GB2029581A - Accelerometer noise signal reduction - Google Patents

Abstract

A self-adjusting filter for use in an underwater seismic system of the kind that employs a towed body and peripheral equipment to produce profiles of the terrain beneath bodies of water. The filter receives from an accelerometer 14 located in the body an acceleration signal, including noise corresponding to the effect of gravity on the accelerometer, and reproduces the acceleration signal with an attenuated accelerometer noise signal. The filter accomplishes this by first generating 18 a correction signal proportional to portions of the accelerometer noise signal. A scaled correction signal is generated by a variable scaling device 20. The scale factor is made proportional to a correlation signal which is indicative of the correlation between the correction signal and the sum of the acceleration signal and the scaled correction signal so that signal components of the filtered acceleration signal corresponding to the portions of the accelerometer noise and to the correction signals tend to cancel completely. <IMAGE>

Description

SPECIFICATION Adaptive pitch and roll compensation system The invention relates to a self-adjusting filter for use in determining the position of a body travelling through water relative to a datum such as mean sea level and, more particularly, for use in compensating for gravity effects on an accelerometer located in such a body.

The invention has specific application to an underwater seismic system for use in surveying the terrain under a body of water. Such systems commonly include a towed body, generally referred to as a "fish", which is provided with a sound source and hydrophones or like sound sensors. Very briefly, a sound pulse is generated and directed towards the bottom terrain and the reflected signal is detected by the hydrophones. From the delay between generation of the sound pulse and detection of the reflected pulse, an estimate of the distance to the reflecting layer of the terrain below may be obtained. By towing the fish at a relatively constant speed and by sampling the distance to the bottom terrain at regular intervals, it is possible with a chart recorder to produce a profile of the bottom terrain.

The quality of the profile obtained may be seriously degraded by vertical movement of the fish during the sampling process. Upward movement of the fish makes the bottom terrain appear farther from the datum; downward movement makes the terrain appear closer. A very significant factor in the respect is heaving of the fish as the towing vessel is buffeted by surface waves. This heaving motion translates onto the chart recorder as an oscillatory pattern which tends to reduce the resolution and usefulness of the profile. U.S. Patent No. 4,019,356 to Hutchins discloses apparatus for compensating for such heaving motion, including pressure and acceleration transducers for use in determining the instantaneous vertical displacement of the fish with respect to the mean sea level.

Pressure and acceleration transducers presently used are subject to noise problems. This noise tends to degrade the quality of chart recordings in a manner not unlike that of the heaving motion experienced by the fish.

More specifically, the pressure transducer used will generally derive from pressure measurements a position signal indicative of the vertical displacement of the fish with respect to a datum such as mean sea level. The position signal is likely to be subject to noise owing to variations of pressure caused by surface wave action. Since this same wave action buffets the towing vessel, the pressure variations tend generally to have a frequency range similarto that of the heaving motion.

The accelerometer used will generally produce an acceleration signal proportional to the acceleration of the fish along a specific axis through the accelerometer. The axis will normally be arranged to be in a substantially vertical position when the fish is moving smoothly through water so that the acceleration signal is substantially indicative of the vertical acceleration of the fish. Such an accelerometer can generally be expected to to have a zero frequency offset corresponding to the effect of gravity on the accelerometer. Because the accelerometer axis tends to tilt from a vertical position as the accelerometer moves with the pitching and rolling of the fish, the gravity offset will at any instant be attenuated by the cosine of the angle by which the axis is tilted from a vertical position: the gravity offset is in effect modulated by the pitching and rolling of the fish.

The modulated gravity offset is an accelerometer noise signal which can be expected to have a very broad frequency range and a significant zero frequency component owing to the fact that over the typical range of angles formed by the accelerometer axis with respect to a vertical position the cosine function produces a positive result. The zero frequency noise component can in practice be the principal portion of the accelerometer noise and can be difficult to remove without distortion of the vertical acceleration signal and ultimately of the displacement signal to be produced.

