GB2054145A

GB2054145A - Heading-Attitude Reference Apparatus

Info

Publication number: GB2054145A
Application number: GB8016002A
Authority: GB
Original assignee: Bodenseewerk Geratetechnik GmbH
Current assignee: Bodenseewerk Geratetechnik GmbH
Priority date: 1979-06-01
Filing date: 1980-05-14
Publication date: 1981-02-11
Also published as: FR2458051B1; FR2458051A1; DE2922414C2; DE2922414A1; GB2054145B

Abstract

Heading-attitude reference apparatus for determining the heading and the attitude of a vehicle comprises inertial (20,22,24) responsive to rotary speeds about vehicle-fixed input axes; two accelerometers (42,44) having vehicle-fixed axes parallel to the input axes of two of the rotary speed sensors; and computers (58, 66-76) to which signals from the rotary speed sensors and from the accelerometers are supplied and which provide signals representing parameters which provide a heading angle in an earth- fixed coordinate system. The computer provides signals representing the time derivatives of two elements of the last line of a directional cosine matrix in terms of the rotary speed which are integrated with respect to time to form a signal representing the third element of the last line of the cosine matrix from the other two elements. A signal is formed from the signals representing the three elements and from the rotary speed signals, and this signal is integrated with respect to time to provide a signal representing the heading angle. <IMAGE>

Description

SPECIFICATION Heading-attitude Reference Apparatus This invention relates to a heading-attitude reference apparatus for determining the heading and the attitude of a vehicle, the apparatus being of the type comprising three rotary speed sensors responsive to rotary speeds about three mutually perpendicular vehicle-fixed input axes; two accelerometers having vehicle-fixed, mutually perpendicular input axes which are parallel to the input axes of two of the rotary speed sensors; and a computer, to which the signals from the rotary speed sensors and from the accelerometers are supplied and which provides signals representing parameters for transformation between a vehicle-fixed coordinate system and an earth-fixed coordinate system, and provides heading angle in the earth-fixed coordinate system.

A heading-attitude reference unit for land vehicles is known from German Offenlegungsschrift 2 741 274 wherein a gyro having a substantially horizontal spin axis is gimbal-mounted with two degrees of freedom. A position sensor and a torquer are located on an axis parallel to the transverse axis of the vehicle. A further position sensor and a torquer are located on an axis parallel to the vertical axis of the vehicie. The signal of the position sensor on the first axis is amplified and applied, crosswise, to the torquer on the second axis, and, vice-versa, the signal of the position sensor on the second axis is amplified and applied to the torquer on the first axis. Thereby the gyro is restrained electrically to a position of rest. The signals supplied to the torquers are proportional to the angular speeds about the transverse and vertical axes, respectively, of the vehicle.Furthermore two accelerometers are provided, the input axes of which are parallel to the transverse axis and parallel to the longitudinal axis, respectively of the vehicle. These accelerometers supply accelerometer signals to a computer, which derives attitude information, i.e. pitch and roll angles of the vehicle, therefrom. From these pitch and roll angles, the computer determines the elements of the directional cosine matrix. With the elements of the directional cosine matrix thus obtained, the rotary speed signals provided by the gyro and compensated for the rotation of the earth are linearily combined to provide signals, which represent the time derivatives C,1 and C2, of elements of the directional cosine matrix.These latter signals are integrated with respect to time, and the ratio of the integrals provides the inverse tangent of the true heading angle, i.e. the heading angle referenced to an earth-fixed coordinate system.

In this prior art apparatus, pitch and roll angles are derived from the accelerometer signals. It is assumed that the accelerometer signals are caused only by components of the acceleration due to gravity. This condition is not met, if the vehicle is accelerated over ground.

Furthermore a navigational instrument is known (British Patent Application No. 2,020,019), wherein the position ofa vehicle is derived from the heading and the speed measured by means of a speed sensor. Also there an inertial measuring unit comprising an electrically-restrained, two-axis gyro and a pair of accelerometers is provided. The signals from the inertial measuring unit are applied to a transformation parameter computer which is adapted to compute transformation parameters for the transformation from a vehicle-fixed coordinate system into an earth-fixed coordinate system. From the transformation parameters, those components of the accelerometer signals are determined which are due to gravity, whereby translatory acceleration signals representing the pure Newtonian acceleration of the vehicle are obtained.These translatory acceleration signals are integrated with respect to time and thus provide inertial speed signals. The inertial speed signals together with the speed signals from the speed sensor are applied to an optimizing filter, which therefrom generates an optimized speed signal referenced to vehicle-fixed coordinates. This optimized speed signal is transformed by means of the transformation parameters into an earth-fixed coordinate system. A position computer computes therefrom the position of the vehicle.

