycle errors (see Equation 1).
These coefficients can then be utilized by the computer, or by some other L.
parts of the heading reference system, to compensate for the one and two cycle errors.
As mentioned, the logic and computation required is typically performed by a digital computer of the microprocessor class; however, other computational devices may be employed, such as analog computers, etc. Further, various computation techniques may be used to compute the compensation coeffi-cients. These include, but are not limited to, methods using weighted least squares, Fourier transform/series, or Kalman filter algorithms. Also the choice of the technique used depends upon the accuracy and speed of calibra-tion desired, the type of vehicle and magnetic sensor, the heading reference used, and the type of computer employed, etc~
It may be possible, through the use of computational techniques, to calibrate the flux valve without stopping the vehicle at a particular heading to collect data, as noted above. The calibration would be performed while the vehicle is continuously rotated. `
The use of a strapdown magnetic sensor, rather than the typical pendulous type, would make it easier to calibrate the magnetic sensor while the vehicle is continuously rotated, though an accurate vertical reference is required for the coordinate transformation under these circumstances.
The performance of the system outlined above was verified in a series of test fli~hts made with a fully-instrumented helicopter over both ~~lat an~ ~ountainous terrain. Comparing calibrated lleading ~lith inertial heading, four types of tests were conducted:
1) Straight and level 2) Nap-of-the-Earth (NOE)

3) Special ~lission

4) Self-Calibration In a typical straight and level flight, the aircraft flew 3308 Km at a head-ing of 133, then 32.7 Km at a heading of 24, then 19.8 Km at a heading of 162 , then 23.5 Km at a heading of 270, then 23~3 Km at a hesding of 230.
During this test, the aircraft flew at from 20 to 200 ft. above ground level at speeds of from 70-100 knots and better than 30 knots over the checkpoints. Between checkpoints, maximum pitch and roll attitudes were 5 and 15, respectively. At checkpoints, pitch and roll increased to 15 and 30, respectively.
Table I, below, summarizes the results of the above, and other similar, test fli~hts.
T A B L E
S~ARY OF_STRAIGHT AND LEVEL FLIGHTS

STANDARD
MEAN DEVIATION RMS
Test Flight ~1 -0.18 0.63 0.65 Test Flight ~2 -0~26 0.49 0.55 Test Flight ~3 -0.38 0.72 0.82 Test Flight ~4 -0.40 0.55 0.68 CO.~OSITE
RESULTS -0.32 0.61 0.69 A typical NOE flight covered approximately 28.2 Km over two legs. The altitude varied from 5 to 20 ft. above ground level at speeds of from 10 to 30 knots with occasional bursts up to 60 knots. The maximum pitch and roll attitudes were 25 and 45 , respectively.

Table II, below, summarizes the results of a series of NOE flights.

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T A B L E II
. _ :
SU~RY OF NOE FLIGHTS
STANDARD
MEAN DEVLATION RMS
Test Flight ~1 -0.57 1.07 1.22 Test Flight ~2 -0.18 0.39 0O43 Test Flight ~3 -0 59 0.83 1.02 Test Flight ~4 0O03 0.93 0.93 .
~OMPOSITE
RESULTS -0.31 0.87 0.92 The special mission flight profile consisted of a series of unusual maneuversO
The first was a 720 pedal turn (a complete 720 Left/Right turn in 30-40 -seconds) at less than 25 feet. The second was an accelerate/decelerate (0-100-0 knots) once at normal rates (1.5 minutes) and once at slow rates ..
(4 minutes) again at 25 feetO
The other maneuvers, all performed at 1000 feet, were a snake-like .
course at 75 knots, a "Figure-8" course at 70 knots, a racetrack course with .
flat turns at 50-60 knots in the turn and 80 knots in the straightaway, flat ..
circles at 50-60 knots and simulated pop-ups on the same target from different points.
'.
Table III below, summarizes the results of these special maneuvers, .
20each of which was performed at least three times~ ~

- . T A B L E III :
SUMMARY OF SPECIAL MISSION FLIGHTS :
STANDARD ..
MEAN DEVIATION RMS .

Figure 8 -0.58 1088 1.97 Snake 0.31 1O20 1O24 Plat Circles -0.29 0.46 0O54O

720 Hover Turn0.54 0~52 0O75O

Racetrack 0006 0061 0.62 .

Accel/Decel-0O27 0~66 . . .
Pop-Up 0O33O 0.45 0.56 .

