GB2366617A - Towed sonar array - Google Patents

Abstract

The left/ right ambiguity in bearing of a target from a towed array is resolved by determining heading oscillations of a towed array with bearing oscillations. A time varying function of these oscillations is produced and the sign of the correlation then determines the left/ right position. By using a selected algorithm with a data integration time of a few minutes the bearing ambiguity of a detected target can be resolved much more quickly than current arrangements which require about 20 minutes, needing the towing ship to make a turning maneouvre before returning to course while observing the positional change of the target. The array 11 has at least two heading sensors 13,14 which are averaged 21 to give a mean heading. High frequency signal components due to measurement noise are filtered from the heading and bearing sensors. Bearing is measured by beam steering using controlled elements W <SB>1</SB>- W <SB>n</SB> and selecting the direction of maximum signal 23. The target bearing measurements from the phased sonar array sensors are the processed 24 with the averaged heading measurements 21.

Description

2366617 A Towed Sonar Array &;pAratus f= Resoly Left/Right.Ambiguity The

invention relates to towed linear sonar arrays which have axial Symmetry and to a means for resolving directional ambiguity of a detected source of sound.

The towed array comprising a linear line of.hydrophones possesses a conical beam pattern. It follows that there exists an inherent left/right ambiguityr so that it cannot tell whether a target is on the left or the right of the array. The conventional method of resolving the ambiguity is for the tow vessel to make a course change of 10 to 20 degrees. Depending upon whether the apparent bearing of the targetr as seen by the arrayt moves f orward or aft through the beams, the target can be correctly assigned to port or starboard. The disadvantages of this method are that it takes time to perfom the manoeuvre and return to the original courser and scmetimes a weak target can be lost while the manoeuvre is being performed.

The object of the present invention is to provide a solution to the left/ right ambiguity which overcomes the disadvantages of the existing solution.

The invention provides a linear towed sonar array apparatus comprising: a means connectable to the array for determining the array heading; signal processing means connected to the hydrophones, of the array for determining the bearing of a source of sound relative to the array heading; and means to correlate the array heading and bearing measurements as a function of time; the arrangement being such that the source lef t/right ambiguity relative to the array is resolved by the sign of the measured correlation.

Preferably the array includes two heading sensors, one at the f ront and one at the rear of the array, the array heading being determined f rom the mean heading of the two sensors. Advantageously the heading and bearing measurements are filtered to remove high frequency fluctuations due to measurement noise.

The invention will now be described by way of example only with reference to the accompanying Drawings of which:.

Figure 1 schematically illustrates the lef t/right ambiguity existing when a towed sonar array receives sound from a remote source; Figure 2 is an exploded block diagram illustrating the towed array signal processing for resolving left/right ambiguity; Figure 3 illustrates the hypotheses: Hl that the sound source is to port and H2 that the sound source is to starboard; Figure 4 shows graphs of successive measurements of mean array heading and source bearing; Figure 5 shows the Figure 4 data after digital filtering; and Figure 6 shows plots of two algorithms Fl (assumed constant bearing of source f ram array) and P2 (assumed linear change in relative bearing of source f rom array).

As shown in Figure it when a vessel 10 tows a linear sonar array 11 of spaced hydrophones, l2r the array is able to estimate the bearing e of a sound source SR by means of array beam steering. The outputs f rom each hydrophone 12 in the array are added with appropriate relative phase delays such that the array has a high sensitivity in a pre-selected direction e which can be scanned to search for sound sources. Because of axial symmetry the towed array cannot resolve the real source SR from the virtual source SV: the -so- called left/right ambiguity.

The normal method for resolving this ambiguity is f or the towing vessel 10 to make a course change by an angle j6,, sayr and to observe the effect of the resulting change of heading of the towed array 11 on the observed bearing e. If the angle er as shownr increases then the source must be on the right of the array ll,, in the direction of the course change j6r and conversely if the angle & decreases then the source must be on the left of the array.

Experience of the inventor has shown that the heading of an array under tow is rarely constant. It oscillates in the horizontal plane about the mean heading with an amplitude of 1 or 2 degrees and with a period of several minutes. These oscillations are most likely due to the tow vessel not following a perfectly straight courser but they may also be due to environmental effects. Howevert the cause is unimportant. These oscillationst assumed to be small amplitude#, long periodr transverse oscillations in the array form the basis of the present invention for resolving the L - R bearing ambiguity.

