GB2124372A - Gyro apparatus for determination of the north direction - Google Patents

Abstract

Apparatus for determination of the north direction by means of a gyro which is influenced by the rotation of the earth comprises a two-axis gyro (10), the spin axis (z<K>) of which is substantially vertical and which has two input axes (x,<K>, y<K>) perpendicular to each other and to the spin axis. A position pick-off and a torquer are provided at each input axis, and the pick-off signal associated with each input axis is applied through an amplifier (12, 14) crosswise to the torquer of the respective other input axis to restrain the spin axis of the gyro electrically. A rotation device (18) continuously rotates the gyro about the spin axis. Integrating circuitry (78, 82; 80, 84) integrates the amplified pick-off signals supplied to the torquers to derive signals to be stored in a memory (86), the integrating circuitry being reset automatically to zero after formation of the integral and transfer thereof to the memory. Signal evaluation circuitry (98, 100), to which the stored signals are applied, forms an azimuth signal compensated for gyro errors and indicating the north direction. <IMAGE>

Description

SPECIFICATION Gyro apparatus for determination of the north direction This invention relates to apparatus for the determination of the north direction by means of a gyro which is influenced by the rotation of the earth.

From German Auslegeschrift 27 41 274 an apparatus for automatic determination of the north direction is known, in which a two-axis gyro with a substantially vertical spin axis is provided. A position pick-off and a torquer are provided on each of the two input axes of the gyro, which input axes are mutually orthogonal. The signal of each position pick-off associated with an input axis is applied crosswise to the torquer of the respective other input axis to restrain the gyro electrically with its spin axis vertical. The signals fed to the two torquers are at the same time applied to a north deviation computer, which generates, from the ratio of the signals, a signal representing the deviation of an apparatus-fixed reference direction from the north direction.When the reference direction is defined by one of the two input axes, then the north deviation angle is equal to the inverse tangent of the ratio of the torques exerted by the two torquers due to the applied signals. Herein it is assumed that the spin axis of the gyro is exactly vertical.

From German Auslegeschrift 27 41 274 it is also known to provide a pair of accelerometers which are mounted in a fixed positional relationship with the gyro housing and having axes of sensitivity which are mutually orthogonal and which extend parallel to the two input axes of the gyro. A computer is provided to which both the signals supplied to the torquers of the gyro and the accelerometer signals are supplied. This computer calculates the real north deviation angle by taking into consideration the inclination of the spin axis of the gyro relative to the vertical determined by the accelerometers. Thus it is possible to determine the north deviation angle or the azimuth angle relative to north even when the spin axis of the gyro is not exactly vertical.

The signal of the two-axis gyro is subjected to systematic errors caused, for example, by assembly tolerances, unbalance or anisoelasticity. To compensate for these systematic errors, if possible, it is known to rotate the gyro by 1 800 about a horizontal axis and/or about a vertical axis and to store the signals obtained in the two positions, respectively, and supplied to the torquers; see German Auslegeschrift 29 03 282 (British Patent Specification No. 2 040 450). By forming sums and differences of the signals, stored signals for determining thenorth deviation may be obtained, in which certain systematic errors of the gyro are compensated for.

Apparatus for the determination of the north direction, in which a gyro with a substantially horizontal spin axis is rotatable about a vertical axis into a 0 -1 position, a 900-position and a 180 - position, is furthermore described in German Offenlegungsschrift 29 22412 (British Patent Specification No. 2 049 931) and in German Offenlegungsschrift 30 1 9 372.

The prior art apparatuses supply high accuracy in an absolutely calm environment, if no outside translatory or rotatory interferences act on the gyro housing. Such measuring conditions are found, for example, when the apparatus is operating on a support. However, when the apparatus is used in disturbed environment, for example in a vehicle, the torquer signals measured in the different positions will contain disturbing components caused by the disturbing movements of the gyro housing about its axes. These components cause limitation of the accuracy of the north deviation or azimuth angle even when the substantial systematic errors of the gyro are compensated for.

It is an object of the present invention to eliminate or to reduce such measuring errors which are caused by disturbing movements of the gyro housing caused by environmental influences while compensation for gyro errors obtained in the prior art is maintained.

