On methods to improve time delay estimation for underwater acoustic source localization
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1 Indian Journal of Geo-Marine Sciences Vol. XX(X), XXX 215, pp. XXX-XXX On methods to improve time delay estimation for underwater acoustic source localization Bipin Patel, Siva Ram Krishna Vadali, Sambhunath Nandy & Sankar Nath Shome Robotics & Automation Division, CSIR-Central Mechanical Engineering Research Institute, Durgapur, India. [ Received 3 September 214; Revised 16 November 214 This paper addresses the problem of acoustic source localization in shallow water environment commonly dominated by impulsive noise and multipath phenomenon. Traditionally acoustic source localization with sensors spaced several wavelengths apart involves Time Delay Estimation (TDE) via Generalized Cross-Correlation Phase Transform (GCC- PHAT) 1. However multipath signals and impulsive noise in underwater ambience result in spurious peaks leading to anomalous time delay estimates, and in turn erroneous computation of source location. In the present work we recommend two methods to improve time delay estimation, based on order statistics and via signal detection. Simulation results indicate a significant improvement in time delay estimation as compared to GCC-PHAT in presence of impulsive noise and multipath induced fading. [Keywords: Detection, GCC-PHAT, localization, time delay estimation, underwater acoustic communication] Introduction Background In underwater context, acoustic source localization is of tremendous importance in several applications such as climate and ocean observation, naval surveillance and oil platform monitoring 1-6. Many techniques are available to estimate the location of a sound source based on energy densities, intensity of received signals, trilateration, triangulation, particle velocity etc 5. However, a common approach for passive source localization is to exploit time delayed signals received by a pair of sensors 5,6. The basic idea behind time delay estimation is that sensor arrays may be deployed to extract phase information present in signals picked up by spatially separated sensors. For instance, in sonar signal processing hydrophones are used to estimate the sources range and bearing. When sensors are spatially separated, the acoustic signals arrive at the sensors with difference in their times of arrival. From the known array geometry, direction of arrival (DOA) of the signal can also be obtained from the measured time delays for each pair of sensors in the array. Clearly for TDE based localization, precise time delay estimation is indeed highly essential. There are several methods for estimating the time delay of signal arrival, a few of which include, correlation 1,7, higher order statistics based methods etc 8. Other time delay estimation methods include Generalized Cross Correlation Phase Transform (GCC-PHAT), Maximum Likelihood (ML) method, Average Square Difference Function (ASDF) method and Least Mean Square (LMS) adaptive filter method. Of all these, GCC-PHAT is the most widely used method to estimate time delay 9,1 in the context of source localization. Motivation Two major deterrents for source localization in shallow water are multipath phenomenon and impulsive noise. While, multipath phenomenon leads to small scale fading, impulsive noise leads to non- Gaussian signal modeling. Further, both the aspects effectively lead to false identification of correlation peaks, and hence erroneous time delay estimates Moreover time delay estimation in passive ranging is in the order of micro-seconds and fluctuating at such a low time delay leads to inaccurate localization and it is necessary to devise alternate methods which can increase the accuracy of estimated time delay. Since GCC-PHAT is one of the most commonly used method, its performance analysis was taken up and simulation analysis is carried in underwater
