Apparatus for the automatic determination of a vehicle position

• US 4,321,678 A
• Filed: 12/07/1979
• Issued: 03/23/1982
• Est. Priority Date: 09/14/1977
• Status: Expired due to Term

• Current Assignee: Bodenseewerk Geratetechnik GmbH 777 Uberlingen/Bodensee W Germany
• Original Assignee: Bodenseewerk Gerätetechnik Gmbh
• Inventors: Krogmann, Uwe
• Primary Examiner(s): Smith, Jerry
• Application Number:
  US06/101,736
• Time in Patent Office: 837 Days
• Field of Search: 364/434, 364/450, 364/453, 364/556, 364/559, 364/571, 33/318, 33/320, 33/324, 33/326
• US Class Current: 701/220
• CPC Class Codes: G01C 19/38 with north-seeking action by other than magnetic means, e.g. gyrocompasses using earth's rotation
• CPC Class Codes: G01C 21/185 for gravity
• CPC Class Codes: G01C 21/188 for accumulated errors, e.g. by coupling inertial systems with absolute positioning systems

Abstract

The position of a vehicle is derived from vehicle speed and heading. A two-axis electrically restrained gyro, the spin axis of which is parallel to the vehicle vertical axis, serves at first to determine the north direction with stationary vehicle. The attitude of the vehicle about the longitudinal and transverse axes is measured by means of a pair of vehicle-fixed accelerometers. True north direction is derived from the signals of the accelerometers and of the gyro. Subsequently the gyro is rotated through 90° about one input axis and serves as heading-attitude reference during the mission. The rotary speed about a third axis perpendicular to the input axes of the gyro is measured by means of a rotary acceleration meter the output of which is applied to an integrator. During the mission, the attitude parameters of the vehicle are computed continuously from the initial attitude parameters and the rotary speeds. An estimated value of the gyro drift is obtained in a filter by comparison with a magnetic heading and is taken into account. The speed signal from a vehicle speed sensor and inertial speed signals which are derived from the acceleration signals are applied to a filter which provides an estimated value of the error of the speed signal. The speed signal is corrected for this estimated value. The corrected speed signal is resolved into components in accordance with the attitude parameters. The position of the vehicle is derived from these speed components by integration.

Claims

1. Navigational instrument for a vehicle, wherein the north direction is determined by means of a gyro, comprising:

a two-axis gyro having a spin axis, a first and a second input axis,

a first angle pick-off and a first torquer on the first input axis,

a second angle pick-off and a second torquer on the second input axis,

first amplifier means for applying the amplified angle signal from the first angle pick-off to the second torquer, second amplifier means for applying the amplified angle signal from the second angle pick-off to the first torquer, and

signal processing means, to which the amplified angle signals are applied,

characterized in that;

(a) the gyro with the angle pick-offs and the torquers is arranged in an intermediate housing,

(b) the intermediate housing is mounted for rotation about an axis of rotation parallel to one input axis through 90°

from a first position with substantially vertical spin axis into a second position,

(c) a pair of vehicle-fixed accelerometers is arranged with its input axes parallel to the transverse and longitudinal axes, respectively, of the vehicle, said accelerometers producing accelerometer signals A_x^F, A_y^F respectively,

(d) the signal processing means comprise

(d₁) first computer means for providing initial vehicle attitude signals from the amplified angle signals with stationary vehicle and said first position of the intermediate housing, and

(d₂) second computer means for continuously providing vehicle attitude signals representing the attitude of the moving vehicle in an earth-fixed coordinate system from said initial vehicle attitude signals, said angle signals from the angle pick-offs and said accelerometer signals with the second position of the intermediate housing.

2. Navigational instrument as set forth in claim 1, characterized by

(a) speed measuring means for generating a speed signal representing the longitudinal speed of the vehicle in a vehicle-fixed coordinate system,

(b) a coordinate transformation computer to which vehicle attitude signals and said speed signal are supplied for providing speed component signals indicative of the components of the vehicle speed in an earth-fixed coordinate system, and

(c) integrating computer means, to which the speed component signals are supplied for computing the vehicle position in the earth-fixed coordinate system.