The frequency spectra of the various signals will vary depending on the physical circumstances in which the fish and the towing vessel are located; however, it has been found practical for design purposes to assume that the period of the heaving motion will be in the order of 6 to 10 seconds with a resultant frequency spectrum centered about .125 Hz. As mentioned above, the frequency spectrum of the pressure transducer noise can tend to overlap of the heaving motion.

As mentioned above, the invention relates specifically to a self-adjusting filter for compensating for the effects of gravity on an accelerometer located in a body travelling through water. The use of such a filter, however, will be discussed in the context of an electronic filter, with which the invention will normally be used, that produces a displacement signal indicative of the true vertical displacement of a body travelling through water relative to a datum such as mean sea level from acceleration and pressure signals as described above.

A filter constructed according to the invention includes correction signal generating means for generating a correction signal proportional to portions of the accelerometer noise signal produced by the accelerometer. The correction signal is received by variable scaling means that produce a scaled correction signal proportional to the product of a scale factor, which varies in a manner discussed more fully below, and the correction signal. The scaled correction signal and the acceleration signal are then effectively combined by summing means that generate a summation signal proportional to the sum of the acceleration signal and the scaled correction signal.In practice, the polarity of the correction signal and the scaling factor will be chosen so that summation signal components corresponding to the portions of the accelerometer noise signal and to the correction signal tend to cancel one another.

Correlation means are provided to make the filter self-adjusting. The correlation means generate a correlation signal substantially indicative of the correlation between the summation and correction signals. The manner in which a correlation function is obtained is described more fully below. However, assuming that the acceleration signal, but for the accelerometer noise signal, and the correction signal would be substantially incoherent, it is expected that the polarity of the correlation signal will be indicative of insufficient or excessive scaling of the correction signal, and that the magnitude of the correlation signal will be indicative of the extent of such insufficiency or excess, as the case may be.The scale factor is made to vary in proportion to the correlation signal so that the summation signal components corresponding to the portions of the accelerometer noise and to the correction signal tend to cancel completely.

The invention will be better understood with reference to drawings in which: Figure lisa schematic representation of a selfadjusting filter constructed according to the invention; Figure 2 is a schematic representation of another embodiment of a filter constructed according to the invention; Figure 3 is a schematic representation of the filter of Figure 1 in use in conjunction with a filter that produces a displacement signal indicative of the vertical displacement of a body travelling through water from pressure and acceleration signals as described above; Figure 4 is a three dimensional representation of the relationship between the axis of an accelerometer and projections of the axis on mutually perpendicular, vertical planes; Figure 5 is a schematic representation of apparatus for generating a correction signal;; Figure 6 is a schematic representation of an alternative embodiment of apparatus for generating a correction signal; Figure 7 is a diagrammatic representation of an underwater seismic system comprising a towed body and towing vessel, shown above a stratafied bottom; and Figure 8 is a schematic representation of a compensation system included in the underwater seismic system of Figure 7 that incorporates the combination filter of Figure 3.

Reference is made to Figure 1 which shows a self-adjusting filter 10 constructed according to the invention. The filter 10 has an input terminal 12 where an acceleration signal is received from an accelerometer 14, as described above, and an output terminal 16 where a filtered acceleration signal is made available.

The filter 10 includes correction signal generating means 18 that produce a correction signal proportional to portions of the accelerometer noise signal included in the acceleration signal. The correction signal is received by variable scaling means 20 that produce a scaled correction signal proportional to the product of the correction signal and a scale factor.

A summer 22 produces a summation signal proportional to the sum of the acceleration signal and the scaled correction signal. As mentioned above, the polarities of the scale factor and the correction signal are chosen so that summation signal components corresponding to the portions of the accelerometer noise signal and to the correction signal tend to cancel. The summer 22 may be an operational amplifier arranged in a standard summing configuration.