2 INDIAN J. MAR. SCI., VOL. XX, NO. X XXXX 215 ambience. It is observed that GCC-PHAT works well under the Gaussian noise assumption and availability of direct path signals with high SNR. However, when either of these assumptions fails to hold, so does the concept of GCC-PHAT; the end result being erroneous time delay estimation. It is felt that very little work is available to improve the capability of GCC-PHAT in presence of multipath and impulsive noise. Further we also observe that little work is available addressing both the deterrents in the context of underwater acoustic source localization. It is for this reason, in the present work we carry out a simulation analysis of above mentioned problems and demonstrate that it is possible to improve the performance of GCC-PHAT and also estimate the time delay of reception by detecting the presence of a signal. Before we conclude the section, contributions of the present work are summarized next: (a) First demonstrate that GCC-PHAT fails to estimate the time delay of reception in multipath environment and in presence of impulsive noise (modeled as outlier data). (b) We then recommend improving TDE performance of GCC-PHAT in presence of impulsive noise incorporating the concept of order statistics. (c) Next we propose a signal detection based approach for TD estimation which is highly effective as compared to traditional GCC-PHAT, particularly when SNR at the receiver is low. (d) Lastly, we further show that it is also possible to improve the TDE performance of LRT using orderstatistics. The rest of the paper is organized as follows: In the following section we analyze the performance of GCC-PHAT to estimate time delay in impulsive and multipath channels. In view of the difficulties with GCC-PHAT, we propose two methods to improve time delay estimation in underwater channels. As a next step we provide simulation analysis results for proposed methods. Towards the end of the paper a few concluding remarks are drawn on the work done. Material and Methods Performance analysis of CC and GCC-PHAT in Gaussian and non-gaussian channels In this section we first present the signal model for localization in a typical underwater environment. We then analyze the performance of CC and GCC- PHAT in Gaussian and non-gaussian channels. Signal Model Let ( ) represent an acoustic signal source (periodically) transmitting a signal (refer to red dot in Fig. 1). Let (t) and (t) be signals received by two sensors at a distant location, arranged in a known geometry. The received continuous time signals are converted into discrete time signals by an ADC as [ ] and [ ], n {1,2,...,N}, respectively. We then have, [ ] = [ ] + [ ] (1) [ ] = [ ] + [ ] (2) Fig. 1 Sensor arrangement for TDE based source localization. where [n] and [n] represent additive noise and D is the discrete time delay after which the second sensor receives the transmitted signal, which needs to be estimated. CC and GCC-PHAT in Gaussian channels In general, cross correlation of discrete time signals is defined as: [ ] = [ ] [ + ] (3). The time difference of arrival (TDOA) of the two signals at the receivers is given as, = ( [ ])/ (4) where Fs is the sampling rate 13. In case of low SNR at the receiver CC usually fails to estimate the accurate time delay D due to multiple correlation peaks. Generalized Cross Correlation Phase Transform is a generalized version of CC which has received
3 BIPIN et al.: ON METHODS TO IMPROVE TIME DELAY ESTIMATION FOR UNDERWATER ACOUSTIC SOURCE LOCALIZATION considerable attention due to its ability to avoid spreading of correlation peak 1. GCC-PHAT can be mathematically expressed as: = ( ) ( ) ( ) ( ) (5) ( ) = ( ) (6) where ( ) represents inverse fourier transform of the argument within the parentheses. The TDOA is then obtained as, = { ( )} (7) Once time delay D is computed, one may also compute direction of arrival of signal at source as: = (8) where d is the distance between two sensors, D is the estimated time delay, θ is the angle of arrival of signal and c is the speed of sound in water. Since signal and noise are uncorrelated ( ( ) = ) ( ) has a correlation peak at n=d. Fig. 2 shows time delay estimation performance of CC and GCC- PHAT in the presence of additive white Gaussian noise. indicates improvement of GCC- PHAT over CC. CC and GCC-PHAT in non-gaussian channel: A. Impulsive nature of shallow water channels As mentioned earlier, a shallow water channel is a combination of several spiky signals 13. It is for this reason such a channel is commonly modeled to behave impulsive in nature. It is also well known that, generally, impulsive noise is modeled in two ways: (a) Heavy tailed non-gaussian distributed noise (αstable) (b) Contaminated Gaussian noise (i.e. Gaussian noise with outlier data) Since α-stable distributions do not possess closed form PDF except for α {.5, 1, 2}, in this work we evaluate the performance of GCC-PHAT