3. Navigational instrument as set forth in claim 1, characterized in that said first computer means comprise

(a) matrix element forming means connected to receive the acceleration signals A_x^F, A_y^F of the accelerometers and for forming therefrom estimated values of the elements C₃₁ and C₃₂ of the directional cosine matrix for the transformation from a vehicle-fixed coordinate system (x^F, y^F, z^F) into an earth-fixed coordinate system (x^R, y^R, z^R) in accordance with the relation

4. Navigational instrument as set forth in claim 3, characterized by

(a) the signals supplied to the torquers from the angle pick-offs, which signals are proportional to the rotary speeds, and the acceleration signals from the accelerometers constituting sensor signals,

(b) a pair of filters, each filter comprises three integrators, three multipliers and a summing point, each filter being connected to receive a respective sensor signal,

(c) as to each of the filters:

(1) each of the three integrators produces a respective output signal,

(2) the summing point receives three input signals and produces an output signal therefrom,

(3) a first of the integrators is connected to receive the respective sensor signal and integrates it with respect to time to produce one of said three input signals,

(4) two of the multipliers being connected to receive the output signal of the summing point and to respectively multiply that output signal by factors of K₁ (t) and K_o (t) to produce respective output signals,

(5) a second of the integrators is set to the instantaneous value of the respective sensor signal at the beginning of each cycle and is connected to receive the output signal of the K₁ (t) multiplier to produce an output signal,

(6) a third of the multipliers is connected to receive the output signal of said second integrator, to multiply that signal by the time t and to feed it back to the summing point with reversed sign as a second of said three input signals,

(7) a third of the integrators is connected to receive the output signal of the K_o (t) multiplier and to produce an output signal which is fed to the summing point with reversed sign as the third of said three input signals.

5. Navigational instrument as set forth in claim 4, characterized in that the third integrator is reset to zero at the beginning of each cycle.

6. Navigational instrument as set forth in claim 3, characterized by

(a) the signals supplied to the torquers from the angle pick-offs, which signals are proportional to the rotary speeds, and the acceleration signals from the accelerometers constituting sensor signals, said sensor signals being detected in cycles with each cycle having a duration T,

(b) a pair of filters, each filter comprises clock means for producing clock pulses with intervals therebetween, five multipliers, two dividers, four delay loops, eight adders and an analog reset integrator,

(c) as to each of the filters:

(1) said integrator is connected to receive the respective sensor signal and resets it with respect to time and produces an increment pulse y_i each time the resulting signal reaches a predetermined level and is reset to zero thereafter,

(2) a first of the adders is connected to receive said increment pulses, said adder adding each increment pulse y_i to the sum y_i of the preceding increment pulses, which sum has been delayed by one clock interval through one of said delay loops,

(3) a second of the adders is connected to receive said clock pulses, said second adder adding each clock pulse to the sum i-1 of the preceding clock pulses, which sum i-1 has been delayed by one clock interval through another of said delay loops, to produce a sum signal n,

(4) a first of the multipliers is connected to the first and second adders to multiply the sum y_i of the increment pulse numbers by the sum i of the clock pulses to produce a pulse signal iy_i,

(5) a third of the adders is connected to said first multiplier for adding each pulse signal iy_i to the sum of the preceding signals iy_i, which sum iy_i has been delayed by one clock interval through another of the delay loops, to produce a pulse signal Σ

iy_i,

(6) a fourth of the adders is connected to the third adder to add the pulse signal Σ

iy_i by itself to produce a pulse signal 2Σ

iy_i,

(7) a fifth of the adders is connected to receive the sum y_i of the increment pulses, said fifth adder adding said sum y_i to the sum y_i of the preceding y_i signals which have been delayed through another of the delay loops to produce a signal Σ

y_i,

(8) a sixth of the adders is connected to receive the signal n representing the sum of the clock pulses and to increase it by one to produce a signal (n+1),

(9) a second of the multipliers being connected to receive and multiply the signals Σ

y_i and (n+1) to produce a signal (n+1)Σ

y_i,

(10) a seventh of the adders being connected to receive the signals 2Σ

y_i and (n+1)Σ

y_i and to subtract the latter from the former to produce a signal 2Σ

y_i -(n+1)Σ

y_i,

(11) a third of the multipliers being connected to receive the signal n representing the sum of the clock pulses and to multiply that signal by itself to produce a signal n²,

(12) an eighth of the adders being connected to receive the signal n² and to reduce it by one to produce a signal (n² -1),

(13) a fourth of the multipliers being connected to receive the signal n representing the sum of the clock pulses and to multiply it by the duration T of the cycle to produce a signal nT,

(14) a fifth of the multipliers being connected to receive the signals (n² -1) and nT and to multiply those signals with each other, to produce a signal nT(n² -1),

(15) a first of the dividers being connected to receive the signal nT(n² -1) and to divide it by a given number x to produce a signal nT(n² -1)/x,

(16) a second of the dividers being connected to receive the signals from the seventh adder and the first divider and to divide the signal from the former by the signal from the latter to produce a quotient signal.