According to the invention, apparatus for determination of the north direction by means of a gyro which is influenced by the rotation of the earth comprises a two-axis gyro, the spin axis of which is substantially vertical and which has two input axes perpendicular to each other and to the spin axis, wherein a position pick-off and a torquer are provided at each input axis, and the pick-off signal of the position pick-off associated with each input axis is applied through an amplifier crosswise to the torquer of the respective other input axis to restrain the spin axis of the gyro electrically; rotation means for continuously rotating the gyro about the spin axis; memory means; integrating means for integrating the amplified pick-off signals supplied to the torquers to derive signals to be stored in the memory means, the integrating means being arranged to be reset automatically to zero after formation of the integral and transfer thereof to the memory means; and signal evaluation means to which the stored signals are applied, for forming an azimuth signal compensated for gyro errors and indicating the north direction.

Thus the gyro is not displaced stepwise to different angular positions in which a stationary measurement is then made. Instead, the gyro is rotated continuously at a constant angular rate through 3600. The integrals of the signals applied to the torquers are measured. The integration is carried out from a predetermined angular position of the gyro to the next, the integrals being stored and then the integrating means being reset to zero. It can be shown that by this integration the compensation for the systematic gyro errors is maintained and also the influence of outside interference is reduced.

Embodiments 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 of a first embodiment of apparatus for determination of the north direction with a gyro having a vertical spin axis and with integrating, memory and signal processing means, Fig. 2 is a block diagram of the signal processing means of the apparatus of Fig. 1, Fig. 3 is a block diagram, similar to Fig. 1, of another embodiment of apparatus for determination of the north direction, Fig. 4 illustrates vectorial measuring equations for the apparatus of Fig. 3, Fig. 5 shows schematically first computer means of the apparatus of Fig. 3 for computation of the parameter vectors, Fig. 6 shows schematically second computer means of the apparatus of Fig. 3 for computation of the output quantities, and Fig. 7 shows a modification of the second computer means of Fig. 6.

Referring to Fig. 1, a gyro housing 10 contains a two-axis gyro of the type shown in Fig. 1 of German Auslegeschrift 29 03 282. The gyro housing defines a coordinate system xK, yK and zK; the gyro-fixed coordinate system. The coordinate axis zK coincides with the spin axis of the gyro. The spin vector is designated by H. The coordinate axis xK coincides with a first input axis of the gyro, and the coordinate axis yK coincides with a second input axis of the gyro. In a manner not described herein in detail, a first position pick-off and a first torquer are located on the first input axis xK. A second position pick-off and a second torquer are located on the second input axis yK. The pick-off signal of the first position pick-off is applied through an amplifier 12 to the second torquer.Correspondingly, the pick-off signal of the second position pick-off is applied through an amplifier 14 to the first torquer. The amplified pick-off signals, which are applied to the torquers, are designated by Tx and Ty, respectively.

The gyro housing 10 is rotatably mounted about the spin axis ZK in a housing 1 6. The housing 1 6 is for example vehicle-fixed. The coordinate axis ZK is essentially vertical. The housing 1 6 defines a coordinate system with the coordinate axes xe, yG and ZG, in the "0 -position" illustrated in fig. 1 the coordinate axis xK of the gyro fixed coordinate system is parallel to the coordinate axis xG of the housing fixed coordinate system. Correspondingly, the coordinate axis yK, the second input axis of the gyro, is parallel to the housing-fixed coordinate axis yG, and the coordinate axis zK is parallel to the coordinate axis za.

The angle between the housing-fixed coordinate axis xO and the north direction is designated by W (O).

The gyro housing 10 is rotatable with a constant angular rate o about the gyro spin axis, that is the axis ZK, by a motor 1 8. The position of the gyro housing 10 relative to the housing 1 6 is picked-off by a position sensor 20.

The signal Tx supplied to the first torquer is integrated by an integrator 22. The signal Ty supplied to the second torquer is integrated by an integrator 24. The integrators 22 and 24 may be reset to zero through reset inputs 26 and 28, respectively.