in presence of contaminated Gaussian noise and cauchy distributed noise. Fig. 3 shows performance of GCC- PHAT in presence of 1% outlier data. Clearly, several peaks are seen and we may conclude that the probability of incorrect estimation of time delay is very high, leading to erroneous localization of the acoustic source. correlation peak 1-1 Comparison of CC and GCC in presence of outliers CC correlation peak GCC-PHAT correlation lag Fig. 3 Performance GCC-PHAT in presence of outlier data. Fig. 2 Performance of CC and GCC-PHAT in presence of Gaussian noise. A sharp peak corresponding to the true time delay (D=7) may be seen in case of GCC-PHAT. It may be noted that though CC also peaks at (D=7) several smaller peaks are seen in case of CC, which clearly B. Multipath phenomenon in shallow water channels Coming to the other problem, we observe that GCC fails to accurately estimate the time delay in multipath channels. Typically, shallow water channels are multipath dominated, that is, signals travelling through acoustic channel suffer from
4 INDIAN J. MAR. SCI., VOL. XX, NO. X XXXX 215 multipath induced fading effects. Such multipath phenomenon may lead to constructive as well as destructive interference, effectively resulting in phase shift of the signal. The mathematical model of such multipath scenario is commonly represented as: ( ) = ( ) h, ( ) + ( ) (9) ( ) = ( ) h, ( ) + ( ) (1) where is the delay, k is the number of signals seen atthe receiver; ( ), ( ) represent additive noise and h, ( ), h, ( ) represent the impulse response of underwater channel as seen by (Fig. 1). correlation peak correlation peak Comparison of CC and GCC in presence of outliers Fig. 4 Performance of CC and GCC-PHAT in multipath scenario. Also it may be observed (Fig. 4) that performance of CC and GCC-PHAT are degraded in multipath environment 3. Thus we may conclude there is a strong need to improve the performance of available TDE based localization methods in underwater scenario. Proposed methods to improve time delay estimation for UWA source localization It is evident from previous section that the performance of GCC-PHAT degrades in an underwater environment. To improve estimation of time delay and subsequently localization in such environments, we propose two approaches namely: Order statistics based approach (OSA) Signal detection based approach (SDA) CC GCC-PHAT correlation lag Order statistics based approach In this method we propose to improve the TDE performance of GCC-PHAT in channels modelled with impulsive noise by exploiting the feature of order statistics of a sample. Going by the proposed method, we first find order statistics of the sample obtained at the two sensors, independently. As a next step, we replace a few of the extreme order statistics by the assumed (underlying) noise. Finally we reorder the data in the order of its acquisition. In other words we substitute the outlier data by assumed noise. The point we have in the above procedure is, typically impulsive noise is responsible for multiple correlation peaks. When a signal is masked with such large instantaneous amplitudes, we may reduce the resultant effect on correlation either by eliminating them or by assuming it to be underlying noise. At this juncture, we make a point to mention that the proposed OSA can only subdue multiple correlation peaks in impulsive noise, but not in multipath environments. We also note that in the above recommended procedure though the number of extreme order statistics to be substituted (with the underlying noise) is a qualitative, one may exploit channel sounding and obtain a fair knowledge of the channel behaviour (and the number of extremes to be substituted). Signal detection based approach In previous subsection, we have recommended to exploit order statistics to improve performance of GCC-PHAT in presence of impulsive noise. However, as mentioned earlier order statistics based method does not improve the accuracy of time delay estimation in multipath dominated environments. In order to improve the accuracy of localization using TDE methods, it is felt that one may also view the time delay estimation problem to be a detection problem. At this point we note that to the extent of our knowledge, no work is available in the context of signal detection based underwater acoustic source localization. The point is, in TDE based localization, we find the time delay between receiving signals at different sensors. That is if one sensor, has received the transmitted signal, then the other, does not receive until a certain period, which depends on geometrical arrangement of sensors. It is for this reason, in the following we propose to solve