A correlation signal as described above is generated by first and second error enhancing filters 24, 26, a multiplier 28, and integration means 30, connected as shown. The first filter 24 receives at its input the summation signal which contains an error signal proportional to the difference between the accelerometer noise signal and the scaled correction signal. The first filter 24 enhances the error signal by effectively attenuating relative to the error signal, summation signal components of zero frequency and preferrably also summation signal components lying outside the frequency range of the error signal (which frequency range is commensurate with that of the accelerometer noise signal).The filter 24 produces a first filtered signal that tends to ensure that the multiplier 28 operates within its dynamic range and that the correlation signal tends more to reflect only the correlation between the correction signal and the error signal component of the summation signal. In practice, the filter 24 may typically be a band pass filter which removes zero frequency signals and which has a pass band encompassing the frequency range of the accelerometer noise signal.

The second filter 26 receives at its input the correction signal and it generates therefrom a second filtered signal. The second filter 26 is required principally to ensure that the first filtered signal is not effectively phase shifted relative to the correction signal, thereby distorting the correlation signal to be produced. The second filter 26 preferrably has a transfer function substantially identical to that of the first filter, but a transfer function having a substantially identical phase shifting characteristic will suffice.

A product signal proportional to the product of a first and second filtered signals is generated by the multiplier 28, and the integration means 30 generates therefrom the correlation signal, the correlation signal being proportional to the integral of the product signal. The correlation signal is not in fact a true mathematical correlation of the summation and correction signals, as these signals have been altered by the first and second filters 24,26 in order to enhance the correlation signal produced. It will be' appreciated that such a correlation signal is nevertheless indicative of the correlation between the summation and correction signals.

The variable scaling means 20 is controlled by the correlation signal generated by the integration means 30. The scale factor of the variable scaling means 20 is made proportional to the correlation signal so that errors in compensating for the accelerometer noise signal adjust the scale factor in a manner that tends to enhance the effective cancellation of the accelerometer noise signal and the correction signal. It will be appreciated that there is considerable freedom in choosing the polarity of the signals generated by the various components of the filter 10 and that in practice these must be appropriately chosen to obtain the desired cancellation.

Figure 2 illustrates a filter 32 similar to the filter 10 of Figure 1, like components being indicated by like reference numerals. The filter 32 differs from the filter 10 in essentially the following respects: a dead zone buffer 34 follows the multiplier 28; the integration function provided by the integration means 30 is now provided by the combination of a voltage comparator 36, an absolute value circuit 38, a voltage to frequency converter 40, and an up-down counter 42; and the variable scaling means 20 has been replaced by a digital-to-analogue (D/A) conver ter44.

The dead zone buffer 34 produces a buffered signal which is essentially proportional to the product signal generated by the multiplier 28 except that the buffered signal assumes a zero value when the absolute value of the product signal is less than some predetermined value representing the extent of the "dead zone". The dead zone buffer 34 serves to eliminate small-valued noise signals that might otherwise tend to cause drifting of the integration function provided by the voltage comparator 36, the absolute value circuit 38, the voltage-to-frequency converter 40, and the up-down counter 42. The extent of the dead zone provided by the buffer 34 will vary according to the noise expected in particular applications.

The absolute value circuit 38 generates an absolute value signal proportional to the buffered signal.

The absolute value signal in turn drives the voltageto-frequency converter that generates a stream of pulses whose frequency varies in proportion to the absolute value signal.

The up-down counter 42 produces a tally signal that is a running total of the number of pulses generated by the voltage-to-frequency converter 40.

The tallying function of the up-down counter42 is controlled by the output signal of the voltage comparator 36 which compares the buffered signal to ground. The voltage comparator signal will assume first and second values, generally a supply voltage and ground, depending on the polarity of the product signal generated by the multiplier 28. Depending on whether the voltage comparator output signal has the first or second value, the counter 42 will count upwardly or downwardly with each pulse generated by the voltage-to-frequency converter 40.

The tally signal is thus effectively proportional to the integral of the product signal.

It will be appreciated that the dead zone buffer 34 and the absolute value circuit 38 may be realized with operational amplifiers and diodes in standard configurations, and that the voltage comparator 36, the voltage-to-frequency converter 40, and the updown counter 42 are standard circuit components.

The D/A converter 44 receives the correction signal and the tally signal and produces therefrom the scaled correction signal, the scaled correction signal now being proportional to the product of the correction signal and the analogue value of the tally signal.