The output of the integrator 22 is applied to a memory 30 and a memory 32 in parallel. The output signal from the integrator 22 is transferred to the memory 30 by a signal at an input 34 and to the memory 32 by a signal at an input 36. The output from the integrator 24 is applied to a memory 38 and to a memory 40 in parallel. The output signal from the integrator 24 is applied to a memory 38 and a signal at an input 42 and to the memory 40 by a signal at an input 44. Switching logic illustrated in fig. 1 as a switch contact is controlled by the position sensor 20 such that it supplies pulses to an output 48 and output 50, respectively, int he 1 800-position of the gyro housing 10 and in the 3600-position after a complete turn. The output 48 is connected to the input 34 and to the input 42. The output 50 is connected to the input 36 and to the input 44.Furthermore, the two outputs 48 and 50 are connected through an OR-gate 52. The output of the OR-gate 52 engages the reset inputs 26 and 28 of the integrators 22 and 24 through a delay circuit 54.

The signals stored in the memories 30, 32, 38 and 40 are applied to a signal processing circuit 56 which is illustrated in detail in fig. 2. The signal processing circuit 56 supplies the azimuth angle w (O) between the housing-fixed coordinate axis xG and the north direction. Furthermore, the signal processing circuit supplies the sine and the cosine of this azimuth angle.

The described circuit operates as follows: The gyro is continuously rotated with the gyro housing 10 and the input axes xK and yK about the spin axis ZK from the illustrated 0 -position through 360 into a 3600-position by the rotating device.

The signals Tx and Ty supplied to the first and to the second torquer are integrated by integrating means in the form of the integrators 22 and 24. A pulse appears at the output 48 of the switching logic 46 when passing the 1800-position, which pulse causes the signals from the integrator 22 to be transferred to the memory 30 and the signals from the integrator 24 to be transferred to the memory 38. The integrators 22 and 24 are reset to zero through the OR-gate 52 with a short delay caused by the delay element 54. The signals supplied to the torquers are integrated once again, until the 360or position is reached. Then a pulse appears at the output 50 of the switching logic 46, which pulse causes the signals from the integrator 22 to be transferred to the memory 32 and the signals from the integrator 24 to be transferred the memory 40. The same pulse then causes, through the OR-gate 52 and the delay element 54, that the integrators 22 and 24 are reset.

Thus, when this revolution is completed, integral values lx (180), lx (360), (180) and --1, (360) are stored in the memories 30, 32, 38 and 40. These signals are applied to the signal processing circuit 56 which is illustrated in detail in fig. 2 as a block diagram.

The integrals are, as mentioned, picked-off and transferred when the gyro is in a 1 800-position and in a 3600-position angularly offset with respect thereto by 1800. The signal evaluation means contains means 58 for forming the difference of the integrals lx (180) and lx (360) of the amplified pickoff signals supplied to the first torquer located on input axis xK, which integrals are picked-off in the 1 800-position and in the 360 -position, respectively. Thereby, a first difference signal A lx is generated.

Furthermore, means 60 is provided for forming the difference of the integrals -ly (180) and -ly, (360) of the amplified pick-off signals supplied to the second torquer located on the second input axis yK, the integrals being picked-off in the 1 800-position and in the 3600-position, respectively. Thereby, a second difference signal å Iy is generated.Furthermore, the signal evaluation means contains means 62 for multiplying the first difference signal A lx by a factor 1w Kx =---- 4 Qc and means 64 for multiplying the second difference signal Iy by a factor 1w K, =-- 4 Qc wherein a; is, as mentioned, the angular rate with which the gyro is rotated by the rotating means 18, and Qc is the horizontal component of the rotary speed of the earth.Furthermore, the signal evaluation means 56 contains summing means 66, by which the second difference signal Aly multiplied by a correction factor cx, illustrated by block 68, and by the factor Ky is added to the first difference signal Alx multiplied by the factor Kx, for forming a signal representing the cosine of the azimuth angle cos # (O) to the north, as well as summing means 70, by which the first difference signal Alx multiplied by a correction factor cy, illustrated by block 72, and by the factor Kx is added to the second difference signal Aly multiplied by the factor Ky, for forming a signal representing the sine of the azimuth angle sin qlr (0) to the north.By forming the inverse cosine and the inverse sine, respectively, the azimuth angle Sl (0) may be obtained from the cosine and the sine, respectively, as illustrated by blocks 74 and 76.