5 BIPIN et al.: ON METHODS TO IMPROVE TIME DELAY ESTIMATION FOR UNDERWATER ACOUSTIC SOURCE LOCALIZATION the TD estimation by exploiting the concepts of signal detection. With this hypothesis, we may devise a binary detection problem at sensor as follows: : ( ) = ( ), (11) : ( ) = + ( ), (12) where n:, 1, 2, 3... N-1. Understanding the above detection problem, assuming the first sensor to have received a signal, the second sensor receives only noise under for a time duration D, and the signal after this period. In the detection problem devised, ( ) represents the signal received at sensor (assuming has received the transmitted signal D secs ago), A represents constant amplitude of the signal and ( ), the additive noise, which is typically modeled in one of the two mentioned ways in previous section. According to 15, a Neyman Pearson likelihood ratio test (LRT) in the above detection scenario decides H1, if the log likelihood function, ( ) = ln ( ( ( ) )) ln ( ( ( ))) > ln (η). It is well known that the expression on the left hand side boils down to ( ) = ( ), for Gaussian, distributed scenario and ( ) = ln ( ( ) + 2) ln ( 2+ 2), for Cauchy noise scenario. Note, for any other α one needs to adopt numerical methods. It is for this reason in the present work we model the underlying noise to be contaminated Gaussian noise and/or to be Cauchy distributed noise. We now note that, the purpose of detection in present scenario is to estimate the time delay between signals received at the two receivers. For this we define a window length, by which we compute both the variants of ( ) within this window. In computing ( ), we substitute N by where is the window length to compute ( ). If ( ) does not cross the threshold ln (η), the window is moved by one sample and an initialized count is incremented by one. As the window is moved progressively, the count accumulates and when the signal is accepted to be detected (for one of the shifts), by crossing the threshold the accumulated count amounts to the estimated time delay. We shall demonstrate in the following section that signal detection based approach, i.e. the LRT based TDE improves accuracy of estimated time delay as compared to GCC-PHAT in multipath environments as well as in impulsive noise (modeled to be contaminated Gaussian). We shall also demonstrate that the performance of LRT based TDE improves with signal to noise ratio (SNR), i.e. with A. However, for α < 2, SαS random variables do not have finite variance, and hence we associate the term Generalized SNR (GSNR). Furthermore, if the sample contains a few outliers, we recommend employing order statistics based methodology (proposed in the previous subsection) to improve the TDE performance of LRT based approach. Results and Discussion In this section we analyze the TD estimation performance of the two methods proposed in the previous section. Through Montecarlo simulations first we present the scope of improvement of GCC- PHAT in presence of impulsive noise. We then analyze the performance of proposed signal detection based approach (SDA) for improving TD estimation as compared to GCC-PHAT in presence of impulsive noise as well as in multipath environments. Towards the end of the section, we also compare the performance of GCC-PHAT and SDA based TDE when order statistics based approach (OSA) is also incorporated for TD estimation. Performance improvement of GCC-PHAT in impulsive noise using proposed order statistics based approach (OSA) As seen in the previous section, GCC-PHAT accurately estimates the time delay in presence of Gaussian noise at least in high SNR case, i.e. strong direct path signal availability. However, GCC-PHAT fails to estimate, when these assumptions fail to hold. In such poor channel conditions, when GCC-PHAT is used with order statistics based (OSA), performance of GCC-PHAT to estimate the time delay improves greatly. Fig. 5 depicts one of the received signals (generated in matlab), and the signals before and after incorporating order statistics. It is evident from the figure that as the outlier data is substituted by underlying (assumed) Gaussian noise, the shape of received signal at the sensor, is at least visually retrieved. Fig. 6 compares the performance of GCC-PHAT
