Clean Data Training Approach to Active Sonar Classification

Transcription

1 Clean Data Training Approach to Active Sonar Classiication Alexei Kouzoubov (1), Binh Nguyen (1), Shane Wood (1) and Chris Gillard (1) (1) Deence Science and Technology Organisation, Edinburgh, SA, Australia ABSTRACT An approach to oring a training data set or active sonar classiication ro the ree-ield noiseless echoes o underwater objects is considered. The approach has been tested on siulated data based on laboratory easureents. Both the test and the training data are generated ro the clean data by applying two environent paraeters: noise and a channel altipath. It was investigated how well the paraeters o the channel used or oring the training data should atch those used or generating the test data. The dependence o classiication accuracy on the pulse requency bandwidth was also investigated and shown to increase with increasing bandwidth.. Soe knowledge o the environent is required or the application o this approach to real sonar data. INTRODUCTION An ability to classiy active sonar echoes is iportant in Anti-Subarine Warare (ASW). The supervised classiication techniques, which are used in this paper, require training data or each object class (Theodoridis & Koutroubas, 2006). In the ost coon approach to active sonar classiication, all sonar echoes are divided into two classes: those originating ro the target o interest, such as a subarine, and all other, non-target, echoes. The training data or both classes should be representatively sapled ro all possible echoes to provide good classiication accuracy. In the underwater environent this task is coplicated by the act that the echoes ro the objects are distorted by the propagation eects, such as ultipath, reverberation etc. As a result o this, training classiiers on the echoes obtained ro targets in the ree-ield, noiseless conditions does not necessarily lead to accurate classiication o the echoes ro the sae targets because they are odiied by the propagation in the underwater environent (Ainslie, 2010). Obtaining the reeield data or the targets o interest is not an easy task. It is uch ore diicult, however, to obtain echoes ro these targets in all possible environents to or a universal training data set. It is thereore o interest to develop a classiication approach based on the noiseless ree-ield target echoes, or in other words clean training data, to classiy target echoes distorted by the underwater propagation. In atheatical ters the proble can be orulated as ollows. Assuing that we have clean target echoes x i ( t), classiy the test echo x() t distorted by the propagation, so the recorded echo available to the classiier is () t h() t x() t w() t z = +, h () ( ) where t is the propagation transer unction and w t is the noise. There are several solution strategies or this proble. They include: - Use o channel invariant eatures, i.e. the eatures not aected by the propagation (Okopal et al., 2008). - Use o the so-called blind deconvolution to reconstruct the clean target signal (Kil & Shin, 1996). This ethod required soe knowledge o the environent paraeters. - Use o orward odelling to odiy the clean data by the propagation and use it as the training data. This ethod also requires the knowledge o the environent (Liu et al., 2004). In the present research we apply orward odelling or a range o environental paraeters to or the training data set and investigate how well we need to know the environent or building the training data set. DATA DESCRIPTION The clean acoustic data or this research were obtained in the water tank located in the Underwater Acoustic Scattering Laboratory (UASL) at Maritie Operations Division o DSTO. Two objects were used to represent dierent classes: a odel o a generic subarine and a concrete cylinder o siilar size. The generic subarine odel is ade o brass with a hull length o about 700 and a diaeter o 80. The concrete cylinder length is 560 and the diaeter is 72. A scheatic diagra o the experient setup or the acoustic scattering easureents is shown in Figure 1. To collect acoustic scattering data, the object was suspended in the tank on our thin wires at a depth o 2. The tank is o 9 length, 6 width and 4 depth. The acoustic unit transducer, which cobines both transitter and receiver in one housing, was positioned about 4 away ro the object at the sae depth. The object was insoniied with short pulses o 200 μs in duration. The echoes o the objects were recorded by the data acquisition syste. The aspect angle o the object with respect to the transitter was changed in the range ro -5 to 362 degrees with one degree increent resulting in 368 echoes or each object. In case o the subarine odel, zero degree aspect angle corresponds to the position o the odel with its bow directed towards the transitter. Siilar or the cylinder, zero aspect angle eans that its axis is aligned with the direction to the transitter. Australian Acoustical Society Paper Peer Reviewed 1

