GB2103364A

GB2103364A - Gyroscopic instrument for determining north direction

Info

Publication number: GB2103364A
Application number: GB08221650A
Authority: GB
Inventors: Uwe Krogmann
Original assignee: Bodenseewerk Geratetechnik GmbH
Current assignee: Bodenseewerk Geratetechnik GmbH
Priority date: 1981-08-06
Filing date: 1982-07-27
Publication date: 1983-02-16
Also published as: FR2511145B1; DE3131111C2; DE3131111A1; FR2511145A1; GB2103364B

Abstract

In a tape-suspended meridian gyro, the deflection (???A) of the gyro spin axis (26) with respect to a housing reference (y) is monitored by a pick-off (20) and the pick-off signal is supplied to a torquer (24) through a high gain amplifier (22). This torquer acts on the meridian gyro about its vertical axis (z) to restrain the gyro to the housing reference. A Kalman filter (52) is provided which simulates the system of the restrained meridian gyro. The difference of the signal (Mg) applied to the torquer and an estimator (M<^>g) of this signal provided by the Kalman filter is supplied as a filter input signal to the Kalman filter. <IMAGE>

Description

SPECIFICATION Gyroscopic instrument for determining north direction This invention relates to a gyroscopic instrument for determining north direction.

From German Patent No. 1 941 808, a gyroscopic instrument for determining north direction is known having a meridian gyro suspended in a housing by means of a tape. A pick-off is provided for generating a signal corresponding to the azimuth deflection of the gyro with respect to a housing reference defined by the tape zero position. A torquer acts upon the meridian gyro, to which torquer the signal of the pick-off is applied by means of a high gain amplifier. This torquer exerts a torque about the azimuth axis upon the meridian gyro, which torque counteracts the gyro directing torque, i.e. the torque caused by rotation of the earth which orientates the gyro spin axis towards the north direction.The meridian gyro then does not align itself with North with its gyro spin axis, which would be tedious, as a meridian gyro suspended on a tape represents a practically undamped oscillating system having a long oscillating period. On the contrary, the meridian gyro is restrained to the housing reference, i.e. the tape zero position. The torque which has to be exerted upon the meridian gyro is, therefore, proportional to the gyro directing torque and is thus proportional to this angle for small angles between the gyro spin axis and north. If with sufficiently high amplification of the signal supplied by the pick-off the angle between the gyro spin axis and the housing reference may also be neglected, the torque of the torquer is proportional to the angle between the housing reference and north.If it can be assumed that the torquer works linearly, the amplified signal of the pick-off, which is applied to the torquer, provides a measure of this angle between the housing reference and north.

This signal may be utilised for indicating north direction (see German Auslegeschrift 20 08 702) or for navigational purposes (see German Auslegeschrift 2545 025).

The oscillating period of the system is substantially shortened by the electrical restraint of the meridian gyro. The north deviation, i.e. the angle between the housing reference and north, may then be determined in a short period of time compared to the prior art meridian gyros which are suspended by a tape and which freely adjust themselves. Nevertheless, it still takes an undesirably long time before a stable value for the north deviation is obtained. Additionally, the measurement is affected by external interference.

To eliminate the influence of such external interference, it is known to feed the signal which is applied to the torquer, and which serves as a measure of the north deviation, to an analog-to-digital converter which provide a digital signal corresponding to this signal. This digital signal is fed to a computer which is adapted for recursive average forming from the digital signals sampled at predetermined time intervals. The influence of interference is eliminated due to the average forming. It is ensured, however, by the average forming being recursive, that a measuring value is relatively rapidly available (see German Offenlegungsschrift 24 45 026, German Offeniegungsschrift 26 18868 and US Patent 4 075 764).Whilst the measuring value may, in some circumstances, be at first subject to error, it will be improved to the degree to which the average forming is effected. Usually, a low-pass filter is provided at the input of the analog-to-digital converter.

It is an object of the present invention to further shorten the period of time within which a measuring value of desired accuracy is obtained in a gyroscopic instrument and to reduce the influence of mechanical interference on the measurement.