6 INDIAN J. MAR. SCI., VOL. XX, NO. X XXXX 215 before and after finding order statistics and replacing 1% extremes in presence of 1% of outliers. Clearly before finding order statistics, multiple peaks are seen whereas after finding order statistics a sharp peak corresponding to delay of D=7 may be observed, thereby justifying the recommended usage of order statistics (OSA) with GCC-PHAT to improve the TD estimation and in turn source localization. Amplitude Amplitude Amplitude time Fig. 5 Signals received by sensor 2 at different conditions: Signal without outlier (top); with outliers (middle); after using OSA (bottom). Correlation peak Correlation peak GCC-PHAT in Presence of outliers GCC-PHAT in outliers after using Order Statistics time Fig. 6 Performance of GCC-PHAT in impulsive noise (contaminated Gaussian): before (top) and after using OSA. Improved time delay estimation using proposed signal detection based approach (SDA) In this subsection we present simulation results and observations for the proposed signal detection based approach for time delay estimation. For this we assume a signal with N (= 45) samples is received at. We also assume that receives no signal for a duration D (= 55 samples) sec and then receives the transmitted signal with amplitude (A) after D samples. We consider a fixed window length ( = 45) for present simulations and perform detection of the signal as discussed in previous section. That is, for a given Probability of False Alarm (PFA) we find a corresponding threshold and compute the detection statistic. In case no signal is detected we move the window by one sample further and perform detection once again. This way we move the window (by a sample) till a signal is detected. Each time we move the window to detect a signal, we increment the estimated delay by one. The number of times the detection window is moved, the delay is estimated as the effective delay count. For different PFA, the probability of correct time delay estimation is evaluated and subsequently the Receiver Operating Characteristic (ROC) of the detector is plotted. Probability of detection (correct TDE) 1 LRT LRT-1% Outlier Probability of False Alarm Fig. 7 ROC of the detector devised to compute estimated time delay: with and without outliers. As may be seen in Fig.7, when a few (1%) outliers were overlaid on the signal, performance of the detector degrades. However, performance of SDA-TDE was better than GCC-PHAT, as may be seen in Table 1. Fig. 8 compares of SDA-TDE performance in presence of Cauchy noise with and without outliers, which once again demonstrates a similar performance as the contaminated Gaussian noise scenario. Table 1 demonstrates performance improvement of the LRT based TDE as compared to GCC-PHAT when 1% outliers were present in the data, especially for low SNR (or GSNR for Cauchy) case. Clearly, for low SNR at receiver (i.e. smaller A), SDA based TDE out performs GCC-PHAT.
7 BIPIN et al.: ON METHODS TO IMPROVE TIME DELAY ESTIMATION FOR UNDERWATER ACOUSTIC SOURCE LOCALIZATION Probability of correct time delay estimate LRT in presence of Cauchy noise LRT in presence of Cauchy noise with outlier Amplitude Fig. 8 Performance of SDA-TDE in presence of Cauchy noise with and without outliers. However, as SNR increases probability of peak detection and hence time delay estimation improves in case of GCC-PHAT, which may be attributed to the basic characteristic of GCC. Probability of detection (correct TDE) 1 Table 1 Comparison of GCC-PHAT and LRT for TDE in presence of outlier data. A (Amplitude) (GCC-PHAT) (SDA TDE) compares the performance of proposed signal detection based TDE for 3 cases, namely, no outlier, only multipath and multipath in contaminated Gaussian noise. LRT LRT in Multipath with no Outlier Probability of False Alarm Fig. 9 ROC of LRT detector without and with multipath inclusion. Fig. 9 compares the performance of proposed SDA-TDE in multipath scenario and Fig. 1 Probability of detection (correct TDE) 1 LRT LRT in Multipath with no Outlier LRT in Multipath with outlier Probability of False Alarm Fig. 1 Receiver operating characteristic based TDE in presence of (a) No multipath (b) Only multipath and (c) Multipath with outliers. We recollect from the previous section that GCC- PHAT (even after incorporating OSA) could not improve TDE accuracy in