In the arrangement of fig. 3 the construction of the gyro with the rotating device and the position sensor is the same as in fig. 1, and corresponding elements are designated by the same numerals as in that figure.

The integrating means contains a first and a second voltage-to-frequency converter 78 and 80, respectively, by which the signals supplied to the first and the second, respectively, of said torquers may be converted to pulse frequencies proportional thereto. The pulse frequencies from the first and the second voltage-to-frequency converters 78 and 80, respectively, are applied to a first and a second counter, respectively, 82 and 84, respectively. Memory means is designated by 86. Means 88 and 90 are provided for transferring the counts to the memory means 86. The position sensor 20 responds to the rotation of the gyro by the rotating device 1 8.The position sensor is connected to a logic 92 controlled by the position sensor and by which the means 88, 90 for transferring the counts may be controlled such that the counts are transferred to the memory means 86 in the 1 800-position and in the 3600-position. The counters 82 and 84 may be reset to zero by pulses at reset inputs 94, 96. These reset inputs 94 and 96 represent "means for resetting the counters to zero". These means for resetting the counters may be controlled by the logic 92 such that the counters 82 and 84 are reset to zero after the transfer of the counts to the memory means 86 in the predetermined angular positions of the gyro.

The gyro is continuously rotatable by the rotating means 18 from a 0 -position by a complete revolution forwards into a 3600-position and then back to the 0 -position. The signals from the integrating means 78, 82 and 80, 84, respectively, are picked-off in different angular positions of the gyro when the gyro is rotating forwards as well as backwards, while resetting the integration means, and transferred to the memory means 86.In the illustrated embodiment the signals from the integrating means 78, 82 and 80, 84 respectively, are picked-off in the 900-position, the 1 800-position, in the 2700-position and the 3600-position and back in the 270 -position, the 1 800-position, the 900- position and the 0 -position while the gyro is rotating forwards and backwards, and transferred to the memory means 86.Thus after such a cycle the memory means each contain eight stored integrals, that is T T T 3 T 3 3 T 3 Iy (-,0), Iy 24 , -), l (-T, Iy 4 (T, -T) Iy (-T, T) l (-, -T), 4 2 4 4 2 4 4 2 4 T T T T T T 3 T ly 4 ) ly (0,-) and lx (-,O), lx (, ), lx (-T, -), 42 4 4 2 4 4 2 3 3 T 3 T T T lx (T, -T), lx (-T, T), lx (-, -T), lx 4), lx (0-) 4 4 2 4 42 4 wherein T is the time which the gyro needs for a revolution from the 0 -position into the 360 -position.

These integrals may be combined to form vectors (Zx and zy). First computer means 98 is provided by means of which parameter vectors xx and xy are formed according to the method of least squares in a way to be described hereinbelow. Second computer means 100 calculates the various output quantities, namely the azimuth angle W (0), the geographic latitude, the gyro drifts and the pitch and roll angles, from the components of the parameter vectors. Pitch and roll angles are fed back to the first computer means 98 as illustrated by lines 102 and 104. Furthermore, the angular rate # and known error parameters (mass unbalance coefficient m, anisoelasticity coefficient n and quadrature coefficient q) are applied to the first computer means 98.

The measuring vectors zz and zy are related to the parameter vectors Xx and xy by the matrix equation illustrated in fig. 4.

As can be seen from fig. 5, the first computer means 98 forms the parameter vectors xx and xy according to the relation A (1) xx = (MxTMx)-1 MxT . Zx A (2) xy = (MyTMy)-1. MyT.Zy wherein Zx is the first measuring vector formed by the eight stored integrals of the signals supplied to the first torquer, zy is the second measuring vector formed by the eight stored integrals of the signals supplied to the second torquer, Mx is the measuring matrix associated with the measuring vector and depending on the angular rate a; with which the gyro is rotated about the spin axis by the rotating device, My is the measuring matrix corresponding to the measuring vector by and likewise depending on the angular rate a;; with which the gyro is rotated about the spin axis by the rotating device, Xx is a first parameter vector optimally calculated according to the method of least squares, with the components a1x = C11 #c a2x = C31 #s a3x=C12 #c a4x = 32 S ty.x By in which Cik are the elements of the direction cosine matrix for the transformation from a housing-fixed to a earth-fixed coordinate system, Qc is the horizontal component and #s is the vertical component of the rotary speed of the earth, &alpha; ;yx is the angle of the assembly errors of the gyro and By is the zero drift of the gyro about the second input axis and A xy is a second parameter vector optimally calculated according to the method of least squares, with the components a1y=C11 #c a2y = C31 Qs a3y = C12 Qc a4y = C32 Qs axy Bx in which axy is the angle of the assembly errors of the gyro and Bx is the zero drift of the gyro about the first input axis.