2 Input iles Measureent and control Controlling coputer Target location and orientation Signal generator RF Apliier see ro the igure that the clean data ro the two dierent objects have clearly dierent structure. The subarine odel data have ewer well structured highlights relecting the siple design o the generic odel. The data in the botto plot have any randoly positioned highlights due to the rough surace o the cylinder with nuerous cavities randoly located on the surace. Target Transducer + hydrophone Analysis Figure 1. Setup or scattering easureents in UASL tank. At each aspect angle our incident pulses with dierent requency bandwidth were used. A technique o odiying the input pulse to account or the transer unction o the transitter in order to generate incident pulses with suiciently lat spectru within the bandwidth was applied (Swincer et al., 2012). The ollowing our requency bands o the incident pulses were used: - band 1: khz; - band 2: khz; - band 3: khz; - band 4: khz. The power spectra o the our incident pulses are shown in Figure 2. D d Figure 3. Hour-glass plot o echoes ro the generic subarine (top) and concrete cylinder (botto) or the incident pulse with the requency bandwidth o khz (band 1). The power spectra o the two objects are suarised in Figure 4 as two-diensional requency aspect plots. The data in this plot are shown again or the bandwidth o band 1, khz. Figure 2. Power spectra o the incident pulses. The echoes o the objects are strongly aspect dependent. This is clearly visible in Figure 3, where the so-called hour-glass plots o echoes o the generic subarine and the concrete cylinder are shown or the incident pulse with the requency bandwidth o khz (band 1). These plots show the absolute value o the return signal in two diensions: tie and aspect angle. Thus, at the aspect angle o zero degrees, the earliest highlight is ro the bow o the subarine odel, the iddle is ro the in, and the last is ro the tail structure. At the aspect angle o 180 degrees the sequence o highlights is opposite. O course the shortest and strongest echoes are at the aspect angles o 90 and 270 degrees, when the object is positioned with its side acing the transitter. One can 2 Australian Acoustical Society

3 kernel unction. In this article we use the polynoial kernel, p K(x,z) = ( < x, z > +c). There are any approaches to calculating eatures ro the active sonar echoes. In this report we liit ourselves to the set o twenty ive eatures described in Tucker&Brown (2005). The eatures are based on the Short-Tie Fourier Transor o the object echoes. The results o classiication can be presented in a dierent or such as the Receiver Operating Characteristic (ROC) curve, conusion atrix etc. Here we use two criteria to estiate the perorance o the classiication: the area under the ROC curve (AUC) and the average accuracy o classiication. Those criteria are single valued paraeters allowing presentation o the results o classiication in a siple or. The average accuracy o classiication is the average o the diagonal eleents o the conusion atrix. In other words, it is the average o true positive and true negative classiications o the test data echoes. The ROC curve is built by changing the decision threshold and calculating corresponding True Positive Rate (TPR) versus False Positive Rate (FPR). The True Positive Rate is calculated as the ratio o True Positives to the total nuber o Positives, and the False Positive Rate is calculated as the ratio o False Positives to the total nuber o Negatives. In our ipleentation the eleents o class one are considered as Positives and the eleents o class two are as Negatives. The decision threshold is speciic to a classiier. Figure 4. Frequency aspect power spectru plots or the generic subarine odel (top) and the concrete cylinder (botto) or the incident pulse with the requency bandwidth o khz (band 1). CLASSIFICATION FEATURES AND ALGORITHM In this research we use the kernel ridge regression classiier