Heading sensors 11? 14 are provided at the f ront and rear of the towed array 11. The array heading is then assumed to be the mean of the headings measured by the two sensors 13#,14,, derived by adding the sensor outputs (21 in Figure 2). The bearing (e) of a measured sound source is found by cyclically changing the beam steering angle of the array 11 by appropriate changes of the relative phasesL-\l... Z-n applied to the outputs of the n hydrophones of the array by a phase programmer 22. The phase delayed hydrophone outputs are sumied in an adding circuit 23 arranged to store the bearing corresponding to the maximum detected sum. Since the beam steer angles are discrete and non-continuous the bearing of the sound source is found by interpolation, using the beam bearing that produces the maximum signal output together with the two adjacent beam bearings. The heading and bearing readings are correlated (24) over a period of about 10 minutes and the left/right position relative to the line of the array is determined f rom the sign of the correlationt as will be described below.

To illustrate. the ideas suppose that there exists a moving contact on a truer ambiguous bearing X (t) r a function of time. This true bearing is relative to some f ixed reference direction which we chooser for conveniencer to coincide with the mean course followed by the array. Although unrealiStiCr we assume to start with that X (t) is known. Let a (t) denote the array heading relative to the mean courser and let b (t) denote the ambiguous bearing of the contact measured by the array. This gecmetry is shown in Figure 3.

Let H 1 be the hypothesis that the contact is to port and H2 the hypothesis that it is to starboard. We require a method for choosing between HI and H2.

Suppose f irst that a (t) and b (t) are exact, noise f ree measurements. It is then evident frcm Figure 3 that a(t) and b(t) are related under each hypothesis as follows:

Hl: b(t) = X(t) - a(t) H2: b(t) = X(t) + a(t) This suggests that a suitable criterion for resolving the ambiguity of the 4 contact is F = a(t) [X(t) - b(t)] (2) By substituting (1) in (2) it follows that Hl: F = + a2(t) (3) H2: F = -a2(t) so that for all times t the ambiguity is resolved according to the sign of F.

In practice the measurements a (t) and b (t) are not noise free. Errors will exist in a (t) due to inherent inaccuracies in the heading sensors and due to imperfections in the method of calculating array heading f rom the data generated by these sensors. Also errors will exist in b (t) due, for example, to the f inite signal to noise ratio of the contact on the array. These various errors.may contain both systematic and random components.

we can expect to reduce the ef f ect of the random errors by redef ining F in (2) as a temporal mean. Thusr with the integration included, the algorithm becomes F = a M3 - -a-CETEM (4) where T (-) -= of () dt (5) From (1) and (4) we then derive Hl: F = + a2(t) (6) H2: F = - a2(t) and the ambiguity is again resolved to the sign of F.

The immediate difficulty with algorithm (4) is that it assumes a perfect knowledge of the function,\ (t) representing the error freer true, ambiguous bearing of the contact. Such prior knowledge will clearly not be available. In order to make progress it is necessary to make some assumption about the true motion of the contact and then to estimateX (t) from the measured data. The simplest assumption is that the contact is stationary so that > (t) M No (7) an unknown constant. Then taking temporal means in (1) and re-arrangingo, we obtain Hl: Xo = b(t) + a(t) H2: Xo = b(t) - a(t) (8) Since Hi and H 2 are equally likely it is sensible to choose X0 = b(t) (9) as the estimate for the constant target bearing.

Algorithm (4) then becomes F, = 'T-(t). 19(--t-) - a (t) b (t) (10) so that under each hypothesisr using (1) Hl: Fl = + ( az (t) - -aTtET21 H2: Fl = - [ az (t) - a (tT21 and the ambiguity is resolved according to the sign of Fl. Note that the algorithm (10) is insensitive to any constant bias in the estimate of contact bearing b(t) measured by the array: as may be verif ied by direct substitution. It is also evident from its symetry that algorithm (10) is equally insensitive to any constant bias in the estimate of array heading a(t). The reason for this symmetry is that on the basis of the measured data alone it is inpossible to decide whether a bias, if it exists, is assignable to a (t) or to b(t).

Algorithm (10) is still not ideal. The main problem is that it assumes that the contact is stationary during the measurement period. In some circumstances it may be moving at a bearing rate comparable with the rate of change of array headingr in which case the algorithm would be biased. r1be next stage is therefore to generalise assumption (7) to allow for contacts moving at constant but unknown bearing rates. We then assume that the variation with time of the true contact bearing is of the form X (t) = X o + X1 (t/T) (12) where /\o andX1 are constants to be determined from the measured data.