COMPOSITE o 0 RESULTS 0O01 0O7~ 0.79 -9f~
The procedure used for the self-calibration tests, was as follows:
(It should be noted that this is not necessarily the optimum procedure.~
1. Position the helicopter in a magnetically clear area. --2. Start the aircraft engines using standard checklist.
3. Position the aircraft at a heading of 000 + 5 , magnetic, -on visually level ground; switch to calibrate mode; start computer programO
4. Rotate the aircraft to a heading of 045 + 5 when the computer -light illuminates; start computer programc Repeat step (4) seven times (rotating the aircraft clockwise approximately 45 each time through 360)o The computer will indicate -whether or not the calibration was valid. If valid, terminate calibration.
If invalid, repeat steps 3 through 5.
Table IV, below, gives the results of a typical self-calibration.
. .
T A B L E IV
' `-:
Tima of Calibration 5 minO 7 min.

Error Before Swing ERROR ERROR

1 Cycle N-S 0.10 0~10 E-W 1.10 1.10 :
2 Cycle Cardinal 0.0 0.0 :
Inter-Cardinal -0.18 -0.18 Calibration Check . . .
AIRCRAFT HEADING ERROR ERROR
::
000 0.02 0~04 045 -0O33 -0.06 090 -0O03 0.04 135 0.27 0.09 180 0.07 0.19 225 -0.23 -0.16 270 -0.13 -0.11 315 0~37 -0.06 ~a.3,.f~z~l Residual Error ERROR ERROR

1 Cycle ~-S -0.03 -0c08 E-W 0.05 0.08 2 Cycle Cardinal 0.06 0.08 Inter-Cardinal -0.30 -0006 Based on a large number of tests, the following observations were made:
COMPASS CALIBRATION RESULTS
Average time required/calibration 9 minutesO
Standard deviation of the residual errors = 0018 0~-~
~These results are based on 10 different compass swings at two 10geographic locations.
~ The index or mean error was assumed to be equal to zero, due touse o~ a pre-indexed flux valve. In the real world, however, the error contributed by this pre-indexed flux valve misalignment would be 0.1.
It is interesting to compare the time, accuracy and manpower needs to perform a conventional compass calibration with that required when the method according to the invention is employed. This comparison is shown in Table V, below:
T A B L E V
_ COMPARISON OF COMPASS ~ALIBRATION METHODS

COMPASS ROSE SWING CALIB~ATION

Time Required 3-4 hours 4-6 hours 10 minutes Personnel Required 2 minimum 1-2 Test Equipment Size ----- 1708ft.3 Weight 3 lbso 285 lbs. NONE

Cost $20.00 $40,000 Pre-Indexed Flux Valve Special Surveyed Surveyed Magnetically Requirements Compass Rose N-S Line Stable Area Accuracy Achieveable 2 25 O 5o The following conclusions can be drawn from the foregoing tests.

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CONCLUSIONS
1. ~luch of the heading error during straight and level flight can be attributed to a non-constant velocity (i.e. pilot induced accelerations and decelerations along the course~ which generated a flux valve hang off;
and 2~ The self-calibration technique performed well within specifica-tions requirements: A typical calibration took 7 minutes with the errors <0.5 O
If increased accuracy is required, the use of a gyro having a lower drift rate to minimi~e error during long periods of cutout, ~ 3 suggested.
One skilled in the art may make various changes and substitutions to the layout of parts shown without departing from the spirit and scope of the invention.

Claims (47)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. A method of calibrating a gyroscopically-stabilized, magnetically-slaved heading reference system, said system being mounted in a vehicle and including a flux valve magnetic sensor and a gyroscopic compass both of which generate an output signal which is a function of the heading of the vehicle, which comprises the steps of:
(a) orienting said vehicle in a first direction;
(b) comparing the output signal from said flux valve magnetic sensor with the output signal from said gyroscopic compass, thereby to generate an error signal;
(c) storing said error signal; and then (d) re-iterating steps (a) through (c) until sufficient error signals have been stored to calibrate said reference system.

2. The method according to claim 1 wherein the outputs from said flux valve magnetic sensor and said gyroscopic compass are analog, said method comprising the further steps of:
(e) prior to step (b), converting said outputs from analog to digital.

3. The method according to claim 2 comprising the further step of:
(f) prior to step (c), filtering said error signal to reduce noise.

4. The method according to claim 3 wherein said error signal is given by an equation of the form DAi = I + A Cos (?) + B Sin (?) + C Cos (2?) + D Sin (2?) + W + H
Where DAi = angle difference at one heading I = index error A,B = magnitudes of one cycle error C,D = magnitudes of two cycle error ? = heading W = error due to gyro drift H = higher order terms, and step (d) further comprises:
(g) re-iterating steps (a) through (c) until sufficient error signals have been stored to simultaneously solve the above equation for the constants A, B, C, D, W and H.