as described in Saunders et al. (1998). The algorith ay be suarized as iniizing a quadratic loss unction: l ( y i g( xi )) 2 2 L = λ w +, i= 1 where x is the data vectors o the training saples, i,1 i l y i is their class labels, and λ > 0 regulates the nor. Given the training data, the classiication algorith inds the real valued linear unction g ( x) = w, φ( x) that iniizes the above quadratic loss unction. The unction φ ( x) aps data vector x into the eature space. It can be shown that the label g(x) o a test vector x is calculated as g ( x) = y ( K + λι ) train λ 1 K test where y is the vector o class labels o the training data. For exaple we ay assign y = -1 or eleents o class 1 and y = 1 or eleents o class 2. Ι λ is the identity atrix o diension l corresponding to the nuber o training exaples. The training and test kernel atrices, K and are ored train Ktest ro training and test data vectors according to a selected To build the ROC curve or the Ridge Regression Classiier we threshold the decision unction g( x). In its traditional or the decision is ade according to the ollowing rule: i g i g ( x) < 0, x P ( x) > 0, x N where P stands or Positives, or class one, and N denotes negatives, or class two. Introducing threshold in the decision rule will result in the ollowing rule: i g i g ( x) < T, x P ( x) > T, x N The ROC curve is built by sweeping the threshold in the interval ax( g( x) ) T ax( g( x) ) and counting True Positives and False Positives or each value o the threshold. The AUC can be calculated by nuerical integration o the ROC curve or directly according to the ollowing equation: AUC = n + n i= = > j 1 g ( xi ) g ( x j ), + n n + where x and x denote the positive and negative saples, + respectively, n and n are the nuber o positive and negative saples, respectively. 1 π is deined to be 1 i the predicate π holds and 0 otherwise. SYNTHETIC DATA GENERATION To test the classiication approach we use synthetic active sonar data generated ro the laboratory acoustic scattering data described above. The synthetic data are generated by Australian Acoustical Society 3

4 applying the channel ilter and noise to the clean data echoes obtained in the laboratory in a ree-ield noiseless environent. Both test and training data are constructed in a siilar way but using dierent values o paraeters or the channel ilter and noise. The algorith or building the synthetic data () i is as ollows. The clean data echo, x k, where i is the tie saple index and k is the aspect angle index, is convolved with the specially constructed channel ilter, h ( i;s ). The paraeter characterises echo elongation due to ultipath. S The randoly generated noise, convolved signal: z () i = h( i; S ) x () i w() i k k + h ( i S ) = h ([ ns ]), 0 i [ ns ] ; 0 M h0[ n] = γ δ = 1 [ n d ], M = 15, 0 n 99, d γ = ± e βd, β = = rand(0,99) w ( i) is then added to the The construction o the base channel ilter,, is taken ro Anderson&Gupta (2008). We have introduced the paraeter to describe additional elongation o the echoes. S The noise is generated as ollows: w () i = αri r i where is the rando Gaussian nuber with zero ean and unit standard deviation. The coeicient α is calculated ro the required SNR: α = ax 1 ( /10) 10 ( ) SNR r i Figure 5 and Figure 6 show the eect o applying the noise and channel ilter, respectively, to the clean data at a certain aspect angle. h 0 Figure 6. Eect o applying channel ilter to the clean data. RESULTS AND DISCUSSION In this research we generate the test data using a ixed single value o SNR and the channel paraeter, S, or all our requency bands. The training data are generated or SNR and channel paraeter values selected randoly ro an interval: ( ) [, ] SNR tr SNR (1) ( tr ) [ S S ] in, in SNR ax S (2) ax The above intervals include the corresponding values used or generating the test data. For each clean data echo N tr training data echoes are generated with N tr pairs o SNR and channel paraeter each tie randoly selected ro the above intervals. In this research N tr = 3 is used. Here we investigate how the width o the above intervals aects the classiication accuracy. First, we consider eect o the SNR interval. In this case we do not apply the channel ilter to either the training or to the test data. The test data set is ored with SNR = 10 db. Figure 7 shows the plots o the accuracy o classiication as a unction o the training data SNR range, or the length o the interval (1), SNR ax SNR. One can see ro the igure in that increasing the SNR range o the training data certainly leads to the decrease o the classiication accuracy. However, it is still suiciently high or the irst two requency bands. This plot also clearly shows the iportance o the wide requency bandwidth or accurate classiication. Figure 5. Eect o adding rando noise to the clean data. 4 Australian Acoustical Society