After substituting assumption (12) into (1) and taking temporal means we obtain Hl: Xo +1/2 Xl = E-W + a(t) H2: X0 +1/2 Xl = U-(-t) - a (t) Since Hl and H2 are equally likely hypotheses it is sensible to choose Xo + 1/2 AI = b (t) (14) A second equation is obtained by post-multiplying equation (1) by t and again taking temporal meansr providing the relation 1/2 \o + +1/3,\l = (t/T)b(t) (15) The solution of equations (14) and (15) for the two unknowns is Xo = 4 F(-t) - 6 (t/T)b(t) (16) Xl = 12 (t/T) b (t) - 6 b (t) This solution can also be obtained as the best least squares f it of the assumed form (12) for X(t) to the measured data b(t).

Finally, substitution of equations (12) and (16) into (4) provides the algorithm F2 = i-M-F-M - a(t)b(t) + 121(t/T)a(t)-1/2 T(-t)] 1(t/T)b(t)-1/2 b(t)] (17) We then find that under each hypothesis Hi: F2 = + (az (t) -aTt-T2 - 12 [ (t/T) a (t) - 1/2 -a-TET) 2) H2: F2 = - (a2 (t) - -a-(-tT2 - 12 [ (t/T) a MY - 1/2 -aTtTi 2) So that the ambiguity is now resolved according to the sign of F2. This algorithm works for a moving contact provided that the bearing rate is constant. By symmetryt it is also insensitive to errors of constant drift rate in the estimate a(t).

The algorithms in equations (10) and (17) above were derived by an intuitive approach and are not necessarily optimal for resolving the leftright ambiguity,, although under certain circumstances they can be shown to be so. Optimal algorithm have been derived in the form of generalised likelihood ratio tests on the basis of the two sets of assumptions employed in (7) and (12) abover namely a. stationary contactr unknown bearing b. moving contactr constant but unknown bearing rate.

In additiony it was assumed that a (t) and b (t) are sampled discretely in time rather than continuously; for exampler each discrete value of b might represent a bearing estimate obtained f rom processing a single time f rame of acoustic array data. It was also assumed that the noise on each sample is Gaussiant though not necessarily uncorrelated over the measurement period. In particularr the noise covariance matrices are denoted by Ba and Bbf respectively, each being an n x n matrix where n is the number of time samples. The resulting algorithms were found to depend only on the sum of the noise covariance matrices -R = Ra + -Bb (19) It is then useful to examine specific cases. It is realistic to assume that the noise on the contact bearing estimates is uncorrelated between samples. This assumption may not be so realistic for the noise on the array heading estimates, particularly if the heading sensor outputs are quantized. Neverthelessr we shall assume for simplicity that all noise components are uncorrelated between samplesi, so that R is proportional to the identity matrix.

The algorithms then reduce to:

Fl = ar.Fr- - -ir-b-r (20) for the case of a stationary contact with an unknown bearingr and F2 = ar.-1Tr-:a-r-br + n2-llrar-1/2(n+l)arl Erbr-1/2(n+l)br] (21) for the case of a moving contact with a constant but unknown bearing rate where n I - h () (22) r=1 denotes the mean value.

These algorithmsi, derived by the likelihood approachr are seen to be precisely the discrete versions of algorithms (10) and (17) derived earlier by an intuitive approach. it follows that under the conditions and assumptions stated these algorithms are optimal for resolving the L-R bearing anbiguity.

Whichever of the above algorithms is employed to resolve the left/right anbiguityr the output after a given observation period is a single nuffber which then forms the basis for a decision. Since the problem is symmetric in the two hypothesest the threshold is set to zero and the decision made according to the sign of the output F. But F is itself a random variable with probability density p(F) rsay. The probability of a correct decision is therefore 05, '0 Pr = lop (F/Hl) dF = lp(F/H2)dF. (23) d, Evaluation of Pr requires p(F) to be calculated from the algorithm definition. We shall not attempt an exact analysis but instead suppose that the integration time is sufficiently long for the distribution of F to be considered Gaussian. Only the mean m and the variance o2 of F need then be calculated. It follows that p(F/Hl) = J(2T%)"2 61-1 exp [ -(m-F)2/2621 (24) where m = F(ALb/Hl)/ (25) 62 = KF2 (ALb/Hl) ra - (26) Equation (23) then reduces to Pr = 1/2 11 + erf(2-1/2d)] (27) where erf denotes the standard error function and d = m/6 (28) is a decision index incorporating the performance of the algorithm F. For example, employing tables f or the error functiont we f ind that to obtain 98% confidence that the decision is correct d > 2 must be satisfied.