5. Apparatus for calibrating a gyroscopically-stabilized, magnetically-slaved heading reference system, said system being mounted in a vehicle and including a flux valve magnetic sensor and a gyroscopic compass, both of which generate an output signal which is a function of the heading of the vehicle, which comprises:
a first A/D converter for converting the analog output of said flux valve magnetic sensor into a digital output;
a second A/D converter for converting the analog output of said gyroscopic compass into a digital output; and means, connected to said first and second A/D converters, for generating an error signal corresponding to the difference between the two digital outputs.

6. The apparatus according to claim 5 wherein said generating means comprises a programmed digital computer, including:
means for filtering said error signal to reduce noise; and memory means for storing said filtered error signal.

7. Apparatus for compensating for errors in the heading output signal of a magnetic azimuth detector mounted in an aircraft, comprising inertial heading reference means for providing a heading reference signal in accordance with the heading of said aircraft, heading compensation means responsive to said heading output signal and said heading reference signal for compensating said heading output signal for said errors in accordance with the differences between said heading output signal and said heading reference signal at a plurality of predetermined headings of said aircraft, and drift compensation means for compensating said heading reference signal for drift of said inertial heading reference means with respect to said plurality of predetermined head-ings, thereby providing a compensated heading output signal compensated for said errors.

8. The apparatus of claim 7 in which said drift compensation means includes means for providing a measure of elapsed time, said plurality of predetermined headings include an initial heading and a final heading, and said drift compensation means comprises means for compensating said heading reference signal for said drift in accordance with the values of said heading reference signal at said initial and final predetermined headings respectively and said measure of time elapsed therebetween.

9. The apparatus of claim 8 in which said initial and final predeter-mined headings comprise the same heading.

10. The apparatus of claim 1 in which said inertial heading reference means comprises directional gyroscope means.

11. The apparatus of claim 7 in which said magnetic azimuth detector and said inertial heading reference means comprise part of a gyro magnetic compass system for said aircraft, said inertial heading reference means comprising the directional gyroscope means thereof.

12. The apparatus of claim 7 in which said plurality of predetermined headings comprise eight points of the compass spaced 45 degrees apart.

13. The apparatus of claim 9 in which said plurality of predetermined headings comprise eight points of the compass spaced 45 degrees apart, said initial and final heading being zero degrees.

14. The apparatus of claim 9 in which said heading compensation means includes compensation signal generating means for generating heading compensa-tion signals in response to said heading output signal and said heading refer-ence signal at said plurality of predetermined headings, and compensation com-bining means for combining said heading compensation signals with said heading output signal thereby providing said compensated heading output signal.

15. The apparatus of claim 14 in which said heading compensation signal generating means includes compensation signal storage means for storing said heading compensation signal for application to said compensation combining means .

16. The apparatus of claim 15 in which said compensation signal genera-ting means comprises means for generating heading compensation update signals in accordance with said differences between said heading output signal and said heading reference signal at said plurality of predetermined headings, said heading compensation means including means for updating said heading compensa-tion signals stored in said compensation signal storage means with said heading compensation update signals.

17. The apparatus of claim 14 in which said aircraft is successively oriented at said plurality of predetermined headings and said drift compensa-tion means comprises means for compensating said heading reference signal for drift in accordance with the difference in said values of said heading reference signal at said initial and final predetermined headings multiplied by the proportionate elapsed time at each predetermined heading with respect to the time elapsed between said initial and final predetermined headings.

18. The apparatus of claim 17 in which said drift compensation means further includes means for compensating said heading reference signal addi-tionally in accordance with the difference in values of said heading output signal at said initial and final predetermined headings.

19. The apparatus of claim 14 further including compensation signal testing means responsive to said heading compensation signals for reperforming the compensation procedure when said heading compensation signals exceed a pre-determined threshold.

20. The apparatus of claim 17 further including drift testing means responsive to said drift compensation means for reperforming the compensation procedure when said drift between said initial and final predetermined headings exceeds a predetermined threshold.

21. The apparatus of claim 9 in which said aircraft is successively oriented at said plurality of predetermined headings, said apparatus further including heading indicating means responsive to said heading reference signal to provide a heading indication to the pilot of said aircraft whereby in response to which said pilot orients said aircraft to said plurality of predetermined headings.

22. The apparatus of claim 21 in which said heading indicating means includes a predetermined heading indicium and said apparatus further includes means for offsetting said heading indicating means a predetermined amount from said heading indicium whereby said pilot orients said aircraft to the next predetermined heading by maneuvering the aircraft so that said heading indi-cating means is positioned from said predetermined offset to said predetermined heading indicium.