According to the invention, a gyroscopic instrument for determining north direction comprises a meridian gyro pendulously suspended in a housing; a pick-off responsive to deflection of the meridian gyro with respect to a housing reference to provide an output signal; a torquer which acts upon the meridian gyro about its vertical axis and which has applied thereto the pick-off output signal in a sense to restrain the meridian gyro to the housing reference; and a signal evaluation circuit which has applied thereto the signal supplied to the torquer and provides a filtered signal representing the deviation of the housing reference from north, the signal evaluation circuit comprising a Kalman filer which simulates the system of the restrained meridian gyro, and to which the difference between the signal applied to the torquer and an estimator of this signal provided by the Kalman filter is supplied as a first filter input signal.

In a Kalman filter, the system supplying measured values is simulated by means of a model. An estimator for one of the measured quantities resulting from such a model is compared to the value of the quantity actually measured in the system, and a filter input signal is formed of the differnce. These filter input signals are multiplied by suitable time-dependent functions and are supplied to integration means, and vary parameters of the model until the filter input signals reduce to zero. Then, the model corresponds to reality, and, from the model thus obtained, estimators can be obtained of measured quantities of the system, e.g. of the angle a0 between the housing reference and north, in the present case.

It has been found that by using such a Kalman filter for determining an estimator h, of the angle between the housing reference and north in a gyroscopic instrument of the present type, a considerable improvement with regard to both the response time and the elimination of mechanical interference may be achieved compared to the above-described prior art instruments.

An embodiment of the invention will now be described, by way of example, with reference to the accompanying drawings, in which Figure 1 is a schematic perspective view of the mechanical structure of a gyroscopic instrument in accordance with the invention.

Figure 2 is a block diagram showing the combination of the various measured quantities of the gyroscopic instrument and the Kalman filter for the signal processing, Figure 3 illustrates the transient response of a prior art gyroscopic device and that of a gyroscopic device including a Kalman filter, and Figure 4 illustrates the influence of interference on the transient response of a prior art gyroscopic instrument and on that of the gyroscopic instrument with the Kalman filter.

Referring to Figure 1 of the drawings, a gyroscopic instrument comprises a housing 10 in which a meridian gyro 12 having a mast 14 is suspended by means of a tape 16. The housing 10 defines a coordinate system having a vertical axis z and axes x andy perpendicular thereto and to each other. They axis is an instrument reference. If the meridian gyro 12 lies with its spin axis in the plane defined by they and the z axes, the tape 16 is relaxed. This position is therefore designated the tape zero position. The deflection of the meridian gyro 12 relative to the instrument (housing) reference y is detected by means of a pick-off 20, here shown as a potentiometer. The signal of the pick-off is applied to a torquer 24 through a high gain amplifier 22. The gyro spin axis is designated by 26.

In the following, the following designations are used, which may also be seen in Figure 1.

a = azimuth angle between the gyro spin axis 26 and north a0 = azimuth angle between the housing reference and north aA = deflection of the gyro spin axis 26 relative to the housing reference ss = elevation angle of the gyro spin axis 26 ca = torsion spring constant of the tape suspension m = mass of the gyro pendulum formed by the meridian gyro 12 r = length of the gyro pendulum g = acceleration due to gravity lx = moment of inertia of the gyro pendulum about the x-axis lz = moment of inertia of the gyro pendulum about the z-axis H = gyrospin We = angular rate of the earth rotation (p = latitude M9 = the signal supplied to the torquer 24 by the amplifier 22 Mv = HWe5in(p MN = HWecO5(p V = gain of the amplifier VFR (s) = V 1 + Tc = transfer function of the amplifier 1 + T1 S s = variable of the Laplace transform Kik (i,K = 1,2,3,4) = time dependent functions VMG = the variance of the measuring noise process of the signal supplied to the torquer VaA = the variance of the measuring noise process of the deviation of the gyro spin axis 26 from the housing reference Ma = interfering torque about the vertical axis Z Mp = interfering torque aboutthex-axis Wv, Wz = power levels of the system noise inputs.