5 range or the training set. As beore this eans that in equation (1) SNR in = SNR ax = 10dB. The channel ilter paraeter or generating the test data is kept constant, S = 3, at the centre o the paraeter S interval o the training data. The results o this test are presented in Figure 9 or the classiication accuracy and in Figure 10 or the area under the ROC curve. In both igures the horizontal axis shows the length o the channel ilter paraeter interval, i.e. S. ax S in Figure 7. Classiication accuracy versus width o the training data SNR interval or our dierent requency bands. No channel ilter applied. Next, we apply a channel ilter to both the test and the training data. First, we use the sae channel ilter paraeter or both data sets, S = 2. In other words, S ax = S in = 2 in the equation (2). We should note here that even i we use the sae channel ilter paraeter, S, the ilter still has an eleent o randoness in it due to the way it is generated. Thereore every echo in both test and training sets is generated using a slightly dierent channel ilter. This leads to a change in the dependence o the classiication accuracy on the training data SNR range ( Figure 8). The variation o the channel ilter ro echo to echo leads to soe decrease in the classiication accuracy or the irst two bands. However, the classiication or two narrower bands, bands 3 and 4, actually iproves. It could be explained by the ollowing. Pulses o the narrow requency bands are ore elongated coparing to the pulses o the wide requency bands. As a result the hour-glass plots look ore blurry or narrow requency bands (Swincer et al., 2012). Obviously, ultipath environent has the sae eect o elongating, or blurrying, the object echoes. As a result, application o the channel ilter blurrs the originally sharp wide band echoes and thus reduces the dierence between the echoes o dierent bands. Figure 9. Classiication accuracy versus width o the training data S interval or our dierent requency bands. SNR=10 db or both test and training data. One can see ro these igures that trying to include a wide range o ultipath environents into the training data set ay lead to a signiicant reduction in classiier perorance. However, a reasonable range o ultipath environents in the training data keeps the classiier perorance at a suicient level. The question o course is what is the reasonable range o ultipath environents. Fro Figure 6 we can see that change ro no ultipath to the channel ilter with the paraeter S = 5 gives a signiicant stretch to the echo. The question how this corresponds to the real environent can be answered using a higher idelity acoustic environent odel, which is let or uture work. We also see ro these igures that again, the perorance o the classiier is better in the two widest requency bands. Figure 8. Classiication accuracy versus width o the training data SNR interval or our dierent requency bands. Channel ilter paraeter S =2 applied to both test and training data. Now we will use the sae SNR o 10 db or both the test and the training sets and change the channel ilter paraeter Australian Acoustical Society 5

6 Figure 10. Area under the ROC curve versus width o the training data S interval or our dierent requency bands. SNR=10 db or both test and training data. Finally, we generate the training data by randoly selecting both SNR and the channel ilter paraeter in gradually increasing intervals. Again, the procedure o selecting both paraeters is repeated three ties, so or each cobination o the intervals o SNR and the channel ilter paraeter the nuber o echoes in the training data set is three ties the nuber o clean data echoes. As beore, the test data set is generated ro the clean data using SNR=10 db and S = 3. The results or the accuracy o classiication are presented as surace plots in Figure 11 to Figure 14. As beore, the perorance o the classiier decreases with increasing SNR and channel ilter paraeter intervals or the training data. Apparently in these plots the eect o the channel ilter paraeter is uch stronger than that o SNR. S Figure 12. Classiication accuracy versus training data intervals