A suitable D/A converter is the Burr-Brown DAC AD2 SM.

The specific application for which a self-adjusting filter constructed according to the invention is intended will be better understood with reference to figure 3 which shows a filter 46 comprising a first filter 48 that generates a displacement signal from acceleration and pressure signals as described above, and a second filter 50 corresponding more particularly to the filter 10 of figure 1, like components being indicated by like reference numerals.

The filter 48 is connected to a pressure transducer 52 from which it receives a pressure signal as described above. The pressure signal is double differentiated by a double differentiator 54 to produce a differentiated signal indicative of the vertical acceleration of the body in which the pressure transducer 52 and the accelerometer 14 are located.

The filtered acceleration signal available at the terminal 16 and the differentiated signal are then individually scaled and added by a summer 56 to produce a first summation signal. The scaling is such that components of the first summation signal corresponding to the vertical acceleration signal from the accelerometer 14 and to the double differentiated position signal from the pressure transducer 52 effectively cancel. The first summation signal thus consists substantially of signal components corresponding to the accelerometer and pressure transducer noise signals.

The first summation signal is then highpass filtered by a filter 58 to produce a filtered signal effectively free of zero frequency components corresponding to accelerometer noise. The filtered signal is then double integrated by a double integrator 60 to produce an integrated signal substantially proportional to the pressure transducer noise. The double integrator 60 will also serve to substantially attentuate higher frequency components of accelerometer noise.

The integrated signal and the pressure signal are then individually scaled and added by a summer 62 to produce a second summation signal. The scaling is such that the integrated signal is effectively used to cancel or attenuate noise components corresponding to pressure transducer noise in the second summation signal.

The filter 50 is substantially the filter 10 of Figure 1 except that the summation signal from the summer 22 is now sampled at the output of the double integrator 60. If the pressure signal and the correction signal are relatively incoherent, but for zero frequency components, the presence in the filtered signal from the double integrator 60 of signal components corresponding to the pressure signal should not substantially affect the correlation function provided by the multiplier 28 and the integration means 30. The portions of the filter 48 between the output of the double integrator 60 and the terminal 16 serve to error enhance the summation signal for the summer 22.In practice, it is possible to sample the summation signal directly from the summer 22, although significant changes in the gains of the multiplier 28 and the integration means 30 may be required.

The filter 26 will preferably be arranged to have a transfer function substantially identical to that of combination of the filter 58 and the double integrator 60.

The operation of correction signal generating means constructed according to the invention will be better understood with reference to Figure 4 which illustrates the instantaneous orientation of an axis A, the axis ofthe accelerometer 14 referred to above, with respect to three mutually perpendicular axes X, Y, and Z. The axis A is inclined at an angle 6 with respect to a vertical position which in Figure 4 is indicated by the Z axis. The axis A has a first projection B on a first plane, the YZ plane, and a second projection C on a second plane, the XZ plane.

Projections B and C will at any instant be inclined respectively at angles Oi and 62 from a vertical position. In practice, the angles 01 and 62 may be measured by the appropriate mounting of gyrosco pictransducers in the body containing the accelerometer 12. A suitable transducer for such purposes is the Timex Rate Gyro SD-000. Pendulum pots tend to be less expensive than such gyroscopic transducers, but also tend to display signal transfer characteristics that vary with the motion of the body in which they are located. The self-adjustment feature of a filter constructed according to the invention can permit use of such non-ideal devices.

It will be appreciated that in the framework presented by Figure 4 the accelerometer noise signal will be proportional to Gocos 6 where Go is the acceleration due to gravity. Since 6, , and 62 will be related by the relationship cos6 = cos 01. cos 62, a signal proportional to the product cos 0,. cos 62 will also be proportional to the accelerometer noise signal.For small variations of 6 about zero, cos 01 is approximately equal to 1 - 012/2, the first two terms of the MacLaurin series expansion of cos 01. A similar expression will also be a good estimator in such circumstances of cos 02. It will be apparent that for small 6 the expression (1 - 012/2 - 022/2) will be a reasonable estimator of the product cos 01. cos 62, and that a signal proportional to the expression will in turn be substantially proportional to the accelerometer noise signal.Where the filter in association with which the apparatus is to be used has a transfer function zero which removes zero frequency components of the accelerometer signal, a sufficient correction signal may be obtained by generating a signal proportional to the sum of 62i and 622. It will further be appreciated that a correction signal proportional to power series expansions of cos 6 incorporating higher order terms may be used to obtain a more complete cancellation of noise.