Furthermore Patent Application No. 2,020,019 provides for transformation parameter corrective signals being applied to the transformation parameter computer.

In Patent Application No. 2,020,019 the attitude angles are determined in the manner of German Offenlegungsschrift 2 741 274. The attitude angles and the transformation parameters, respectively, are however, corrected by the optimizing filter-in a manner not shown there -also Newtonian accelerations being taken into account. Such a solution, however, requires a high order optimizing filter which is rather complex.

It is an object of the invention to provide a heading-attitude reference apparatus of the type defined above such that it provides the heading and the transformation parameters for transformation from a vehicle fixed coordinate system into an earth fixed coordinate system, without being affected by Newtonian accelerations of the vehicle with respect to ground.

According to the invention, apparatus of the type defined above is characteristed in that (a) the computer provides signals representing C31=C32wzFC33a)yF C32 C33GE)Z C3X;)Z wherein C3r"C32, C33 are the elements of the last line of the directional cosine matrix, C31,C32 are the associated time derivatives, coXF is the rotary speed about an input axis xF in the vehicle-fixed coordinate system, and a)F is the rotary speed about the second input axis yF in the vehicle-fixed coordinate system, d)ZF is the rotary speed about the third input axis zF in the vehicle-fixed coordinate system, (b) the signals C31 and C32 are integrated by the computer with respect to time (c) the computer forms a signal

from the signal C31 and C32 thus obtained, (d) the signals C31,C32 and C33 are in turn fed back to the computer for providing C'31 and C32 from the rotary speed signals, (e) a signal

is formed from the signal C31,C32,C33thus obtained and from the rotary speed signals d)ZF and Xt)yF F and (f) this signal is integrated with respect to time to provide a signal representing the heading angle in the earth-fixed coordinate system.

Thus, according to the invention the transformation parameters are derived exclusively from the rotary speeds about the vehicle-fixed coordinate axis, thus independent of the influence of Newtonian accelerations. The initial values C32(O) and Cs,(O) for the integration can be determined in accordance with the teaching of German Offenlegungsschrift 2 741 274, for example.

In practice, the transformation parameters and the heading angle thus obtained. exhibit a drift, which result in inadmissible errors, if the gyros do not meet stringent requirements. In order to construct such a heading-attitude reference unit with gyros on which less stringent requirements are made, and which therefore are cheaper, a preferred embodiment of the invention provides that (g) the signals C32 and C31, each multiplied by the acceleration g due to gravity are superposed on the signals AyF and AxF respectively, from the accelerometers, (h) additional signals are superposed on each signal from an accelerometer, (i) the signals from the accelerometers with the respective superposed signals are integrated with respect to time to provide inertial speed signals, (j) at least one speed sensor is provided, which provides a speed signal indicative of the component of the vehicle speed in the direction of the input axis of an accelerometer, (k) the inertial speed signal derived from said accelerometer is superposed with opposite sign on the speed signal from the speed sensor to provide a difference signal (I) the difference signal multiplied by a factor KV(t), which is a function of time, provides said additional signal superposed on the signal from the accelerometer, and (m) the difference signal with a factor KC(t), which is a function of time, is superposed on the C32 -and C31 signals, respectively.

Furthermore the heading may be updated in that (n) the signal M representing the direction of the magnetic field of the earth is superposed with opposite sign on a heading signal #, obtained by integration of the I signal to provide a difference signal (+ M) ^ (o) a first signal AM with the same and a second signal A with opposite sign are superposed on this difference signal, (p) the first signal M is provided by integration with respect to time of the signals thus superposed multiplied by a first factor K,(t) which is a function of time, (q) the superposed signals multiplied by a second factor K2(t), which is function of time, are integrated with respect time to provide an estimated value Dz of the heading drift, and (r) the superposed signals multiplied by a third factor, which is a function of time, are superposed on said estimated value Dz of the gyro drift and are integrated with respect to time to provide said second signal A, the signal representing the estimated value D2 of the heading drift being, at the same time, superposed on the 0 signal prior to the integration thereof.