In the upper part of Figure 2, the gyroscopic instrument generally designated by 28 is shown as block diagram.

The torque equation for the torques about the vertical axis z (Figure 1) reads (1) izä M,-Ho,coscpsina-HP -IVFR(s)+C,I*A.

Thus, lzä is equal to the sumof the torques being effective about the vertical axis z, namely the interfering torques Ma, the gyro directing torque due to the horozontal component of the earth rotation Hoe cos (p sin a, the gyro torque due to a rotational speed about the x-axis H pas well as the torque exerted upon the meridian gyro 12 by the torquer 24 and the tape 16. This lattertorque is proportional to the angle aA, through which the gyro spin axis 26 is deflected relative to the housing reference. The proportionality factor, on one hand, contains the gain of the amplifier 22 (in which the factor of the torquer 24 is taken into account for simplicity).

The gain of the amplifier 22 has a time response FR (S) with a transfer function, which (mathematically not quite correctly) is implied by a factor in equation (1).

The torque equation about the x-axis is as follows: (2) lxss = Mp + Ho)esin(p+ Ha- mrg sin p.

Again, lxss equates the sum of the torques which act around the x-axis, namely the interfering torques Mp due to external interferences, the gyro torque Hoe sin (p to be attributed to the vertical component of earth rotation, a gyro torque H adue to rotational speedsaabout the vertical axis z as well as, with reverse sign, a pendulum torque P = mrg sin ss occurring with deflection of the meridian gyro 12 with the mast 14 out of the vertical direction and thus with deflection of the gyro spin axis 26 out of the horizontal plane.As a heavy gyro is considered, ä and p, that means the nutation, may be neglected. sin a may be replaced by a and sin p may be replaced by pin the case of the fine alignement, thus when the gyro spin axis 26 is already substantially oriented towards north, and a0 is small. The following linearized model equations then result from the equations (1) and (2): (3) Hcr=PP-W,-M, (4) H ss=MNaMg + Wz with the compensation torque and the signal supplied to the torquer 24 being (5) Mg (s) = (V. FR (s) + Ca) aA (5).

The torsion spring constant Ca is negligible, as the gain V in practice is by three powers of ten larger than Ca. The interfering torques Mss and Ma are designated by Wv and Wz as stochastic signals in the equations (3) and (4).

These model equations (3) and (4) are illustrated in the block diagram in the upper part of Figure 2.

A summing point 30 represents equation (4). The deviation a of the gyro spin axis 26 from north, which, as will be seen, appears in the point 32 of the block diagram, is multiplied by MN = HWe cos (p, as illustrated by the block 34. This product appears at the summing point with negative sign. Another summand at the summing point is the torque Mg supplied by the torquer 24, which torque is proportional to the deviation aA of the gyro spin axis 26 (having the azimuth angle a) from the housing reference (having the azimuth angle aO) and appears at the point 36 of the block diagram.This deviation a0 obtained by the pick-off 20 is multiplied by the gain factor of the amplifier 22, as shown by block 37, and also appears at the summing point 30 with negative sign. The third summand being effective at the summing point is the value Wz representing the interfering torque about the z-axis. According to equation (4), the summing point 30 yields as sum Hp. The deviation of the gyro spin axis from north in the azimuth, i.e. about the z-axis, thus causes an angular ratepabout the x-axis (Figure 1). This angular rate results from the sum signal at the summing point 30 by division by H, which is represented by a block 36. The deflection angle p about the x-axis results therefrom by integration, represented by a block 38.The gyro spin axis 26 thus tries to change its elevation angle p with respect to north with an angle a in the azimuth. The elevation angle p, however, causes an angular rateaabout the azimuth axis z due to the pendulum torque P = m.r.g., in accordance with equation (3).

A summing point 40 in Figure 2 represents equation (3).

The elevation angle ss resulting from the integration symbolized by block 38 (effected by the system) is multiplied by P = m.r.g. This product is effective at the summing point 40 with positive sign. With negative signs, futhermore Mv = Hoe sin (p and the value Mv symbolizing the interfering torque are effective. In accordance with equation (3), Hais then obtained in the summing point 40. The angular rateaabout the azimuth axis z is obtained by division by H, which is represented by the block 44. In the point 32, a is obtained by integration of the angular ratea, as represented by block 46.