For the purpose of the invention, the vector A may be decomposed into projections in any two mutually perpendicular, vertical planes. In practice, it is sufficient to locate two gyroscopic transducers in a towed body so that the transducers measure mutual lyperpendicularcomponents of the tilting of the body.

Figure 5 shows correction signal generating means 64 for generating a correction signal substantially proportional to portions of the accelerometer noise signal. The correction signal generating means 64 comprises first and second transducers 66, 68 physically located within the towed body to respectively produce a signal proportional to 01 and a signal proportional to 62, as defined above. First and second cosine circuits 70, 72 respectively receive the first and second transducer signals and respectively produce therefrom a first signal proportional to the cos 81 and a second signal proportional to the cos 62.

It will be appreciated that the gains of the transducers 66, 68 must accommodate the transfer functions of the cosine circuits 70,72 so that the first and second signals are in fact indicative of cos 01 and cos 62, respectively. A suitable device for generating the cosine of a transducer signal is the INTERSIL 8038, a wave form generator which provides a diode array implementing a sine function which may effectively be used as a cosine function generator by introducing a constant offset voltage at the input of the diode array.

A multiplier 74 generates a cosine product signal proportional to the product of the first and second signals. As mentioned above, the cosine product signal would be proportional to the accelerometer noise signal. The cosine product signal thus serves as the correction signal.

Figure 6 shows alternative correction signal generating means once again comprising the first and second transducer 66, 68 as described above. First and second squaring circuits 78, 80 respectively produce a first squared signal proportional to the square of the first transducer signal and a second squared signal proportional to the square of the second transducer signal. A summer 82 produces a square sum signal proportional to the sum of 62i and 622. The square sum signal serves as the correction signal.

The intended use for a self-adjusting filter constructed according to the invention will be better understood with reference to Figures 7 and 8.

Figure7 shows an underwater seismic system 100 comprising a body 102 being towed with a cable 104 from a towing vessel 106. A sound pulse 108 is shown emanating from the towed body 102 and travelling towards a reflecting layer 110. The reflecting layer 110 causes a reflected sound pulse 112 to be directed upwardly toward the towed body 102.

Further layers 114 would also produce reflected pulses, but the latter are not shown forthe sake of clarity.

Figure 8 shows the filter 46 of Figure 6 connected to the accelerometer 14, the pressure transducer 52, described above, and a delay circuit 120. The filter 46 also includes the first and second transducer 66,68, described above. The accelerometer 14, the pressure- transducer 52, and the first and second transducers 66,68 are physically located within the body 102, as shown, and respectively produce acceleration, pressure, and first and second transducer signals also as described above.

The underwater seismic system 100 includes a recorder 122 which is a conventional chart or drum recorder of a type having a repetitive sweep provided by sweep circuit 124. Each time the sweep circuit 124 initiates a sweep across the chart (not shown) a trigger signal is generated by a trigger signal generator 126. The delay circuit 120 receives the trigger signal, delays it in time, and then couples the trigger signal via the cable 104 to a sound source 128 located in the body 102. The delayed trigger signal activates the sound source 128 causing it to generate a sound pulse such as the pulse 108 of Figure 7.

Reflected pulses such as the pulse 112 of Figure 7 are detected at intervals by hydrophones receivers 130 which generate response signals indicating that reflected pulses have been detected. The amplitude and duration of each response signal will generally correspond to the amplitude and duration characteristic of each reflected sound pulse; however, variations in the characteristics of the successive response signals will normally not affect the operation of the underwater seismic system 100 in a material way.