Therein Mx My are the measuring matrices illustrated in fig. 4.

Output quantities are formed from the components of the parameter vectors A xx and A Xy by the second computer means 1 00. As can be seen from fig. 6, the second computer means 100 comprises means 106 for forming quantities A a.

from components of the parameter vectors according to the relation A 1 A A (3) a. = - (aix + aly).

2 The parameter vectors xx and xy are supplied to these means 106. The means 106 directly supply the drifts BxBy of the gyro about the two input axes.

Furthermore, means 108 is provided for forming the azimuth angle to north according to the relation

This angle is provided at an output 110. Equation (4) is ambiguous. It requires the input of the quadrant or a greater azimuth pre-orientation, respectively, so that the angle pi is located between 900 and +900. The second computer means 100 comprises means 112 to which the angle + and the quantities A A a1 , a3 are supplied and which determines the horizontal component Qc of the rotary speed of the earth according to the relation

(depending on the quadrant).Means 114 is provided for determining the geographic latitude according to the relation #c (6) cos = #E #c (7) # = are cos #E (8) sin (t'= (1 - cos#) wherein #E is the rotary speed of the earth. The means 114 supply the geographic latitude , which is provided at an output 1 16, and sin cp.

Means 118 to which sin # is supplied determine the pitch angle v according to the relation

Means 120 determines the roll angle 9? according to the relation

Pitch and roll angles p and 9?, respectively, are provided at outputs 122 and 124.

If the quadrant of the north direction is not known and no pre-alignement is made respectively, the geographic latitude Q, has to be input into the second computer means 100 as illustrated in fig. 7.

in fig. 7 numeral 106A designates the means forming the quantities A a, from the components A aix and A a1y of the parameter vector and at the same time supplying the gyro drifts Bx and By. These means correspond to the means 106 in fig. 6. Means 126 is however provided, in the embodiment according to fig. 7, to which means, in addition to the quantities A a1, the geographic latitude is supplied. Therefrom means 126 forms the cosine and the sine of the azimuth angle # to the north according to the relation A a1 (11) cos = = #c A a3 (12) sin #c .

These quantities appear at an output 128 with, if required, the azimuth angle # itself, which can unambiguously be determined from cos qlr and sin # in any quadrant. Furthermore, means 130 is provided supplying the pitch and roll angles v and , respectively, according to the relations A a2 (13) p- #s A a4 (14) 9? - Qs As illustrated in fig. 5, the variances of the parameter vectors may be determined in further modification of the invention.For this purpose, means 132 is provided for determining vectors Wx and wy according to the relations A (15) Wx = ZX - MxXx A (16) Wy = Zy Myxya The vectors Wx and wry thus obtained are transferred to means 134. Therefrom, these means form the variances of the vectors A xx and A Xy according to the relations

Thus, a measure of the accuracy of the measurement made is available. With the calculated variances of the parameter vectors optimally determined, the corresponding variances of the output quantities determined according to fig. 6 also may be determined.

It is possible to compensate further gyro-specific measuring errors (mass unbalance m, quadrature drift q, anisoelasticity n). For this purpose the stored components of the measuring vectors of both measuring axes are corrected by corresponding terms depending on the acceleration due to gravity before optimal values for the parameter vectors are determined. For compensation, the pitch and roll angles are required. The parameter vectors and the output quantities are calculated iteratively in that the parameter vectors and therefrom the output quantities, at first, are determined without compensation. With the values found for the pitch and roll angles, the parameter vectors are then determined again with compensation of the mentioned gyro parameters, as illustrated by the lines 102 and 104. This results in improved values of the output quantities.This procedure may be repeated until sufficient accuracy in the determination of the output quantities is obtained. This is indicated by the variances.