An embodiment of the invention will now be described, by way-of example, with reference to the accompanying drawings, in which: Fig. 1 is a block diagram and illustrates the overall system of a heading-attitude reference apparatus according to the invention, Fig. 2 is a schematic-perspective illustration of the vehicle and illustrates the construction and arrangement of the various sensors, Fig. 3 illustrates the relative positions of the vehicle-fixed and earth-fixed coordinate systems, Fig. 4 shows the details of an inertial measuring unit, Fig. 5 shows the set-up of the computer for the transformation parameters, Fig. 6 shows the set-up of the computer for generating the heading angle signal, Fig. 7 shows the set-up of the computer for estimating the heading drift, Fig. 8 shows the set-up of a filter for measuring a directional cosine from the accelerometer signal and the speed signal, as also used in Figure 5, and Fig. 9 shows a simplified version of the computer of Figure 6.

The navigation system comprises magnetic field sensors 10,12,14 for the components GxF, GyFt GzF of the magnetic field of the earth. The magnetic field sensors are so-cailed "fluxgates". These magnetic field sensors 10,12 and 14 are mounted on the vehicle 16 (Fig. 2) such that they respond to the components of the magnetic field of the earth along the longitudinal axis xF, the transverse axis yF and the vertical axis zF of the vehicle, respectively. Thus they provide the components of the magnetic field of the earth in a vehicle-fixed coordinate system. In Fig. 1, the magnetic field sensors 10,12,14 are represented by the block 1 8.

Furthermore sensors for the rotary speeds wxF, wvF, wzF about the vehicle-fixed coordinate axes yF, ZF are provided. These are illustrated in the block diagram of Fig. 1 as sensors 20, 22 and 24. In practice the sensors 22 and 24 are a two-axis rate gyro 26 (Fig. 2). This rate gyro 26 is of the type illustrated in Fig. 4 or Fig. 5. In the position illustrated of the rate gyro 26, the spin axis H is parallel to the longitudinal axis xF of the vehicle. Its two axes 28 and 30 are parallel to the transverse axis yF and the vertical axis ZF of the vehicle, respectively.The third sensor 20 comprises a rotary acceleration meter 32 the output signal of which is applied to an integrator 34 (Fig. 6). The rate gyro 26 is mounted for rotation about its input axis 28 parallel to the transverse axis of the vehicle in a vehicle-fixed frame or intermediate housing 36. It may be rotated by a servomotor 38 from an operational position "northing", with which the spin axis H is vertical, through 900 into the operational position "headingattitude reference unit". The movement of the servomotor is monitored by an angle sensor.

Furthermore two vehicle-fixed accelerometers 42 and 44 are provided. The input axis 46 of the accelerometer 42 is parallel to the longitudinal axis xF of the vehicle. The input axis 48 of the accelerometer 44 is parallel to the transverse axis yF of the vehicle.

The sensors 20, 22, 24 and 42, 44 together define an "inertial measuring unit" 50.

A speed sensor 52 is provided as additional sensor and measures, as indicated in Fig. 2, the speed of the vehicle 1 6 in the direction of the longitudinal axis of the vehicle.

The measurements are made in a vehicle-fixed coordinate system with the coordinate axes xF, yF and zF. For navigation, however, the heading angle and the vehicle speed are required in an earth-fixed coordinate system with the coordinates x (north), yR (east) and zR (vertical). The relation between the two coordinate systems can be seen from Fig. 3. The vertical plane 54 of the longitudinal axis xF of the vehicle forms the true heading angle # with the xRzR plane. The longitudinal axis xF of the vehicle is inclined by the pitch angle with respect to the intersection 56 of the plane 54 and the horizontal xRxR plane. The coordinate axes yF and zF are rotated through the roll angle about the vehicle longitudinal axis thus located.

A vector measured in the vehicle-fixed coordinate system is transformed into the earth-fixed coordinate system by means of a "directional cosine matrix"

In order to save space, "sin" has been abbreviated as "s", and "cos" has been abbreviated as "c".