A summing point 48 represents the pick-off 20, where the difference is formed of the angle a0 between housing reference and north and the angle a between gyro spin axis 26 and north and provides the angle aA.

A value w00 (t) =aO illustrates interferences of a, which integrated, as represented by block 50, yield the angle aO. aO(t) is given as initiat value of the integration.

This block diagram thus represents the gyroscopic instrument 28 shown in Figure 1 in linearized form.

A signal evaluation circuit contains a Kalman filter 52 illustrated in the lower part of Figure 2. This Kalman filter 52 simulates the model of the gyroscopic instrument 28 represented by the block diagram. It provides estimators of the different quantities, which are characterized by a roof ( ). Mg, for example, is an estimator of the torque exerted by the torquer 24 upon the meridian gyro and the signal supplied to the torquer. The difference between the signal Mg and the estimator Mg of this signal provided by the Kalman filter serves as a first filter input quantity.

To the Kalman filter 52 the difference between a signal representing the deviation aA of the meridian gyro 12 from the housing reference y and an estimator aA of this signal supplied by the Kalman filter 52 may additionally be supplied as second filter input signal. This is indicated in dashed lines in Figure 2.

The filter input signals are multiplied by time-dependent factors and are integrated, the parameter of the model being varied by the integrals until the filter input signals disappear. It can be assumed that the model thus modified corresponds to the real system such thatthe estimators picked-off from the model represent the real values appearing in the system.

In the preferred embodiment, the Kalman filter 52 has the following structure.

In a first summing point 54, the difference is formed between a first signal which is an estimator Mg of the signal supplied to the torquer 24 and a second signal which is the estimator â of the angle between gyro spin axis 26 and north multiplied by HWe cos ; H, as has been mentioned before, being the gyro spin, We the angular rate of earth rotation and (p the latitude. The difference obtained is divided by the gyro spin H, as indicated by block 56. In a second summing point 58, the sum is formed of the difference from the first summing point 54 divided by the gyro spin H and the first filter input signal multiplied by a time-dependent factor K22, the multiplication being represented by a block 60. The sum formed in the second summing point 58 is integrated by integration means 62.The signal thus obtained representing an estimator p of the elevation angle of the gyro spin axis 26 is multiplied by a factor P = mrg, as represented by block 64, m being the mass of the meridian gyro 12, r being the length of the gyro pendulum (Figure 1) and g being the acceleration due to gravity. In a third summing point 66, the sum is formed of the integral from the integration means 62 multiplied by P and a signal Mv = HW0 sin .

The sum formed in the third summing point 66 is divided by the gyro spin H, as indicated by block 68. In a forth summing point 70, the sum is formed of the sum divided by H from the third summing point 66 and the first filter input signal multiplied by a time-dependent factor K12, the factor K12 being represented by block 72.

The sum formed in the forth summing point 70 is integrated by integration means 44, the signal thus obtained representing said estimator â of the angle between gyro spin axis and north, which, multiplied by the factor MN = HWa cos (p represented by block 76, is subtracted in the first summing point 54. The first filter input signal is multiplied by a time-dependent factor K32, illustrated by block 78, and is then integrated by integration means 80, whereby a signal is obtained representing the estimator a0 of the angle between housing reference V and north.In a fifth summing point 82, the difference is formed of the integrated sum from the fourth summing point 70 and the first filter input signal multiplied by the factor K32 and integrated, whereby a signal is obtained representing an estimator âA of the deflection of the meridian gyro 12 with respect to the housing reference y.In a sixth summing point 84, the sum is formed of a signal multiplied by a factor VTDI(Tl), which signal has been obtained in point 86 by the division of the sum from the third summing point 66 by the gyro spin H, of the difference from the fifth summing point 82, multiplied by a factor V/(T1), of the filter input signal multiplied by a time-dependent factor K42 as well as, with negative sign, of the estimator Mg of the signal supplied to the torquer 24 multiplied by a factor 1/(T1). Factor VT & T1) is symbolized by block 88, factor V/(T1) by block 90, factor K42 by block 92 and factor 1/(T1) by block 94. The sum formed in the sixth summing point is integrated by integration means 96, whereby said estimator Mg of the signal supplied to the torquer 24 is obtained.