7. Navigation instrument as set forth in claim 6, characterized in that each of the filters further comprises

(17) a fifth delay loop,

(18) a ninth adder connected to receive said quotient signal of the second divider after a predetermined number of clock pulses, said ninth adder adding the quotient signal so received to the sum of the quotient signals previously received, which sum has been delayed by one clock interval by the fifth delay loop, to produce a sum output signal,

(19) a third divider connected to receive said sum output signal and to divide it by the total number of quotient signals.

8. Heading-attitude reference unit for determining the heading and the attitude of a vehicle, comprising:

rotary speed sensor means, which are arranged to respond to the rotary speeds about three mutually perpendicular, vehicle-fixed input axes, said means including at least two rotary speed sensors producing sensor signals, two accelerometers having vehicle-fixed, mutually perpendicular input axes which respectively are parallel to the input axes of the two rotary speed sensors, said accelerometers producing sensor signals, and computer means, to which the signals from the rotary speed sensors and from the accelerometers are supplied for providing signals representing transformation parameters between a vehicle-fixed coordinate system and an earth fixed coordinate system, as well as the heading angle in the earth-fixed coordinate system, said computer means comprising

(a) means for receiving said sensor signals and providing signals

space="preserve" listing-type="equation">(4) C.sub.31 =C.sub.32 ω

.sub.z.sup.F -C.sub.33 ω

.sub.y.sup.F

space="preserve" listing-type="equation">(5) C.sub.32 =C.sub.33 ω

.sub.x.sup.F -C.sub.31 ω

.sub.z.sup.F

wherein

C₃₁,C₃₂,C₃₃ are the elements of the last line of the directional cosine matrix,

C₃₁,C₃₂ are the associated time derivatives,

ω

_x^F is the rotary speed about an input axis x^F in the vehicle-fixed coordinate system,

ω

_y^F is the rotary speed about the second input axis y^F in the vehicle-fixed coordinate system, and

ω

_z^F is the rotary speed about the third input axis z^F in the vehicle-fixed coordinate system,

(b) means connected to receive the signals C₃₁ and C₃₂ and integrate the received signals with respect to time to provide signals C₃₁ and C₃₂, respectively,

(c) means connected to receive the signals C₃₁ and C₃₂ from the integration means and for producing a signal ##EQU44## (d) from the signal C₃₁ and C₃₂ thus obtained, means connected to feed the signals C₃₁,C₃₂ and C₃₃ back to the computer for providing C₃₁ and C₃₂ from the rotary speed signals,

(e) means connected to receive the signals C₃₁,C₃₂ and C₃₃ and the rotary speed signals ω

_z^F and ω

_y^F and for producing a signal ##EQU45## therefrom, and (f) means connected to receive this signal ψ

_I and integrating it with respect to time to provide a signal ψ

_I representing the heading angle in the earth-fixed coordinate system.

9. Heading-attitude reference unit as set forth in claim 8 further characterized by

(g) means connected to receive the signals C₃₂ and C₃₁ and to multiply each by the acceleration g due to gravity to produce signals gC₃₂ and gC₃₁,

(h) means connected to receive the signals gC₃₂ and gC₃₁ and the signals A_y^F and A_x^F, respectively, from the accelerometers and to superpose the former and the latter respectively,

(i) means connected to receive the signals from the accelerometers and for superposing additional signals to each signal from an accelerometer,

(j) means connected to receive the signals from the last mentioned means and for integrating those signals with respect to time to provide inertial speed signals,

(k) at least one speed sensor, which provides a speed signal indicative of the component of the vehicle speed in the direction of the input axis of an accelerometer,

(l) means connected to receive the inertial speed signal with opposite sign to the speed signal from the speed sensor and for superposing the two to provide a difference signal,

(m) means connected to receive said difference signal and to multiply it by a factor K_v (t), which is a function of time, to provide said additional signal superposed to the signal from the accelerometer, and

(n) means connected to receive said difference signal and the C₃₂ and C₃₁ signals, multiplying the difference signal with a factor K_c (t), which is a function of time, and superposing the resulting product to the C₃₂ - and C₃₁ -signals, respectively.