The attitude angles v, g and P are related to the elements of the directional cosine matrix by the following relations (2) v=-arc sin C C21 (3) r,=arc tan 11 C32 (4) (p=arc tan C33 The acceleration due to gravity is represented in the earth-fixed coordinate system by a vector

gR [ I while the rotation of the earth is represented by a vector

(6) #R = #c # o # -#s wherein (7) sin 4) and (8) #c=#Ecos # if #E is the rotary speed of the earth, and cP is geographic latitude.

The signals GXF, GyF and GZF from the magnetic field sensors 10, 12, 14 (block 1 8) are applied to a computer unit 58, to which signal elements C31, C32, C33 are also applied, which are obtained in a manner still to be described. In addition the computer unit 58 receives a signal DEV, which represents the distortion of the magnetic field lines (deviation) caused by the vehicle. The computer unit 58 provides a signal which represents the magnetic heading angle #M between the intersection 56 in Fig.

3 and the north direction as defined by the direction of the magnetic lines of force (magnetic north).

The signals wxF, WyF, wzF from the sensors 20, 22, 24, which represent the rotary speeds relative to inertial space in a vehicle-fixed coordinate system are compensated at summing points 60, 62, 64 for the components of the rotation of the earth and for the transport rate, i.e. the rotary speed due to the movement of the vehicle on the surface of the earth, by signals Tx, Ty, Tz, which yields the rotary speeds #xF, s9yF, w2F of the vehicle relative to earth.

These signals Ct)xF, cl)yF, cszF together with the acceleration signals A F AyF from the accelerometers 42 and 44 respectively, and the speed signal vxF from the speed sensor 52 are supplied to a computer unit 68. This computer unit 68 provides the elements C31, C32, C33 of the directional cosine matrix as well as inertial speed signals VjxF and V##F.

The computer unit 66 receives the elements C31, C32, C33 of the directional cosine matrix CRr from the computer unit 68, the trigonometric functions sin and cos of the true heading angle and, for taking the transport rate into account, the components vRx and vRy of the vehicle speed in the earth-fixed coordinate system.

A computer unit 70 receives the elements C31, C32, C33 from the computer unit 68, and the compensated rotary speeds WxF #yF, ZF, and the magnetic heading angle #M from the computer unit 58. It provides therefrom the trigonometric functions sin # and cos # of the true heading angle . These functions are applied to the computer unit 66 and to a computer unit 72.

The computer unit 72 receives, as mentioned above, the trigonometric functions sin # and cos from the computer unit 70, as well as the element C31=sin v of the directional cosine matrix From the computer unit 68, and a corrected speed signal. It provides therefrom the components VXR, vyfl, VZR of the vehicle speed in the earth-fixed coordinate system. The horizontal speed components vxR, vyR are supplied, as mentioned before, to the computer unit 66. In addition, the components VXR, vyR and VZR are supplied to a position computer 74, to which also a reference altitude hr is applied.The position computer 74 provides the position of the vehicle in terms of geographic longitude A and latitude # and of the altitude h.

The speed signal vxF from the speed sensor 52 is applied to a computer unit 76, to which also the inertial speed signals vyF and vlxF are applied. The computer unit 76 provides an estimated,, value AVXF of the error of the speed signal vxF. The speed signal vxF is corrected for this estimated error AvxF at a summing point 78. The speed signal thus corrected is supplied to the computer unit 72, as mentioned hereinbefore.

The computer unit 68 is illustrated in detail in Fig. 16.

As illustrated by block 80, the computer unit 68 provides signals (9) C31=C32wFzC33a)yF (10) C32=C33c)x C31zF from the elements of the last line of the directional cosine matrix fed back in the manner to be described hereinbelowand the rotary speeds #xF, #yF, #zF from the sensors 20,22,24 and compensated at 60, 62, 64.

The signals C31 and C32 thus obtained are integrated with respect to time by integrators 82 and 84, respectively, in order to get the signals C31 and C32. The initial values C31(O) and C32 for the integration may be obtained as described in German Offenlegungsschrift 2 741 274 (British Patent Application No. 14,781/78 Serial No.

As the matrix CRF is orthonormal, (11) C312+C322+C332=1 or

i.e. the third element C33 results automatically from the two other ones. As illustrated by block 86, a signal representing the element C33 is generated in accordance with equation (12) from the output signals of the integrators 82 and 84. Thus the elements C31 C32 and C33 are available for the signal processing in block 80 in accordance with equations (9) and (10). The elements C31, C32 and C33 are supplied to the computer units 66, 70 and, partly, 72, as illustrated in Fig. 1.