The signal processing described so far assumes that the gyro drifts Bx and By about the input axes xK and yK of the gyro are constant during the entire measuring procedure. This cannot always be assumed in practice. To consider variations of the gyro drifts during the measuring procedure gyro drift being functions of the time in the form (19) BX(t) = BoX + Bix t + B2X . t2 (20) BV(t) = Boy + B1Y t + B2Y . t2 may be considered instead of the constant gyro drifts Bx and By.

Thereby, compared with the measuring matrix according to fig. 4, the following measuring matrices.

result wherein Mx and My are the measuring matrices of fig. 4.

The associated parameter vectors are

For the rest and signal processing remains substantially the same as described above.

Claims (15)

1. Apparatus for determination of the north direction by means of a gyro which is influenced by the rotation of the earth, comprising a two-axis gyro, the spin axis of which is substantially vertical and which has two input axes perpendicular to each other and to the spin axis, wherein a position pick-off and a torquer are provided at each input axis, and the pick-off signal of the position pick-off associated with each input axis is applied through an amplifier crosswise to the torquer of the respective other input axis to restrain the spin axis of the gyro electrically; rotation means for continuously rotating the gyro about the spin axis; memory means; integrating means for integrating the amplified pick-off signals supplied to the torquers to derive signals to be stored in the memory means, the integrating means being arranged to be reset automatically to zero after formation of the integral and transfer thereof to the memory means; and signal evaluation means to which the stored signals are applied, for forming an azimuth signal compensated for gyro errors and indicating the north direction.

2. Apparatus as claimed in Claim 1, wherein the integrals are picked-off and transferred when the gyro is in a 1800-position and in a 3600-position; and wherein the signal evaluation means comprises means for forming the difference of the integrals of the amplified pick-off signals supplied to a first torquer for producing a first difference signal, the integrals being picked-off in the 1 8O0-position and in the 36O0-position, and means for forming the difference of the integrals of the amplified pick-off signals supplied to the second torquer for producing a second difference signal, the integrals being picked-off in the 1800-position and in the 3600-position.

3. Apparatus as claimed in Claim 2, wherein the signal evaluation means comprises means for multiplying the first difference by a factor 1 co Kx= = , 4 Qc and means for multiplying the second difference signal by a factor 1 a; K -, 4 52c wherein c9 is the angular rate with which the gyro is rotated by the rotating means, and Qc is the horizontal component of the rotary speed of the earth.

4. Apparatus as claimed in Claim 3, wherein the signal evaluation means further comprises summing means by which the second difference signal multiplied by a correction factor cx and by the factor Ky is added to the first difference signal multiplied by the factor Kx for forming a signal representing the cosine of the azimuth angle relative to north; the summing means by which the first difference signal multiplied by a correction factor cy and by the factor Kx is added to the second difference signal multiplied by the factor Ky, for forming a signal representing the sine of the azimuth angle relative to north.

5. Apparatus as claimed in Claim 1, wherein the integrating means comprises first and second voltage-to-frequency converters, by which the signals supplied to the first and the second of the torquers, respectively, are converted to pulse frequencies proportional thereto; first and second counters to which the pulse frequencies of the first and second voltage-to-frequency converters respectively, are applied; means for transferring the counts to the memory means; means for resetting the counters to zero; a position sensor responsive to the rotation of the gyro by the rotating device; and a logic circuit controlled by the position sensor by which the means for transferring the counts and the means for resetting the counters are controlled such that, in predetermined angular positions of the gyro, the counts are transferred to the memory means and then the counters are reset to zero.

6. Apparatus as claimed in any preceding claim, wherein the gyro is continuously rotatable by the rotating device from a 0 -position through a complete revolution forwards into a 3600-position and then backwards into the 0 -position.

7. Apparatus as claimed in Claim 6, wherein the signals from the integrating means are picked-off at various angular positions of the gyro, when the gyro is rotating forwards and backwards and the integration means is reset, and the picked-off signals are transferred to the memory means.

8. Apparatus as claimed in Claim 7, wherein the signals from the integrating means are picked-off and transferred to the memory means in the 900-position, the 1800-position, the 2700-position and the 360 -position while the gyro is rotating forwards, and in the 2700-position, the 1800-position, the 900-position and the 0 -position while the gyro is rotating backwards.