o SNR and the channel ilter paraeter. Test data paraeters: SNR=10 db, S =3. Band 2. Figure 13. Classiication accuracy versus training data intervals o SNR and the channel ilter paraeter. Test data paraeters: SNR=10 db, S =3. Band 3. Figure 11. Classiication accuracy versus training data intervals o SNR and the channel ilter paraeter. Test data paraeters: SNR=10 db, S =3. Band 1. Figure 14. Classiication accuracy versus training data intervals o SNR and the channel ilter paraeter. Test data paraeters: SNR=10 db, S =3. Band 4. CONCLUSION We considered an iportant issue in the active sonar classiication o correct selection o the training data. Obtaining training data in situ or all targets and environents is not possible. That is why various techniques based on the use o the so-called clean data obtained ro either atheatical odelling or controlled ree-ield experients are gaining popularity. Here we considered one o such approaches based on the orward odelling to generate the training data. The question we investigated here is how well the environent paraeters used or generating training data should atch to 6 Australian Acoustical Society

7 those o the test data. We based our research on the clean ree-ield echoes obtained at the DSTO Underwater Acoustic Scattering Laboratory test tank or two objects: scale odel o a generic subarine and a concrete cylinder o siilar size. The easureents were conducted or our requency bands to additionally investigate the inluence o the requency bandwidth on the classiier perorance. Both the test and the training data were generated ro the clean data by applying two environent paraeters: noise and a channel ilter to odel echo distortion due to ultipath. While the test data echoes were generated using single values o SNR and the channel ilter paraeter, the paraeters or generating the training data were randoly picked in gradually increasing intervals centred on the values o the test data. IEEE Journal o Oceanic Engineering, vol. 30, pp As expected, the increase o the paraeter intervals or generating the training data leads to a decrease o the classiier perorance. However, the perorance reains relatively high or reasonable intervals o SNR especially at the low values o the channel ilter paraeter. An increase in the channel ilter paraeter leads to a decrease in classiication accuracy even in the cases when the sae single value channel ilter paraeter was used or generating the training data. This is explained by the act that the channel ilter has additional randoness even at the sae value o the channel ilter paraeter. This randoness results in dierence between the echoes, which increases with increasing channel ilter paraeter. In the current research the channel ultipath was odelled artiicially to purely investigate the inluence o the echo distortion on the classiier perorance. In uture work ore realistic approach to accounting or the environent will be conducted using, or eaxple, high-idelity siulation o echoes ro objects in acoustic waveguide (Kouzoubov, 2005). All the results also show that the perorance o the classiier is uch higher when the pulses with wider requency bandwidth are used. REFERENCES Ainslie, MA 2010, Principles o Sonar Perorance Modeling, Springer. Anderson, HS & Gupta, MR 2008, Joint deconvolution and classiication with applications to passive acoustic underwater ultipath, J. Acoust. Soc. A., vol. 124, pp Kil, D & Shin, F 1996, Pattern Recognition and Prediction with Applications to Signal Characterization, AIP Press. Kouzoubov, A 2005, Modelling o Acoustic Scattering ro an Object in a Waveguide, DSTO-TR-1801, Deence Science and Technology Organisation. Liu, H, Runkle, P, & Carin, L 2004, Classiication o distant targets situated near channel bottos, J. Acoust. Soc. A., vol. 115, pp Okopal, G, Loughlin, P, & Cohen, L 2008, Dispersioninvariant eatures or classiication, J. Acoust. Soc. A., vol. 123, pp Saunders, C, Gaeran, A, & Vovk, V 1998, Ridge regression learning algorith in dual variables, Proc. O the 15th International Conerence on Machine Learning (ICML98), pp Madison-Wisconsin. Swincer, P, Nguyen, B, & Wood, S 2012, Method or the Generation o Broadband Acoustic Signals, Australian Acoustical Society, Proceedings o Acoustics 2012 Freantle. Theodoridis, S & Koutroubas, K 2006, Pattern Recognition 3rd edition. Acadeic Press. Tucker, S & Brown, G 2005, Classiication o Transient Sonar Sounds Using Perceptually Motivated Features, Australian Acoustical Society 7