23. The apparatus of claim 22 in which said offsetting means further includes means for offsetting said heading indicating means in accordance with said predetermined offset and in accordance with the amount by which said pilot failed to achieve the desired previous predetermined heading.

24. Apparatus for compensating the heading output signal of a magnetic azimuth detector mounted in an aircraft for one and two cycle errors, said aircraft being oriented to the successive cardinal and inter-cardinal compass headings, one said heading being the initial and final heading of the compen-sation procedure, comprising directional gyroscope means for providing a head-ing reference signal in accordance with the heading of said aircraft, heading error compensation means responsive to said heading output signal and to com-pensation coefficient signals for compensating said heading output signal for said errors in accordance with said compensation coefficient signals, thereby providing a compensated heading output signal compensated for said errors, com-pensation coefficient signal storage means for providing said compensation coefficient signals to said heading error compensation means, compensation coefficient generating means responsive to said compensated heading output signal and said heading reference signal for generating compensation coefficient update signals in accordance with the differences between said compensated heading output signal and said heading reference signal at said cardinal and inter-cardinal headings of said aircraft, means for updating said compensation coefficient signals stored in said storage means with said compensation coeffi-cient update signals, and drift compensation means for compensating said heading reference signal for drift of said directional gyroscope means with respect to said cardinal and inter-cardinal headings of said aircraft.

25. The apparatus of claim 24 in which said drift compensation means comprises means for providing a measure of elapsed time, and means for compen-sating said heading reference signal for drift in accordance with the differ-ence in said values of said heading reference signal at said initial and final headings multiplied by the proportionate elapsed time at each said cardinal and intercardinal heading with respect to the time elapsed between said initial and final headings.

26. The apparatus of claim 25 in which said drift compensation means further includes means for compensating said heading reference signal addition-ally in accordance with the difference in values of said heading output signal at said initial and final headings.

27. The apparatus of claim 26 in which said heading error compensation means compensates said heading output signal in accordance with Sin ? mc = (C - sin ? fv) (1 -? D) + E (B - cos ? fv) Cos ? mc = (C - sin ? fv) (1 + D) E + (B - cos ? fv) where ? mc = said compensated heading output signal ? fv = said heading output signal B, C = one cycle compensation coefficients D, E = two cycle compensation coefficients.

28. The apparatus of claim 27 in which said drift compensation means comprises means for compensating said heading reference signal in accordance with DRIFT = ( ? Gf - ? Gi) - (?mcf - ? mci) where ? Gf = the output of said directional gyroscope means at said final heading ? Gi = the output of said directional gyroscope means at said initial heading ? mcf = said compensated heading output signal at said final heading ? mci = said compensated heading output signal at said initial heading and ? GCxx = ? G xx+ DRIFT where ? GCxx = drift compensated output of said directional gyroscope means at heading xx ?Gxx = uncompensated output of said directional gyroscope means at heading xx ?txx = elapsed time at heading xx t total = elapsed time between said initial and final headings.

29. The apparatus of claim 28 further including means responsive to said magnetic detector for providing a measure of the average magnitude of the magnetic field strength vector, and in which said compensation coefficient generating means comprises means for generating said compensation coefficient update signals in accordance with .epsilon.xx = ? mcxx - ?GCxx where .epsilon.xx = heading error at heading xx ?mcxx = said compensated heading output signal at heading xx ?GCxx = drift compensated output of said directional gyroscope means at heading xx.
and B = ? tan C = ? tan D = 2 tan (- ?45 + ?135 -?225+ ?315) E = tan where ? = average magnitude of magnetic field strength vector.

30. The apparatus of claim 24 in which said aircraft comprises a helicopter.

31. Method for compensating the heading output signal of a magnetic azimuth detector mounted in an aircraft for errors, said aircraft having an inertial heading reference, comprising the steps of orienting said aircraft successively to a plurality of predetermined headings, obtaining differences between the heading output signal of said magnetic azimuth detector and the heading reference signal from said inertial heading reference at said plurality of predetermined headings, compensating said heading reference signal for drift of said inertial heading reference with respect to said plurality of predeter-mined headings, and compensating said heading output signal for said errors in accordance with said differences between said heading output signal and said heading reference signal.

32. The method of claim 31 in which said orienting step includes orienting said aircraft to said plurality of predetermined headings including an initial heading and a final heading, and said drift compensating step comprises compen-sating said heading reference signal for said drift in accordance with the difference in the values of said heading reference signal at said initial and final predetermined headings multiplied by the proportionate elapsed time at each said predetermined heading with respect to the time elapsed between said initial and final predetermined headings.