multipath environments. However, as mentioned earlier and from last two figures (Figs. 9 and 1), the proposed signal detection based method could accurately estimate the time delay in multipath environments, both, in presence and in absence of outliers. Performance of GCC-PHAT and SDA-TDE: In presence of outliers when order statistics incorporated Table 2 compares performance of GCC-PHAT and SDA when order statistics based idea is incorporated in both GCC-PHAT and SDA based methods for signals buried in additive impulsive noise (modeled contaminated Gaussian). Though proposed SDA based approach is effective as compared to GCC- PHAT (refer to Table 1), when GCC-PHAT and SDA are performed after taking order statistics (and replacing 5% extremes of the sample) it is observed
8 INDIAN J. MAR. SCI., VOL. XX, NO. X XXXX 215 Table 2 Comparison of GCC-PHAT and LRT for TDE in presence of outlier after using order stastics. A (Amplitude) (GCC-PHAT) (SDA TDE) that GCC-PHAT gradually outperforms SDA, for large SNR scenario. However near accurate estimation of the number of outliers may not possible due to improper channel sounding, which renders SDA to be more effective towards TD estimation. Conclusions GCC-PHAT a well-known method fails to accurately estimate the time delay in channels dominated by multipath induced fading and impulsive noise. Two methods are proposed to estimate time delay arrival of signals from a distant source in underwater environment. In this work, first it is shown through Montecarlo simulations that performance of GCC-PHAT can be improved by exploiting properties of order statistics. Further, with the proposed signal detection based approach, it is established that effective improvement in time delay estimation is feasible (which may be enhanced further by employing order statistics), for near accurate localization of an acoustic source in underwater channels dominated by multipath intereference and and impulsive noise. Acknowledgment The authors wholeheartedly thank Director, CSIR- CMERI, Durgapur and all the members of Robotics & Automation Division of CMERI for their constant support and co-operation. References 1. Knapp C. H and Carter G. C., The generalized correlation method for estimation of time delay, IEEE Trans. Acoust., Speech, Signal Processing, (1976): Baggeroer, A. B, Kuperman, W. A. and Mikhalevsky, P. N., An overview of matched field methods in ocean acoustics, IEEE J. Oceanic Engineering, 18 (1993): Quazi, A.H., An overview on the time delay estimation in active and passive systems for target localization, IEEE Trans. Acoust. Speech and Signal Processing, USA, 29 (1981): Haykin S, Adaptive Filter Theory (Prentice-Hall Inc., New Jersey), Choi. B., Acoustic source localization in 3D complex urban environments, (212), Ph.D Thesis. 6. Saidi, Z., Boudraa, A.O., Cexus, J.C., and Bourennane, S., Time Delay Estimation Using Cros-ψB Energy Operator, WASET International Journal of Electrical, Electronic Science and Engineering: 1 (27): Juan, Tang, Hongyan, Xing, Time delay estimation based on second correlation, Computer Engineering, Shanghai, 33 (27): Wu. Song, Yongqing, Song, Hongjian, Xu, Feng., Time Delay Estimation in Underwater Positioning for Pattern Time Delay Shift Coding, 6 th International Congress on Image and Signal Processing (213): Zhang, Yushi and Abdulla, Waleed H., A Comparative Study of TimeDelay Estimation Techniques Using Microphone Arrays, Department of Electrical and Computer Engineering The University of Auckland, (25). 1. Tellakula, Ashok Kumar, Acoustic Source Localization Using Time Delay Estimation. Supercomputer Education and Research Centre, Indian Institute of Science Bangalore Masters Thesis (27). 11. Carter, G. C., Coherence and time delay estimation, Proceedings of the IEEE, 75 (1987): Champagne, B., bedard, S., and Stephenne, A., Performance of time delay estimation in the presence of room reverberation, IEEE Trans.Speech Audio Processing (1996): Rogers, J. S., Krolik, J. L., Passive Broadband Source Localization in Shallow-water Multipath Acoustic Channels, IEEE conference on Ocean (28): 1-4, 14. Omologo, M. and Svaizer, P., Acoustic source location in noisy and reverberant environment using csp analysis, Proc. IEEE ICASSP (1996): ,. 15. Kay S. M., Fundamentals of Statistical Signal processing Vol-II, Detection Theory (Prentice-Hall, Inc., New-Jersey), 1998.
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