10. Heading-attitude reference unit as set forth in claim 8, and further characterized by

(a) magnetic field responsive means for determining the direction ψ

_M of the magnetic field of the earth in the earth fixed coordinate system and for providing a signal representing this direction, and

(b) means connected to receive the ψ

_I signal prior to the integration with respect to time and for superposing thereon a signal D_z with opposite sign to produce a signal D_z ψ

_I, said signal D_z representing an estimated value of the heading drift derived by means of the direction of the magnetic field of the earth, the last mentioned integrating means then integrating this D_z ψ

_I signal.

11. Heading-attitude reference unit as set forth in claim 10, and further characterized by

(a) means connected to receive signal ψ

_M and the signal ψ

_I and producing a difference signal (ψ

_I -ψ

_M) therefrom,

(b) means connected to receive the difference signal (ψ

_I -ψ

_M) and for superposing a first signal Δ

ψ

_M with the same and a second signal Δ

ψ

_I with opposite sign to this difference signal,

(c) means connected to receive the last mentioned superposed signals and for multiplying them by a factor K₁ (t), which is a function of time, and for integrating the product with respect to time to provide said first signal Δ

ψ

_M which is then supplied to the last mentioned superposing means,

(d) means connected to receive the last mentioned superposed signals and for multiplying them by a second factor K₂ (t), which is function of time, and for integrating the product with respect to time to produce a signal representing signal estimated value D_z of the heading drift, and

(e) means connected to receive the last mentioned superposed signals and the D_z signal and for multiplying the said superposed signals with a third factor, which is a function of time, for superposing the product to said D_z signal and for integrating the latter superposed signal with respect to time to provide said second signal Δ

ψ

_I which is then supplied to said last mentioned superposing means.

12. Instrument for the automatic determination of the north direction by means of a gyro affected by the rotation of the earth, wherein

the gyro is a two-axis gyro the spin axis of which is substantially vertical,

the position of the gyro is picked off by position pick-offs and torquer is arranged to exert erecting torques on the gyro to keep the spin axis of the gyro vertical,

a position pick-off and a torquer is provided on each of two mutually perpendicular input axes of the gyro,

the signal from each position pick-off associated with one input axis is supplied crosswise to the torquer on the respective input axis to restrain the spin axis of the gyro to the vertical, and

the signal supplied to the two torquers are, at the same time, applied to a north deviation computer, which provides, from the ratio of the signals, a signal representing the deviation of an instrument-fixed reference direction from north,

characterized in that

(a) the north deviation computer comprises a memory for storing the two signals T_y.sup.(1), T_x.sup.(1) supplied to the torquers,

(b) the gyro is arranged to be rotated through 180°

about a horizontal axis by a servomotor, after the signals have been stored,

(c) the signals T_y.sup.(2), T_x.sup.(2) then supplied to the torquers are supplied to the north deviation computer,

(d) the north deviation computer comprises means for providing signals

space="preserve" listing-type="equation">Δ

T.sub.y =T.sub.y.sup.(1) -T.sub.y.sup.(2) (

     8)

space="preserve" listing-type="equation">Σ

T.sub.x =T.sub.x.sup.(1) +T.sub.x.sup.(2) (

     9)

wherein ##EQU46## M_x.sup.(1) and M_x.sup.(2) are the stored signals and the signals applied after the 180°

-rotation to that torquer, which acts about one axis,

M_y.sup.(1) and M_y.sup.(2) are the stored signals and the signals applied after the 180°

-rotation to the other torquer, and

H is the rotary momentum of the gyro, and

(e) the north deviation computer comprises means for providing a signal ##EQU47## as north deviation signal.

13. Instrument as set forth in claim 12, characterized in that

(a) the housing of the gyro is mounted for rotation and is rotatable through 90°

about one of the input axes of the gyro by means of a servomotor, whereby the gyro can be used as heading reference unit, and

(b) the same servomotor is arranged to optionally rotate the housing through 180°

.