33. The method of claim 32 in which said orienting step comprises orienting said aircraft successively to the successive cardinal and inter-cardinal compass headings, said initial and final headings comprising one said cardinal or inter-cardinal heading.

34. The method of claim 33 in which said initial and final headings com-prise zero degrees.

35. The method of claim 33 in which said aircraft comprises a helicopter and said orienting step comprises the step of orienting said helicopter to said cardinal and inter-cardinal headings by lifting and rotating said helicopter successively thereto.

36. Apparatus for calibrating n gyroscopically-stabiiized, magnetically-slaved heading reference system, said system being mounted in a vehicle and including a flux valve magnetic sensor and gyroscopic compass, both of which generate an output signal which is a function of the heading of the vehicle which comprises:
a first A/D converter for converting the analog output of said flux valve magnetic sensor into a digital output;
a second A/D converter for converting the analog output of said gyro-scopic compass into a digital output;
means. connected to said first and second A/D converter for generating an error signal corresponding to the difference between the two digital outputs;
wherein said generating means comprises a programmed digital computer, includ-ing:
means for filtering said error signal to reduce noise; and memory means for storing said filtered error signal;
whereby said programmed digital computer is used to form an equation for calibrating outputs of said flux valve and gyroscopic compass into an actual heading.

37. A method of calibrating a gyroscopically-stabilized, magnetically-slaved heading reference system, said system being mounted in a vehicle and including a strapdown-type flux valve magnetic sensor and a gyroscopic compass both of which generate an output signal which is a function of the heading of the vehicle, which comprises the steps of:
(a) orienting said vehicle in a first direction;
(b) comparing the output signal from said flux valve magnetic sensor with the output signal from said gyroscopic compass, thereby to generate an error signal;
(c) storing said error signal; and (d) continuously rotating the vehicle so as to reiterate steps (a) through (c), continuously generating error signals and wherein a programmed computer is used to generate calibration constants for the reference system.

38. The method according to claim 12 wherein said error signal is given by an equation of the form DAi = 1 + A Cos (?) + B Sin (?) + C Cos (2?) + D Sin (2?) + W + H

where DAi = angle difference at one heading 1 = index error A,B = magnitudes of one cycle error C,D = magnitudes of two cycle error ? = heading W = error due to gyro drift H = higher order terms, and step (d) further comprises:
(e) reiterating steps (a) through (d) until sufficient error signals have been stored to simultaneously solve the above equation for the constants A, B, C, D, W and H.

39. The method of claim 13 wherein the method of calculating the constants comprises use of a Kalman filter algorithm.

40. The method of claim 13 wherein the method of calculating the constants comprises use of a Fourier Transform Series algorithm.

41. The method of claim 13 wherein the method of calculating the constants comprises use of a weighted least squares algorithm.

42. The method of claim 13 wherein the computer is a programmed digital computer which samples and averages, thereby smoothing the error signal, being a difference angle between the compass and sensor generated angles.

43. The method of claim 17 whereby the sampling is done by a simple aver-aging filter.

44. The method of claim 18 wherein the validity of the calibration constants is checked by the computer.

45. The method of claim 19 wherein the constants are stored in non-volatile memory and wherein upon power being applied to the heading reference system, the constants stored in non-volatile memory are used to produce an initially corrected magnetic heading.

46. Apparatus for compensating for errors in the heading output signal of a magnetic azimuth detector mounted in a moving vehicle, comprising:
inertial heading reference means for providing a heading reference signal in accordance with the heading of said moving vehicle, heading compensation means responsive to said heading output signal and said heading reference signal for compensating said heading output signal for said errors in accordance with the differences between said heading output signal and said heading reference signal at a plurality of headings of said moving vehicle, and drift compensation means for compensating said heading reference signal for drift of said inertial heading reference means with respect to said plurality of headings, thereby providing a compensated heading output signal compensated for said errors.

47. Method for compensating the heading output signal of a magnetic azimuth detector mounted in a moving vehicle for errors, said moving vehicle having an inertial heading reference, comprising the steps of:
orienting said moving vehicle successively to a plurality of headings, obtaining differences between the heading output signal of said magnetic azimuth detector and the heading reference signal from said inertial heading reference at said plurality of headings, compensating said heading reference signal for drift of said inertial heading reference with respect to said plurality of headings, and compensating said heading output signal for said errors in accordance with said differences between said heading output signal and said heading reference signal.