9. Apparatus as claimed in Claim 8, wherein the signal evaluation means comprises first computer means for forming A xx = (MxTMx)-1 MxT.Zx A xy = (My'My)! My'.Zy wherein Zx is the first measuring vector formed by the eight stored integrals of the signals supplied to the first torquer, Zy is the second measuring vector formed by the eight stored integrals of the signals supplied to the second torquer, Mx is the measuring matrix associated with the measuring vectorzx and depending on the angular rate # with which the gyro is rotated about the spin axis by the rotation means, My is the measuring matrix corresponding to the measuring vector and likewise depending on the angular rate w with which the gyro is rotated about the spin axis by the rotation means, A xy is a first parameter optimally calculated according to the method of least squares, with the components a1x = C11 #c a2x = C31 Qs a3x = C12 #c a4x = C32 Qs ayx By in which 0ik are the elements of the direction cosine matrix for the transformation from a housing-fixed to a earth-fixed coordinate system, Qc is the horizontal component and Q, is the vertical component of the rotary speed of the earth, ayx is the angle of the assembly errors of the gyro and By is the zero drift of the gyro about the second input axis and A Xy is a second parameter vector optimally calculated according to the method of least squares, with the components a1v= C" Qc a2y = C31 #5 a3y = C,2 #c any = C32 #s axy Bx in which axy is the angle of the assembly errors of the gyro and Bx is the zero drift of the gyro about the first input axis; and second computer means for forming output quantities from the components of the parameter vectors.

10. Apparatus as claimed in Claim 9, wherein the second computer means comprises means fqr forming A 1 A A S = - (aix + ajy) 2 wherei= 1,2,3,4.

11. Apparatus as claimed in Claim 10, wherein the second computer means comprises means for forming the azimuth angle glr relative to north according to the relation A a3 # = - arc tan A a1

12. Apparatus as claimed in Claim 11 , wherein the second computer means comprises means for determining the horizontal component Qe of the rotary speed of the earth according to the relationship A A a, a3 #c = or cos# sin and means for determining the geographic latitude # according to the relationship #c = = arccos #E wherein QE is the rotary speed of the earth.

13. Apparatus as claimed in Claim 12, wherein the second computer means comprise means for determining the pitch angle r according to the relationship A a2 V = - #Esin# and means for determining the roll angle P according to the relationship A a3 #= #Esin#

14.Apparatus as claimed in Claim 8, wherein the signal evaluation means comprises first computer means for forming XX=(MXT, Mx)-1 Mx'. ,.Zy xy=(MyT, M,)-l MyT.@ Zy wherein Zx is the first measuring vector formed by the eight stored integrals of the signals supplied to the first torquer, Zy is the second measuring vector formed by the eight stored integrals of the signals supplied to the second torquer, Mx is the measuring matrix associated with the measuring vector Zx and depending on the angular rate o with which the gyro is rotated about the spin axis by the rotating means, My is the measuring matrix corresponding to the measuring vector and likewise depending on the angular rate a;; with which the gyro is rotated about the spin axis by the rotating means, xx is a first parameter vector optimally calculated according to the method of least squares, with the components 51x = C11 #c a2X = C32 Qs a3x = C12 Qe anx = C32 #s &alpha;;yx Boy Boy Bly B2y in which Cik are the elements of the direction cosine matrix for the transformation from a housing-fixed to an earth-fixed coordinate system, #c is the horizontal component and #s is the vertical component of the rotary speed of the earth, ayx is the angle of the assembly errors of the gyro and Biy are the coefficients of a function By(t) = Boy + B1Y . t + B2e . t2 by which zero drift of the gyro about the second input axis is approached, which zero drift varies with time, and xy is a second parameter vector optimally calculated according to the method of least squares, with the components a1y = C11 Qc a2y = C31 Qs a3y = C12 #c a4y = C32 #s axy Box B1x B2x in which axy is the angle of the assembly errors of the gyro and BiX are coefficients of a function BX(t) = Box + BaX. t + B2X . t2 by which the zero drift of the gyro about the first input axis is approached, which zero drift varies with time; ; and second computer means for forming output quantities from the components of the parameter vectors.

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