14. Instrument for the automatic determination of the north direction by means of a gyro affected by the rotation of the earth, wherein

the gyro is a two-axis gyro the spin axis of which is substantially vertical,

the position of the gyro is picked off by position pick-offs and a torquer is arranged to exert erecting torquers on the gyro ot keep the spin axis of the gyro vertical,

a position pick-off and a torquer is provided on each of two mutually perpendicular input axes of the gyro,

the signal from each position pick-off associated with one input axis is supplied crosswise to the torquer on the respective input axis to restrain the spin axis of the gyro to the vertical, and

the signals supplied to the two torquers are, at the same time, applied to a north deviation computer, which provides, from the ratio of the signals, a signal representing the deviation of an instrument-fixed reference direction from north,

characterized in that

(a) the north deviating computer comprises a memory for storing the two signals T_y.sup.(1), T_x.sup.(1) supplied to the torquers,

(b) the gyro is arranged to be rotated by a servomotor through 180°

about a vertical axis coinciding with the gyro spin axis, after these signals T_x.sup.(1), T_y.sup.(1) have been stored,

(c) the signals T_x.sup.(3), T_y.sup.(3) then supplied to the torquers are applied to the north deviataion computer,

(d) the north deviation computer comprises means for providing signals

space="preserve" listing-type="equation">DT.sub.x =T.sub.x.sup.(1) -T.sub.x.sup.(3) (

     15)

space="preserve" listing-type="equation">DT.sub.y =T.sub.y.sup.(3) -T.sub.y.sup.(1) (

     16)

wherein ##EQU48## M_x.sup.(1) and M_x.sup.(3) are the stored signals and the signals applied to one torquer, after the 180°

-rotation,

M_y.sup.(1) and M_y.sup.(2) are the stored signal and the signals applied to the other torquer after the 180°

rotation, and

H is the rotary momentum of the gyro, and

(e) the north deviation computer comprises means for providing a signal ##EQU49## as north deviation signal.

15. Instrument for the automatic determination of the north direction by means of a gyro affected by the rotation of the earth, wherein the gyro is a two-axis gyro the spin axis of which is substantially vertical,

the position of the gyro is picked off by position pick-offs and a torquer is arranged to exert erecting torques on the gyro to keep the spin axis of the gyro vertical,

a position pick-off and a torquer is provided on each of two mutually perpendicular input axes of the gyro, the signal from each position pick-off associated with one input axis is supplied crosswise to the torquer on the respective input axis to restrain the spin axis of the gyro to the vertical, and

the signals supplied to the two torquers are, at the same time, applied to a north deviation computer, which provides, from the ratio of the signals, a signal representing the deviation of an instrument-fixed reference direction from north,

characterized in that

(a) the north deviation computer comprises a memory for storing the two signals T_y.sup.(1), T_x.sup.(1) supplied to the torquers,

(b) the gyro is arranged to be rotated by a first servomotor through 180°

about a vertical axis coinciding with the gyro spin axis, after these signals T_x.sup.(1), T_y.sup.(1) have been stored

(c) the north deviation computer comprises a memory for storing the two signals T_x.sup.(3), T_y.sup.(3) then supplied to the torquers,

(d) the first servomotor is controlled to rotate the gyro housing through 180°

back into the initial position, after these latter signals have been stored,

(e) the gyro is arranged to be rotated by a second servomotor through 180°

about a horizontal input axis, after it has been rotated back by the first servomotor,

(f) the signals T_x.sup.(2), T_y.sup.(2) then supplied to the torquers are applied to the north deviation computer,

(g) the north deviation computer comprises means for providing signals

space="preserve" listing-type="equation">Σ

T.sub.xc =T.sub.x.sup.(2) -T.sub.x.sup.(3) (

     22)

space="preserve" listing-type="equation">Δ

T.sub.y =T.sub.y.sup.(1) -T.sub.y.sup.(2) (

     23)

wherein

T_x.sup.(2) is the signal which, after rotation of the gyro about said one input axis y, is applied to that torquer which acts on the other input axis,

T_x.sup.(3) is the signal which, after rotation of the gyro about the vertical axis, is supplied to that torquer which acts on said other input axis,

T_y.sup.(1) is the signal which, in the initial position prior to the rotation about the vertical axis, is supplied to that torquer which acts about said one input axis,

T_y.sup.(2) is the signal which, after the rotation about the horizontal axis, is supplied to that torquer which acts on said one input axis, and

(h) the north deviation computer comprises means for providing a signal ##EQU50## as north deviation signal.