Optionally, the second filter input signal multiplied by a time-dependent factor K21 represented by the dashed block 98 can be added in the second summing point 58, which signal, as has been mentioned before, is the difference between a signal representing the deviation of the meridian gyro 12 from the housing reference y and an estimator âA of this signal supplied by the Kalman filter 52. In the fourth summing point 70, then additionally the second filter input signal multiplied by a time-dependent factor K11 represented by the dashed block 100 would be added. Additionally, the second filter input signal multiplied by a time-dependent factor K31 would be integrated by the integration means 80 providing an estimator a0 of the angle between housing reference y and north. The factor K31 is symbolized by block 102. Finally, the second filter input signal multiplied by a time-dependent factor K41 symbolized by block 104 would additionally be added in the sixth summing point 84.

In an eighth summing point 106, the sum is formed of the signal Mg really supplied to the torquer 24, the estimator Mg provided by the Kalman filter 52 of this signal supplied to the torquer 24 with negative sign, and a signal VMs representing the variance of the measuring-noise process of the first filter input signal. In a ninth summing point 108, the sum is formed of signal aA supplied by the pick-off 20 and representing the deviation of the meridian gyro 12 from the housing reference y, with negative sign the estimator bA provided by the Kalman filter 52 of this signal representing the deviation of the meridian gyro 12 from the housing reference y, and a signal VaA representing the varianee of the measuring-noise process of the deviation of the meridian gyro from the housing reference.

As can be seen, the Kalman filter 52 simulates the linearized system of the gyroscopic instrument 28. The blocks 88, 90, 94 including the integrator 96 are a simulation of the amplifier 22, the transfer function of which is assumed to be (6) VFR(s) = V 1 + Tr) +T1s This model is varied due to the filter input signals at the summing points 106 and 108 by time-dependent factors symbolized by the blocks 60, 98, 72, 100, 102,78, 92 and 104 and supplied to the inputs of integration means 62, 74, 80 and 96, until the filter input signals disappear, and the model matches reality.

The Figures 3 and 4 illustrate the advantages compared to the prior art obtained by the design of the signal processing means according to the invention.

In Figure 3, line 110 represents the real value of the angle a0 between housing reference and north. Plot 112 shows how the indication of an instrument e.g. according to German Offenlegungsschrift 1 941 808 approaches this value aO, if the signal Mg supplied to the torquer 24 is merely passed through a low-pass filter for signal processing. Plot 114 shows the transient response of the measured value, if in addition to the low-pass filter an average filter according to US-PS 4075764 is provided. Finally, a plot 116 shows the transient response of the indication approaching the real value, when utilizing the Kalman filter 52 described.

It can be seen that the signal processing described is approximately three times as rapid as the prior art signal processing. The signal processing described permits estimating the angle a0 accurately up to 1 - after approximately 20 seconds, while accuracy of approximately 3- only results still after 60 seconds in the prior art instrument.

Figure 4 shows the behaviour with regard to the elimination of external interferences, again compared to the prior art solutions.

Line 118 shows the real value of the angle aO. Plot 120 shows the variation of the estimator a0 in the presence of interferences, if the signal Mg is only passed through a low-pass filter. Plot 122 shows the variation of the estimator with the same interferences, if a low-pass filter including an average filter according to US-PS 4075764 is used. Finally, plot 124 shows the variation in time of the estimator, if a Kalman filter 52 of the type described is used.