The decision index d in equation (28) has been derived for the particular algorithms Fl and F2- If we specialise to the case of uncorrelated noise the results for m and 6 provider for large nr d n/2 6A2 2) 45 2 + da26 2] (29) 1 ((5a2 + 6b A b where, in the case of a stationary contact of unknown bearing, 6A2 = r2 - Ar2 (30) and in the case of a moving contact of constant but unknown bearing rater 6A2 = -A-r2 - Tr- 2 - 12 ITA-r (n+l) Tr-1 2 (31) 2--l and 6a2 and 6b2 denote the noise variances on the estimates a and br respectively. The parameter 6A2 depends only on the error-free array heading values Ar spanning the observation period.

The generalised algorithms do not readily lend themselves to practical implementation. we shall therefore consider only those simpler algorithms accepting that they may not be quite optimal. In factr since it is more robust to bias errorsr we shall concentrate on algorithm F2 in equation (21) and examine its ability to resolve the left/right ambiguity in a typical situation.

Suppose then that the array heading is described by a sinusoidal. oscillation in time of the form:

A = Ao sin (27t/P), (32) where Ao is the amplitude of the heading oscillation (in radians) r and P is the period. Suppose that estimates of contact bearing and array heading are taken at time intervals 'tr so that af ter an observation period T the number of sampl e points is n = T/t. We then f ind f rom equations (29) (31) and (32) that the decision index d can be expressed as:

d (33) + where H 66) = (1/2) -Bim-26 - (1-- g 5. 16) 2 -_a [2sin 6 -cos6-l] 2 (34) 46 together with the definitions o( 2-iiT'/P'r T'. 26a6j,' T P1 = 126a6j, k, 62 6 2 a+62b) at b) (35) r (62a+62b Wo (36) 262a,62b By writing the result (33) in this form we minimise the effective number of variables. In the definitions (35), T' is the dimensionless observation time and PI is the dimensionless period of array oscillation. 7he parameter r in (36) is a type of signal to noise ratio, incorporating the amplitude of the array heading oscillation on the one hand and the errors in the estimates of heading and bearing on the other. We would expect the algorithm to perform best for large values of r.

We have already deduced that 98% confidence in the left/right decision is obtained if d > 2. Equation (33) may then be employed to determine the observation time required to achieve this degree of confidence.

Generallyr it has been shown that it is not necessary to integrate teiqmrally f or longer than one couplete period of. the array oscillation. This integration time would be expected to lie in the range 1 to 10 minutest depending upon the noise variances.

The algorithmsr developed above for resolving the left/ right ambiguity used the small variations in measured array heading and contact bearing resulting f rom the assumed existence of small amplitude, long periodi, transverse oscillations of the array. The algorithms are robust to bias and drif t errors in the heading and bearing measurementst and under certain conditions are optimal.

The above algorithms have been applied to heading and noise source bearing data obtained f rom a towed array. The heading sensors, one at each end of the arrayr were gimballedr optically seamed magnetic compasses which provide an optically coded signal which is converted to a serial pulse train (N+1 pulsesr where N is the number of degrees of heading). Long period ( c 10 minutes) transverse oscillationsr evident in most of the datar indicated that the variation was not due to random noise.

Figures 4o, 5 and 6 are representative of the results. Figure 4 coupares the mean of the fore and aft array magnetic sensor outputs and the measured source bearingst both sampled at 5 see intervals. Since 240 samples are displayed: the data therefore spans a period of 20 minutes. In both cases the I Y axis I has been shif ted to aid presentation and does not represent absolute headings. 7he effect of applying low pass digital filtering with a time constant of 1 minute to both sets of data is shown in Figure 5. This smooths the high frequency oscillations which are uncorrelated between the two data sets and therefore attributed to noise, leaving the longer term variations which are of interest. The results show evidence of a cyclic oscillation in the latter half of the data sets of period approximately equal to 9 minutes (108 samples).

In order to compare the outputs of the two algorithms,, Fl and F2 given above, it is useful to normalise F1 and F2 such that normalised values of Fl and F2 will lie between -land +1. Confidence in the results will then increase as either of these limits is approached. Thus if Hi is the hypothesis that the noise source is to port and H2 the hypothesis that it is to starboardr then:

Hl: -I<F<O and H2: O<F<+l i.e. the sign of F resolves the ambiguity.