16. Instrument as set forth in claim 15, characterized in that the north deviation computer comprises means for providing signals

17. Instrument as set forth in claim 15, characterized in that

(a) the north deviation computer comprises an additional memory for for storing the two signals T_x.sup.(2), T_y.sup.(2) supplied to the torquers, after the gyro has been rotated back about the vertical axis into its initial position,

(b) the north deviation computer comprises means for providing the mean values

18. An instrument for the automatic determination of the north direction by means of a gyroscope affected by the rotation of the earth and having a spin axis, said instrument having an instrument-fixed reference direction and being characterized by:

gyroscope positioning means secured to said gyroscope and mounting said gyroscope for pivotal movement about two input axes at right angles to each other, said positioning means positioning said spin axis substantially vertical, said positioning means including first and second torquers associated with said input axes respectively for controlling the angular position of the spin axis about the input axes respectively, first and second pickups associated with said input axes respectively for producing signals indicative of the angular position of the spin axis about the input axes respectively, and control means including said pickups and said torquers for actuating the torquer associated with one axis in response to the signal from the pickup associated with the other axis and for actuating the torquer associated with said other axis in response to the signal from the pickup associated with said one axis; and

a north direction computer, connected to said control means to receive said signals, for producing from the ratio of the signals a north deviation signal indicative of the deviation from north of the instrument-fixed reference direction, said north deviation computer providing a signal ##EQU51## wherein U_x is the voltage which is supplied to the one torquer acting about the one input axis of the gyroscope,

K_Tx is the constant of said one torquer,

U_y is the voltage which is supplied to the other torquer acting about the other input axis of the gyroscope, and

K_Ty is the constant of said other torquer,

said north deviation computer comprising a quadrant logic circuit for determining the quadrant of the north deviation, said quadrant logic circuit being connected to receive the two signals supplied to the torquers, and a quadrant computer, to which the signal ##EQU52## is applied together with an output signal from the quadrant logic circuit and which provides a north deviation signal ψ

taking the quadrant of the north deviation into consideration.

19. An instrument as set forth in claim 18 characterized in that the quadrant logic circuit comprises a comparator circuit, which specifies the quadrant of the north deviation in accordance with the following criteria:

##EQU53## and that the quadrant computer provides the north deviation signal ψ

, as a function of an output signal of the quadrant logic circuit representing the quadrant of the north deviation, in the following manner;

##EQU54##

20. An instrument as set forth in claim 19, characterized in that the quadrant logic circuit comprises a null detector circuit for detecting singular values of the north deviation signal in accordance with the following criteria:

##EQU55##

21. An instrument as set forth in any one of the claims 18 through 20, wherein said gyroscope is casing-fixed and including:

accelerometer means operatively associated with the gyroscope for providing a pair of error signals indicative of the deviation of the gyroscope spin axis from the vertical;

an error signal computer connected to receive the north deviation signal from the north deviation computer as an estimated value ψ

of the north deviation ψ

together with the signals which are applied to the torquers and the error signals from the accelerometer means, said error signal computer computing error signals of transformation parameters between said gyroscope and an earth-fixed coordinate system on the basis of estimated values of these transformation parameters, said estimated values of the transformation parameters being, at first, determined by the output signal of the north deviation computer;

a correction signal computer connected to receive the error signals from the error signal computer for computing correction signals to be applied to the transformation parameters from the error signals thus obtained and weighted, if appropriate;

a transformation parameter computer connected to receive said correction signals and for supplying corrected transformation parameters;

means connecting the transformation parameter computer and the error signal computer to supply said corrected transformation parameters to the error signal computer for the computation of the error signals by the error signal computer in a closed loop as new estimated values of the transformation parameters; and

a computer connected to receive the corrected transformation parameters from the transformation parameter computer and producing a signal representing a corrected north deviation corresponding to the corrected transformation parameters.

22. An instrument as set forth in claim 21, wherein the accelerometer means comprises a pair of accelerometers mounted in fixed attitude relation to the gyroscope, said accelerometers having axes of sensitivity which are perpendicular to each other and respectively parallel to the two input axes of the gyroscope.

23. An instrument for the automatic determination of the north direction by means of a gyroscope affected by the rotation of the earth and having a spin axis, said instrument having an instrument-fixed reference direction and for use with a vehicle, said instrument being characterized by:

gyroscope positioning means secured to said gyroscope and mounting said gyroscope for pivotal movement about two input axes at right angles to each other, said positioning means positioning said spin axis substantially vertical, said positioning means including first and second torquers associated with said input axes respectively for controlling the angular position of the spin axis about the input axes respectively, first and second pickups associated with said input axes respectively for producing signals indicative of the angular position of the spin axis about the input axes respectively, and control means including said pickups and said torquers for actuating the torquer associated with one axis in response to the signal from the pickup associated with the other axis and for actuating the torquer associated with said other axis in response to the signal from the pickup associated with said one axis;