Each response signal is received by the recorder 122 which then causes a point to be plotted by an electrically activated pen (not shown) that regularly sweeps the recorder chart (not shown). In effect, the recorder mechanically computes and plots the time elapsed from the generation of the trigger signal to the receipt by the recorder 128 of the response signal. The portion of the chart recording so produced will also be indicative of the distance to the reflecting layer giving rise to the reflected sound pulse, since the average distance to the reflecting layer during the travel time of the sound pulse and reflected sound pulse will be proportional to the time elapsed, the constant of proportionality being the velocity of sound divided by two. In a similar manner, the recorder 122 simultaneously plots from other response signals the distances to other reflecting layers.

The extent of the delay between the initiation of the sweep by the sweep circuit 124 and firing of the sound source 128 depends on the vertical displacement signal produced by the filter 46. The delay circuit 120 receives the displacement signal and delays the trigger signal by a fixed period plus a varying period, the varying period being proportional to the displacement signal. Thus, as the towed body 102 is displaced downwardly, the delay in the firing of the sound source 128 is increased; as the towed body 102 moves upwardly, the delay is decreased and the firing is effectively advanced.

Changes in the delay in firing of the sound source 128 will be related to changes in the vertical displacement of the body 102 by a constant of proportionality which is twice the reciprocal of the velocity of sound in water. With such a constant of proportionality, the vertical displacement of the towed body 102 will appearto be the samed at successive firings, for the purposes of the recorded 122.

A more detailed description of apparatus compris ing an underwater seismic system such as the underwater seismic system 100 may be obtained from the Hutchins patent referred to above.

Claims (16)

1. For use in association with a body travelling through water, the body having an accelerometer that produces an acceleration signal including an accelerometer noise signal corresponding to the effect of gravity on the accelerometer, a selfadjusting filter for reproducing the acceleration signal with an attenuated accelerometer noise signal, the self-adjustable filter comprising:: correction signal generating means connectable to the body for generating a correction signal proportional to portions of the accelerometer noise signal; variable scaling means connected to the correction signal generating means for producing a scaled correction signal proportional to the product of a scale factor and the correction signal; summing means connected to the accelerometer and to the variable scaling means for generating a summation signal proportional to the sum of the acceleration signal and the scaled correction signal whereby signal components of the summation signal corresponding to the portions of the accelerometer noise signal and to the correction signal tend to cancel one another; and correlation means connected to the summation means and to the correction signal generating means for generating a correlation signal indicative of the correlation between the summation signal and the correction signal, and connected to the variable scaling means for varying the scale factor in proportion to the correlation signal so that the summation signal components corresponding to the portions of the accelerometer noise and to the correction signal tend to cancel completely.

2. A self-adjusting filter as claimed in claim 1 in which the correlation means comprise: a first error enhancing filter connected to the summing means to generate a first filtered signal corresponding to the summation signal with at least zero frequency signal components thereof attenuated relative to non-zero frequency components of an error signal component proportional to the difference between the accelerometer noise signal and the correction signal; a second error enhancing filter, connected to the correction signal generating means to generate a second filtered signal corresponding to the correction signal, the second filter having phase shifting characteristics substantially identical to those of the first filter at least over the frequency range of the accelerometer noise;; multiplication means connected to the first and second filters for generating a product signal proportional to the product of the first and second filtered signals; and, integration means connected to the multiplication means for generating the correlation signal, the correlation signal being proportional to the integral of the product signal.

3. A self-adjusting filter as claimed in claim 2 in which the first and second filters have substantially identical transfer functions;

4. A self-adjusting filter as claimed in claim 3 in which the pulse generating means comprise: absolute value generating means for generating an absolute value signal proportional to the absolute value of the product signal; and, a voltage-to-frequency converter connected to the absolute value generating means for generating a stream of pulses whose frequency varies in propor tion to the absolute value signal.

5. A self-adjusting filter as claimed in claim 4 in which the tallying means comprises: sign detecting means for generating a first sign signal when the product signal has the first polarity and a second sign signal when the product signal has the opposite polarity; and, an up-down counter connected to the voltage-tofrequency converter and to the sign detecting means for generating the tally signal, the tally signal increasing by one unit each time a pulse is generated and the sign detecting means generates the first sign signal and decreasing by one unit each time a pulse is generated and the sign detecting means generates the second signal.