A signal

is generated in computer unit 70 from the signals C31, C32 and C33 thus obtained and from the rotary speeds a)yF and WzF, as indicated by block 88. Computer unit 70 is shown in detail in Fig. 17. This signal is the time derivative of the "inertial" heading angle, as it is derived from the measured angular speeds b )XF, )yF, fj)ZF, An estimated value Dz of the heading drift is superposed on this signal ski, at a summing point 90, said estimated value being obtained in a manner to be described hereinbelow.The corrected heading angle rate signal is integrated with respect to time by means of an integrator 92 and provides the true heading angle # in the earth-fixed coordinate system. The heading angle g is applied to a sine function generator 94 and a cosine function generator 96 to provide signals sin qlr and cos #, which are supplied to the computer units 66 and 72, as illustrated in Fig. 1.

The elements C31, C32, C33 of the directional cosine matrix as obtained solely from the angular speeds wxF, WyF and t)ZF are subjected to a drift. Such a drift may result in intolerable errors, unless very high demands on the gyro and on the other components are made. For this reason these values are backed making use of the signals Axe and Aye from the accelerometers 42,44 and of the signal vxrfrom the speed sensor 52.

The signal C31 from the output of the integrator 82 is multiplied by the acceleration g due to gravity, which is represented by block 98, and is superposed at a summing point 100 on the signal AXF from the accelerometer 42. A further signal is applied to the summing point 100, as will be described hereinbelow. The signal AXF of the accelerometer 42 and the superposed signals at the summing point 100 are integrated with respect to time by an integrator 102. Thus an inertial speed signal v,,F, i.e.

speed signal which is derived from the acceleration signal At taking the component of the acceleration due to gravity into account, is provided and is supplied to the computer unit 76 (Fig. 1). The speed signal vxF from the speed sensor 52 is superposed on the inertial speed signal v,xF with opposite sign at a summing point 104 to provide a difference signal. The difference signal multiplied by a timedependent factor KV(t), which is represented by block 106, is said further signal superposed at summing point 100 on the signal AXF of the accelerometer. Furthermore, the difference signal multiplied by a time-dependent factor KC(t), which is represented by block 108, is superposed at a summing point 110 on the C31 signal.The signal formed at the summing point 110 is integrated by the integrator 82.

In similar manner the signal C32 from the output of the integrator 84 multiplied by the acceleration g due to gravity, which is represented by block 112, is superposed in the summing point 114 on the signal AyF from the accelerometer 44. A further signal still to be explained is applied also to the summing point. The signal AyF of the accelerometer 44 and the superposed signals at the summing point 114 are integrated with respect to time by an integrator 116. Thus also an inertial speed signal v,yF is obtained, which is supplied, like the signal v,xF, to the computer unit 76.A speed signal vyF from a transverse speed sensor may be superposed with opposite sign on the inertial speed signal v,yF at a summing point 11 8. With a vehicle of the type in question here, it can, however, be assumed that vyF=O. The signal thus obtained multiplied by a time-dependent factor Ko(t), which is represented by block 120, is further superposed on the signal AyF from the accelerometer 44 at the summing point 124. The signal formed at the summing point 124 is integrated by the integrator 84.

In order to take the centrifugal acceleration into account, an additional signal may be applied to the summing point, which signal is obtained by multiplying the signal vxFfrom the speed sensor 52 by the angular speed WzF about the vertical axis zF, as has been illustrated by block 126.

A filter which provides a signal, which represents the element C31 of the directional cosine matrix CFF, from the accelerometer signal AXF of the accelerometer 42 and from the speed signal vxr of the speed sensor 52 is illustrated in detail in Fig. 8.

As can be seen from Fig. 1, magnetic field responsive means 1 8 and 58 for determining the direction of the magnetic field of the earth in an earth-fixed coordinate system and for generating a signal representing this direction are provided. A signal Dz from the computer unit 58 is superposed to the qi signal with opposite sign at the summation point prior to the integration with respect to time by the integrator 92. This signal represents an estimated value of the heading drift derived by means of the magnetic field of the earth. The generation of this signal Dz is illustrated in Fig. 7.