a north direction computer, connected to said control means to receive said signals, for producing from the ratio of the signals a north deviation signal indicative of the deviation from north of the instrument-fixed reference direction;

accelerometer means operatively associated with the gyroscope for providing a pair of error signals indicative of the deviation of the gyroscope spin axis from the vertical, the accelerometer means comprising a pair of accelerometers mounted in a fixed orientation with respect to the vehicle, said accelerometers having axes of sensitivity which are perpendicular to each other and respectively parallel to the two input axes of the gyroscope;

the gyroscope being rotatable through 90°

about one of the input axes of the gyroscope between the position at which the spin axis is vertical and a position at which the spin axis is horizontal; and

including a computer for computing the true heading of the vehicle from the information provided by the accelerometers about the attitude of the vehicle relative to a horizontal plane, and from the angular speed about the vehicle-fixed input axes of the gyroscope provided by the gyroscope.

24. Navigational instrument for a land vehicle having a fixed longitudinal axis x, a fixed transverse axis y and a fixed vertical axis z, said instrument comprising:

an inertial measuring unit producing inertial speed signals and having rotation-responsive inertial sensors, which respond to rotary movements about said axes and have known drifts d_x, d_y, d_z about their longitudinal, transverse and vertical axes x, y and z respectively, and accelerometers, which respond to linear accelerations along vehicle-fixed axes, the accelerometer sensitive in the direction of the longitudinal axis x producing a signal A_x^F and having a known deviation b_x,

a speed sensor having a scale factor, which speed sensor responds to the speed of the vehicle with respect to ground in the direction of the longitudinal axis of the vehicle and produces a speed singal v_x^F in the direction of the vehicle longitudinal axis,

a transformation parameter computer connected to receive the signals from the inertial measuring unit and which comprises means for computing transformation parameters for the transformation of vector components from a vehicle-fixed coordinate system into an earth-fixed coordinate system,

corrective signal generators connected to receive the accelerometer signals and the transformation parameters from the transformation parameter computer and which provide signals representing the components due to gravity of the accelerations detected by the accelerometers, said gravity component signals being superposed to the signals from the accelerometers to provide translation acceleration signals,

integrators connected to receive the translation acceleration signals to produce inertial speed signals v_Ix^F and v_Iy^F, an optimal filter connected to receive the inertial speed signals and the speed signals from the speed sensor and which, on the basis of these signals, produces estimated speed signals Δ

v_Ix^F and Δ

v_Iy^F referenced to vehicle-fixed coordinates v_Ix^F and v_Iy^F,

a coordinate transformation computer connected to receive the estimated speed signals and the transformation parameters from the transformation parameter computer and which comprises first means for transforming these speed signals into transformed speed signals, which are referenced to an earth-fixed coordinate system, said computer producing signals C₃₁, C₃₂, C₃₃ from the last line of a directional cosine matrix for the transformation from a vehicle-fixed coordinate system into an earth-fixed coordinate system, and

a position computer connected to receive the transformed speed signals and which comprises second means for providing position signals representing the position of the vehicle,

said optimal filter comprising;

(a) a first summing point connected to receive the estimated value Δ

v_Ix^F of the error of the longitudinal component signal v_Ix^F of the inertial speed and the estimated value Δ

v_x^F of the error of the speed signal v_x^F and to produce a difference signal therefrom,

(b) a second summing point connected to receive the inertial speed signal v_Ix^F and the speed sensor speed signal v_x^F and to produce a difference signal v_Ix^F -v_x^F therefrom.

(c) a third summing point connected to receive said two difference signals and to produce a third difference signal z₁ therefrom,

(d) a fourth summing point connected to receive the inertial speed signal v_Iy^F and the estimated value Δ

v_y^F of the error of the transverse component signal v_Iy^F of the inertial speed and to provide a fourth difference signal z₂ therefrom,

(e) a first multiplier connected to receive the difference signal z₁ and to multiply it by a given factor K₁₁ to produce a signal K₁₁ z₁,

(f) third means connected to receive signals d_z, d_y from the inertial measuring unit and signals C₃₂, C₃₃ from the coordinate transformation computer and to produce a signal C₃₂ d_z -C₃₃ d_y therefrom,

(g) a fifth summing point connected to said third means and said first multiplier to produce a signal representing the sum of the signals from said third means and the first multiplier,

(h) a first integrator connected to said fifth summing point to integrate said sum of said signals and thereby produce a signal Δ