6. A self-adjusting filter as claimed in claim 5 in which the variable scaling means comprise: a digital-to-analogue converter that generates the scaled correction signal from the correction and tally signals, the scale factor varying in proportion to the value of the tally signal.

7. A self-adjusting filter as claimed in claim 6 in which the multiplication means comprise a dead zone buffer that reduces the product signal to a zero value when the absolute value of the product of the first and second filtered signals is less than a predetermined value.

8. A self-adjusting filter as claimed in claim 6, comprising filter means connected to the summing means for generating from at least the summation signal a signal indicative of the vertical displacement of the body.

9. A self-adjusting filter as claimed in claim 8 in which the first zero frequency blocking filter comprises portions of the filter means, connected to the summation means, having a transfer function comprising a zero frequency zero.

10. For use in association with a body travelling through water, the body having an accelerometer which produces an acceleration signal indicative of the body's acceleration along an axis whose angle of orientation with respect to a vertical position, H, varies with pitching and rolling of the body, a projection of the axis on a first vertical plane being inclined at any instant from a vertical position by an angle 81, a projection of the axis on a second vertical plane perpendicular to the first plane being inclined at any instant from a vertical position by an angle H2, the acceleration signal including an acceleration noise signal corresponding to the effect of gravity on the accelerometer, a self-adjusting filter for reproducing the accelerometer signal with an attenuated accelerometer noise signal, the self-adjusting filter comprising: correction signal generating means connectable to the body for generating a correction signal proportional to portions of the accelerometer noise signal; variable scaling means connected to the correction signal generating means for producing a scaled correction signal proportional to the product of a scale factor and the correction signal; summing means connected to the accelerometer and to the variable scaling means for generating a summationsignal proportional to the sum of the acceleration signal and the scaled correction signal so that signal components of the summation signal corresponding to the portions of the accelerometer noise signal and to the correction signal tend to cancel one another; and correlation means connected to the summation means and to the correction signal generating means for generating a correlation signal indicative ofthe correlation between the summation signal and the correction signal, and connected to the variable scaling means for varying the scale factor in proportion to the correlation signal so that the summation signal components corresponding to the portions of the accelerometer noise and to the correction signal tend to cancel completely.

11. A self-adjusting filter as claimed in claim 10, in which the correction signal generating means comprise: first signal generating means connectable to the body for generating a first cosine signal proportional to the cosine of e7; second signal generating means connectable to the body for generating a second cosine signal proportional to the cosine of e2; and, cosine product generating means connected to the first and the second cosine signal generating means for producing the correction signal, the correction signal being proportional to the product of the first and second cosine signals.

12. A self-adjusting filter as claimed in claim 11, in which the first signal generating means comprise: a first transducer connectable to the body for producing a first transducer signal proportional to H; and, a first cosine function generating means connected to the first transducer for producing the first cosine signal from the first transducer signal.

13. A self-adjusting filter as claimed in claim 10 in which the correction signal generating means comprise: a first transducer connectable to the body for producing a first transducer signal proportional toO; a second transducer connectable to the body for producing a second transducer signal proportional to e2; and, approximation signal generating means connected to the first and second transducers for producing the correction signal from the first and the second transducer signals, the correction signal being proportional to components of a power series expansion in 01 and H2 of the cosine of H;

14. A self-adjusting filter as claimed in claim 13 < in which the approximating signal generating means comprise: a first squaring means for producing a first squared signal proportional to the square of the first transducer signal; a second squaring means for producing a second signal proportional to the square of the second transducer signal; and, square sum generating means connected to the first and the second squaring means for summing the first and second squared signals to produce the correction signal, the correction signal being proportional to the sum of H12 and 022.

15. A self-adjusting filter for use in determining the position of a body travelling through water, constructed and arranged for use and operation substantially as described herein with reference to the accompanying drawings.

16. A method of determining the position of a body travelling through water, substantially as described herein with reference to the accompanying drawings.