The signal #M representing the direction of the magnetic field of the earth (magnetic heading angle is superposed with opposite sign on an inertial heading signal #, obtained by integration of the rsignal to provide a difference signal (#l-#M). A first signal ARM of the same sign and a second signal A#, of opposite sign are superposed on this difference signal # M at a summing point 128. The first signal ##M is an estimated value of the error of the magnetic heading angle, and the second signal is an estimated value of the error of the inertial heading signal, as will be explained hereinbelow.

The first signal ARM is obtained by integration with respect to time of the signals thus superposed at summing point 128 with a first, time-dependent factor K1(t) by means of an integrator 132.

Furthermore, the superposed signals are multiplied by a second time-dependent factor K2(t), which is represented by the block 134, and are then integrated with respect to time by means of an integrator 136. A signal which represents an estimated value Dz of the heading drift will then appear at the output of the integrator 136. Eventually the signals superposed at the summing point 128 are multiplied by a third time-dependent factor K3(t), which is represented by block 138. The product signal thus obtained and the above-mentioned signal representing the estimated value Dz of the heading drift are superposed at a summing point 140.The signals thus superposed at the summing point 140 are integrated by means of an integrator 142 and provide the above-mentioned second signal A1, which is applied to the summing point 128 like the first signal SlrM.

The signal obtained from the integrator 136 and representing the estimated value Dz of the heading drift is, at the same time, superposed with opposite sign on the #l-signal at the summing point 90 (Fig. 6) prior to the integration of this signal.

The arrangement described operates as follows: According to equation (1), C31=-sin v. Thus, the component g sin v is subtracted from the signal AXF of the accelerometer at the summing point 100 of Figs. 5 and 8, said component being due to the acceleration due to gravity. Thus a signal is provided which represents Newton's acceleration in the direction of the longitudinal axis xF of the vehicle. This signal is integrated by the integrator 102, whereby a signal vixF is provided, thus the inertially measured speed. This inertial speed v,xF is compared to the speed vxF measured by the speed sensor 52. A deviation of these values from each other may be due to an error of the accelerometer or to a wrong C3,.The deviation is applied to the summing point 100 with a predetermined, time-dependent factor kV(t) and thereby corrects the signal AxF of the accelerometer 42. In addition it is integrated with a second, predetermined, time-dependent factor K(t) and corrects the value of C31. A controlled state will then be achieved in which the deviation between vxF and v,xF become zero, whereby the correct value of C3, will occur. By appropriate selection of the factors care can be taken that, taking the typical systematic errors of the sensors into account, an optimum value of C31 will be obtained.

In the case of Fig. 5, the deviation between vixF and vxF causes correction of C31 prior to the integration.

If # designates (at first unknown) true heading angle, which is not falsified by drift or the like, the following is valid: (14) (15) if A4i and ##M are the errors of the inertial and magnetic heading angles, respectively. This yields (16) #l-#M=##l-##M.

With the filter of Fig.18, it has been assumed that the difference # M has the form (17) + M=aO+a1t i.e. is composed of a constant component a0 and a linearly increasing component a1t. Furthermore, it has been assumed that AIM is constant, thus (18) A4iM=O Therefrom follows: (19) M= On the other hand is per definitionem ##l=Dz, the heading drift of the inertially measured heading angle, which therefore corresponds to the coefficient a,. These relations are simulated in the filter of Fig. 7.

At the summing point 128 the difference of estimated values A and ARM is connected in opposition to the difference #l-#M, which has been received from the circuit of Fig.17, the initial estimated values A1(O) and ARM (0) being selected in some reasonable way as also the initial value Dz(o). A deviation of the differences is multiplied by K1(t) and integrated by the integrator 132 and causes variation of AROMA Furthermore, the deviation at the summing point 128 with the factor K2(t) causesa variation of the estimated value through the integrator 136.With zero deviation (#l-#M)- (##l-##M), this estimated value would cause a linear increase of the signal at summing point 128 through the integrator 142, the deviation remaining zero only if Dz is equal to the actual heading drift.

In addition, the deviation is applied directly to the integrator 142 with the factor K3(t), whereby A is additionally corrected by a constant value. It should be noted that K1(t), K2(t) and K3(t) are functions declining with time towards zero. In the stationary state, the deviation (#l-#M)-(##l-##M) at the summing point 128 is zero, and D'2 is equal to the heading drift çk, This signal l)z is tapped and corrects in in Fig. 6.