Plots of normialised Fl and F2, employing as inputs the smoothed data of Figure 5, are shown in Figure 6 against the sample number. After an initial period of stabilisationr both algorithms eventually settle down after about 80 samples to correctly resolve the L-R ambiguity. It will be noted that towards the end of the observation period the output of algorithm Fl approaches zero. on the other hand the algorithm F2, which is less restrictive than Fl in its assumptions about the motion of the sound sourcer continues to-give a confident and correct answer.

The results obtained f rom limited trials database suggest that the algorithms derived above can resolve left/right ambiguity when applied to empirical data. In the cases where bearing ambiguity was firmly resolvedr the time taken to conf irm this decision was less than 10 minutes f rom visual inspection of the F1 and F2 plots. The general experience is that the decision eventually reached by F2 is more reliable than that reached by Fl.

The mst significant effect of filtering the input data on algorithm performance is to increase the amplitude of the normalised Fl and F2 values for each sample. This has the undesirable side-effect that the filtered results give an apparently wre confident decision on the left/right ambiguityr regardless of whether the decision indicated is in fact correct or incorrect.

Normalisation of the algorithms provides a means of comparison between data setst but the method of deriving statistically valid conf idence limits is not innediately evident, since the presence of tim history trends must be taken into account. It is desirable to find a decision index which is a more reliable measure of the confidence assigned to the ambiguity resolution. The foregoing analysis has assumed that the length of the towed array is short compared with the wavelength of the heading fluctuations. If the array is very long compared with the wavelength of the heading fluctuations then the heading and bearing fluctuations will be averaged out. This is not a constraint when considering a long towed array because the array sensors can be processed as a plurality of short array sectionsr each provided with at least one heading sensor. The left-right target awbiguity for the sections can then be averaged to give a final result.

The heading fluctuations previously considered originated as a consequence of manual or automatic pilot ship navigation. small oscillations in heading could be deliberately introduced with a selected period to enhance the array left-right processing. This could be done by modifying the autopilot progrmm,Ling or by introducing minor heading changes.

Claims (6)

Claims

1. A linear towed sonar array apparatus cwprising: a means connectable to the array for determining the array heading; signal processing means connected to the hydrophones of the array for determining the bearing of a source of sound relative to the array heading; and means to correlate the array heading and bearing measurements as a function of time; the arrangement being such that the source left/right ambiguity relative to the array is resolved by the sign of the measured correlation. 2. A linear towed sonar array apparatus as claimed in claim 1 wherein the array includes two heading sensors, one at the f ront and one at the rear of the array, the array heading being determined from the mean heading of the two sensors. 3. A linear towed sonar array apparatus as claimed in claim 1 or 2 wherein the heading and bearing measurements are filtered to remove high frequency fluctuations due to measurement noise. 4. A linear towed sonar array apparatus as claimed in anyone preceding claim wherein the measurements are averaged over a period of time to remove the effects of random fluctuations due to measurement noise. 5. A linear towed sonar array apparatus as claimed in anyone preceding claim wherein a left/right decision algorithm is employed assuming that the sound source is at a constant bearing rate from the towed array. 6. A linear towed sonar array apparatus as claimed in anyone of claim 1 to 4 wherein a left/ right decision algorithm is employed assuming that the sound source is at a constant position.

Amendments to the claims have been riled as follows 1. A linear towed sonar array apparatus for resolving the left/right ambiguity of direction of a source. of sound when the array is subject to variations in heading comprising:

a) a means connectable to the array for determining the array heading; b) signal processing means connected to the hydrophones of the array for dei:ermining the bearing of a source of sound relative to the array heading and to determine a time varying function of the array headings and bearing measurements; the arrangement being such that the source left/right ambiguity relative to the array is resolved by the sign of the function.

2. A linear towed sonar array apparatus as claimed in claim 1 wherein the array includes two heading sensors, one at the front and one at the rear of the array, the array heading being' determined from the mean heading of the two sensors.

3. A linear towed sonar array apparatus as claimed in claim 1 or 2 wherein the heading and bearing measurements are filtered to remove high frequency fluctuations due to measurement noise.

4. A linear towed sonar array apparatus as claimed in any one preceding claim wherein the measurements are averaged over a period of time to N remove the effects of randow I'IUCLWIuions dLie to iiieasLireillent noise.

5. A linear towed sonar array appiratus as cl-aimed in iny one preceding claim wherein a left/right decision algorithm is employed assuming that the sound source is at a constanL beaj-ing rate f'rom the towed array.

6. A linear towed sonar arriy ipptit-atus Es claiiiied in any one of claims 1 to 4 wherein a left/i,j.ght. decjsjo!i is employed assuiiiing that the sound source is at a consLanL position.