C₃₁ which represents an estimated value of the error of the signal C₃₁ of the directional cosine matrix,

(i) a second multiplier connected to receive the difference signal z₂ and to multiply it by a given factor K₂₂ to produce a signal K₂₂ z₂,

(j) fourth means connected to receive signals d_x, d_y from the inertial measuring unit and signals C₃₁, C₃₃ from the coordinate transformation computer and to produce a signal C₃₃ d_x -C₃₁ d_y therefrom,

(k) a sixth summing point connected to said fourth means and said second multiplier to produce a signal representing the sum of the signals from the fourth means and the second multiplier,

(l) a second integrator connected to said sixth summing point to integrate the sum signal of the sixth summing point and thereby produce a signal Δ

C₃₂ which represents an estimated value of the error of the signal C₃₂ of the directional cosine matrix,

(m) multiplying means connected to receive signals C₃₁ and z₁ and to multiply the signal C₃₁ by the accelerating due to gravity and to multiply the signal z₁ by a given factor K₃₁ and by the known accelerator deviation b_x to produce output signals gC₃₁ and K₃₁ z₁ b_x,

(n) a seventh summing point connected to said multiplying means to receive the output signals therefrom and to add those signals together to produce a sum signal,

(o) a third integrator connected to said seventh summing point to receive the sum signal therefrom and to integrate it to produce a signal Δ

v_Ix^F representing the estimated value of the error of the longitudinal component signal v_Ix^F of the inertial speed,

(p) an eighth summing point connected to receive the signals A_x^F and gC₃₁ and add them to produce a signal v_x^F representing the translatory acceleration in the direction of the longitudinal axis of the vehicle,

(q) multiplying means and a fourth integrator connected to receive the difference signal z₁ multiply it by a given factor K₆₁ and integrate the product K₆₁ z₁ thereof to produce a signal Δ

k_x representing the estimated value of the error of the scale factor of the speed sensor,

(r) multiplying means and a ninth summing point connected to receive the difference signal z₁ and the translatory acceleration signal v_x^F, to multiply the difference signal z₁ with a given factor K₅₁ and to add the product K₅₁ z₁ thereof with the signal v_x^F to produce an output signal,

(s) a sixth integrator connected to receive and integrate the last mentioned output signal to produce a signal Δ

v_x^F which represents the estimated value of the error of the speed signal from the speed sensor,

(t) multiplying means connected to receive the signals C₃₂ and z₂, to multiply the signal C₃₂ by the acceleration g due to gravity and to multiply the signal z₂ by a given factor K₄₂ and by the known zero deviation b_x to produce output signals gC₃₂ and K₄₂ z₁ b_x,

(u) a tenth summing point connected to receive the output signals of the last mentioned multiplying means and to add those signals together to produce a sum signal,

(v) a seventh integrator connected to receive the sum signal from the tenth summing point and to integrate that signal to produce a signal Δ

v_Iy^F which represents the estimated value of the error of the transverse component signal v_Iy^F, and

(w) means connected to receive the speed signal v_x^F and the estimated speed error signal Δ

v_x^F and to subtract the latter from the former to produce a corrected speed signal.

25. Navigational instrument as set forth in claim 24, and wherein the vehicle has a significant rotary speed ω

_z^F about its vertical axis z, said instrument further comprising

(a) multiplying means connected to receive the difference signals z₁ and z₂ and to multiply the z₁ signal by a given factor K₂₁ to produce a product signal K₂₁ z₁ and to multiply the z₂ signal by given factors K₁₂, K₃₂ and K₅₂ to produce product signals K₁₂ z₂, K₃₂ z₂ and K₅₂ z₂ respectively,

(b) multiplying means connected to receive the Δ

C₃₂ signal and to multiply it by the rotary speed ω

₂^F to produce a signal ω

₂^F Δ

C₃₂,

(c) said fifth summing point being connected to receive and additionally add said product signal K₁₂ z₂ and said ω

_z^F Δ

C₃₂ signal in the production of the signal by the fifth summing point,

(d) said sixth summing point being connected to receive and additionally add said product signal K₂₁ z₁ and said ω

_z^F Δ

C₃₂ signal in the production of the signal by the sixth summing point,

(e) said seventh summing point being connected to receive and additionally add said product signal K₃₂ z₂ in the production of the signal by the seventh summing point, and

(f) said ninth summing point being connected to receive and additionally add said product signal K₅₂ z₂ in the production of the signal by the ninth summing point.