A simplified modification is illustrated in Fig. 9, in which corresponding elements bear the same reference numerals as in Fig. 5.

In the modified embodiment of Fig. 9 the inertial heading angle # is connected in opposition to the magnetic heading angle at the summing point 144. The difference is, on one hand, with a factor K1 superposed on the , signal at the summing point 146. On the other hand, the difference is integrated by means of the integrator 146, and the integral with a factor K2 is applied to the #, signal at the summing point 146.

Claims

1. Heading attitude reference apparatus for determining the heading and the attitude of a vehicle, comprising three rotary speed sensors responsive to rotary speeds about three mutually perpendicular vehicle-fixed input axes; two accelerometers having vehicle-fixed, mutually perpendicular input axes which are parallel to the input axes of two of the rotary speed sensors; and a computer, to which the signals from the rotary speed sensors and from the accelerometers are supplied and which provides signals representing parameters for transformation between a vehicle-fixed coordinate system and an earth-fixed coordinate system, and provides heading angle in the earth-fixed coordinate system; wherein (a) the computer provides signals representing C3l=C32wzFC33a)VF C32=C33zFC31 WzF wherein C C C33 are elements of the last line of a directional cosine matrix, C31, C32 are the associated time derivatives, WxF is the rotary speed about an input axis xF in the vehicle-fixed coordinate system, WyF is the rotary speed about a second input axis yF in the vehicle-fixed coordinate system, and R)ZF is the rotary speed about the third input axis if in the vehicle-fixed coordinate system, (b) the computer integrates the signals C31 and C32 with respect to time, (c) the computer forms a signal representing

from the signals C31 and C32, (d) the signals representing C31, C32 and C33 are fed back to the computer for providing C31 and C32 from the rotary speed signals, (e) a signal representing

is formed from the signals representing C31, C32, 33 and from the rotary speed signals #zF and #yF, and (f) this signal is integrated with respect to time to provide a signal representing the heading angle in the earth-fixed coordinate system.

2. Apparatus as claimed in Claim 1, wherein (g) the signals representing C32 and C31, each multiplied by the acceleration g due to gravity, are superposed on the signals AyF and AXF, respectively, from the accelerometers, (h) an additional signal is superposed on each signal from an accelerometer, (i) the computer integrates the signals from the accelerometers with the respective superposed signals with respect to time to provide inertial speed signals, (j) a speed sensor provides a speed signal indicative of the component of the vehicle speed in the direction of the input axis of an accelerometer, (k) the inertial speed signal derived from the accelerometer is superposed with opposite sign on the speed signal from the speed sensor to provide a difference signal, (I) the difference signal multiplied by a factor KV(t), which is a function of time, provides said additional signal superposed on the signal from the accelerometer, and (,n)the difference signal with a factor KC(t), which is a function of time, is superposed on the C32-C31 signals, respectively.

3. Apparatus as claimed in Claim 1 or Claim 2, including magnetic field responsive means for determining the direction M of the magnetic field of the earth in the earth-fixed coordinate system and for providing a signal representing this direction; and means to superpose a signal Dz with opposite sign on the , signal prior to the integration with respect to time, said signal Dz representing an estimated value of the heading drift derived by means of the direction of the magnetic of the earth.

4. Apparatus as claimed in Claim 3, wherein (n) the signal M representing the direction of the magnetic field of the earth is superposed with opposite sign on a heading signal 9 obtained by integration of the #, signal to provide a difference signal (# M)t (o) a first signal M with the same sign and a second signal A with opposite sign are superposed on this difference signal, (p) the first signal M is provided by integration with respect to time of the signals thus superposed multiplied by a first factor K1 (t) which is a function of time, (q) the superposed signals multiplied by a second factor K,2(t), which is a function of time, are integrated with respect to time to provide an estimated value D2 of the heading drift, and (r) the superposed signals multiplied by a third factor, which is a function of time, are superposed on said estimated value Dz of the gyro drift and are integrated,with respect to time to provide said second signal 4i, the signal representing the estimated value Dz of the heading drift being also superposed on the #, signal prior of the integration thereof.

5. Apparatus as claimed in Claim 1 and substantially as hereinbefore described with reference to the accompanying drawings.