Claims

1. A gyroscopic instrument for determining north direction, comprising a meridian gyro pendulously suspended in a housing; a pick-off responsive to deflection of the meridian gyro with respect to a housing reference to provide an output signal; a torquer which acts upon the meridian gyro about its vertical axis and which has applied thereto the pick-off output signal in a sense to restrain the meridian gyro to the housing reference; and a signal evaluation circuit which has applied thereto the signal supplied to the torquer and provides a filtered signal representing the deviation of the housing reference from north, the signal evaluation circuit comprising a Kalman filter which simulates the system of the restrained meridian gyro, and to which the difference between the signal applied to the torquer and an estimator of this signal provided by the Kalman filter is supplied as a first filter input signal.

2. An instrument as claimed in Claim 1, wherein the difference between a signal representing the deviation of the meridian gyro from the housing reference and an estimator of this signal provided by the Kalman filter is applied to the Kalman filter as an additional second filter input signal.

3. An instrument as claimed in Claim 1 or Claim 2, wherein the Kalman filter comprises a first summing point in which the difference is formed of a first signal representing an estimator of the signal applied to the torquer and a second signal representing the estimator multiplied by H We cos tp of the angle between gyro spin axis and north, H being the gyro spin, We being the angular rate of the earth's rotation and cp being the latitude; means to divide the difference obtained by the gyro spin H; a second summing point in which the difference is formed of the difference from the first summing point divided by the gyro spin H and the first filter input signal multiplied by a first time-dependent factor; first integration means to integrate the sum formed in the second summing point, the signal thus obtained being an estimator for the elevation angle of the gyro spin axis; means to multiply the latter signal by a factor P = m.r.g., m being the mass of the meridian gyro, r being the length of the gyro pendulum and g being acceleration due to gravity; a third summing point in which the sum is formed of the integral from the first integration means multiplied by P and a signal Mv = Hoe sin cp; means to divide the sum formed in the third summing point by the gyro spin H; a fourth summing point in which the sum is formed of the sum from the third summing point divided by the gyro spin H and the first filter input signal multiplied by a second time-dependent factor; second integration means to integrate the sum formed in the fourth summing point, the signal thus obtained representing the estimator of the angle between the gyro spin axis and north; means to multiply the first filter input signal by a third time-dependent factor; third integration means to integrate the multiplied first filter input signal whereby a signal is obtained representing the estimator of the angle between the housing reference and north; a fifth summing point in which the difference is formed of the integrated sum from the second integration means and the integrated signal from the third integration means, whereby a signal is obtained representing an estimatorforthe deflection of the meridian gyro with respect to the housing reference; a sixth summing point in which the sum is formed of the signal multiplied by a factor VT,/(T1), which has been obtained from the division of the sum from the third summing point by the gyro spin, the difference from the fifth summing point multiplied by a factor V/(T1), the filter input signal multiplied by a fourth time-dependent factor and, with negative sign, an estimator of the signal applied to the torquer multiplied by a factor 1/(T1); and fourth integration means to integrate the sum formed in the sixth summing point, whereby the estimator of the signal applied to the torquer is obtained.

4. An instrument as claimed in Claims 2 and 3, wherein in the second summing point the second filter input signal multiplied by a fifth time-dependent factor is additionally added; in the fourth summing point the second filter input signal multiplied by a sixth time-dependent factor is additionally added; the second filter input signal multiplied by a seventh time-dependent factor is integrated by the third integration means providing an estimatorofthe angle between the housing reference and north; and in the sixth summing point the second filter input signal multiplied by an eighth time-dependent factor is additionally added.

5. An instrument as claimed in Claim 4, wherein in an eighth summing point for forming the first filter input signal, the sum is formed ofthe actual signal applied to the torquer, with negative sign an estimator of the torquer applied signal provided by the Kalman filter, and a signal representing the variance of the measuring-noise process of the signal applied to the torquer; and in a ninth summing point for forming the second filter input signal, the sum is formed of the signal supplied by the pick-off and representing the deviation of the meridian gyro from the housing reference, with negative sign the estimator provided by the Kalman filter of the signal representing the deviation of the meridian gyro from the housing reference, and a signal representing the variance of the measuring-noise process of the deviation of the meridian gyro from the housing reference.

6. A gyroscopic instrument as claimed in Claim 1 and substantially as hereinbefore described with reference to the accompanying drawings.