152 Proceedings of SYMPOL-2011

978-1-4673-0266-1/11/$26.00 ©2011 IEEE

Discrete Sine Transform Based HMM Underwater Signal Classifier

T. Binesh1, M.H. Supriya2 and P.R. Saseendran Pillai3 Department of Electronics, Cochin University of Science and Technology, Kochi–682022, India

1bineshtbt@gmail.com; 2supriya@cusat.ac.in; 3prspillai@cusat.ac.in

Abstract: Underwater target recognition and classification has been a field of considerable importance due to its multidimensional applications. Much attention has been focused on this area and various underwater signal processing schemes have been devised over the time. Hidden Markov Models, because of their robustness, provide an effective architecture for the classification of underwater noise sources. A methodology is presented, in this paper, for the design and performance analysis of an HMM based underwater signal classification system, utilizing the Discrete Sine Transform based target specific features. Simulation results have been presented for typical underwater noise waveforms, such as Boat and Dolphin noises.

Keywords: Discrete Sine Transform, K-means Clustering, Baum Welch Estimation, Hidden Markov Models.

1. Introduction The ocean noise consists of the noises originating from a variety of marine species, shipping, man made sources, etc. and to a large degree will reveal the general characteristics and uniqueness of their generating mechanisms. Any efficient target classification system should be capable of extracting the right feature combinations and by suitable processing, obtain unambiguous recognition of targets. The selection of the source specific features in a classification system is very critical as it determines the efficiency and performance of the classifier in general. The

Discrete Sine Transform (DST) based spectral features, because of their robustness, can be effectively utilized in the design of underwater target classifiers. The Discrete Sine Transform is an invertible function and has applications in solving partial differential equations by spectral methods. DST based feature set possesses the essential traits suitable for the design of statistical models in signal classifying systems. Of the many statistical models, the Hidden Markov Model based systems offer excellent frame work for detection and classification. But the proper selection of features and stable design are major factors determining the performance of any HMM

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classifier. In this paper an HMM based classifier system is proposed which incorporates the DST based techniques for extracting the features of underwater noise sources.

2. Methodology Underwater noise sources, because of the unique features and propagation characteristics, demand special processing techniques in many systems. Source specific features can be utilized for the design of underwater target recognition systems based on the Hidden Markov Modeling. The extracted spectral feature set forms one of the dominant parameters which determines the HMM performance in the detection and classification of underwater noise sources.

2.1 Discrete Sine Transform Discrete Transforms possess many features which make them suitable for significant applications in signal processing. Of these, the Discrete Sine Transform (DST) which can be effectively utilized in the classification of underwater signal sources operates on a function at a finite number of discrete data points. For a sequence x(n), the DST and the Inverse DST can be defined as follows:

]1

sin[)(1

21∑

= ++=

N

nk N

nknxN

X π … (1)

]1

sin[1

2)(1 ++

= ∑= N

nkXN

nxN

kk

π … (2)

where n = 1, 2, …, N and k = 1, 2, …, N. DST is having properties similar to other trans- formations but they are capable of highly efficient performance in data enhancement and other applications [1].

2.2 Hidden Markov Model Hidden Markov Models (HMM), when accurately designed and trained, can be used in underwater target detection and classification. A Hidden Markov Model can be defined as a statistical model in which the system being modeled is

assumed to be a Markov process with indefinite parameters and the model tries to determine the hidden parameters from the recognizable data. The HMM consists of a finite set of states and each state is associated with a probability distri- bution. The transitions among the states are determined by a set of probabilities which forms an important design parameter of the model [2]. A complete characterization of HMM can be obtained by specifying the parameters such as the number of states of the model, N, the number of observation symbols, Ms and the state transition probabilities which denote the probability of transition from a state qt to a state qt+1, given the probability being in state qt. There should also be a probability distribution in each of the states. Under a given set of conditions, the system generates an output based on the associated probability distribution.

2.3 DST Feature Extraction For the underwater noise source, spectral analysis is performed to extract the required design features from a sequence of time samples. The sampled underwater signal is partitioned into frames for the purpose of extracting source specific features with a minimum of distortion.

Each individual frame is windowed to minimize the signal discontinuities at the borders of each frame [3]. Of the many functions available, Hamming window is used in this system which is a typical window possessing the property of reduced side lobes. The spectral magnitudes are being estimated using Fast Fourier Transform (FFT) analysis. This input power spectrum is filtered through a bank of filters to obtain a non linear resolution. This technique possesses good discrimination properties and also flexible to many analytical manipulations. The output, representing the modified spectrum, will be an array of filtered values, each corresponding to the output of filtering the input spectrum through an individual filter. The Discrete Sine Transform of the logarithm of filtered spectrum is computed, which will form the extracted feature set for the classifier system. These are to be utilized in a clustering procedure for the purpose of training

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the Hidden Markov Model. The K means algorithm is used in this system for cluster analysis.

2.4 K-means Clustering The K-means algorithm is one of the efficient learning algorithms that can be used in cluster analysis [4]. It is an algorithm to cluster m objects based on attributes into K partitions, where K < m, in which each object belongs to the cluster with the nearest mean. It attempts to find the centers of natural clusters in the data. The main idea is to define K centroids, placed judiciously, one for each cluster. The objective it attempts to achieve is to minimize the total intra-cluster variance.

2.5 HMM Training Hidden Markov Models (HMMs) can be designed and effectively trained for underwater target detection and classification. The Baum-Welch algorithm which is a procedure for computing the probability of a particular observation sequence can be operated in the context of Hidden Markov Models. For a model with a given number of states, it basically consists of estimating the state transition probabilities by computing the forward probability which is a joint probability and backward probability which is a conditional probability, using recursions [5]. The HMM is trained for a set of underwater signal sources whose DST based features are being extracted by the system.

3. Results and Discussions The system has been validated using simulation studies and correct recognition has been obtained for different underwater signal sources. The noise data waveforms emanating from the underwater target of interest have been sampled and recorded as a wave file data which is being used as the input to the HMM based classifier system. Figure 1 depicts the extracted DST based spectral features for the case of the underwater signal of Boat.

0

5

10

15

0

10

20

30

40-30

-20

-10

0

10

DS

T

Fig. 1: DST Feature Extracted for the Boat Noise

The twelve state HMM is trained using a set of underwater signal inputs. The unknown noise source to be detected is processed for the extraction of features and they are being used in the recognition phase of the HMM classifier. The system recognized the underwater noise of Boat with out ambiguity. The extracted DST features for the target signal of Dolphin is shown in Figure 2 which again is utilized for the correct recognition of this underwater signal by the HMM system. The observation probability distribution set forms another important parameter determining the classification efficiency of the model. For the target signal of Boat, the estimated observation probability distribution is plotted in Figure 3 while for the Dolphin noise, the corres- ponding distribution is depicted in Figure 4.

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15

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20

30

40-4

-2

0

2

4

6

8

DST

Fig. 2: DST Feature Extracted for the Dolphin Noise

T. Binesh et al.: Discrete Sine Transform Based HMM Underwater Signal Classifier 155

0

5

10

15

0

2

4

6

80

0.2

0.4

0.6

0.8

1

HM

M O

bser

vatio

n P

rob.

Dis

trib

utio

n

Fig. 3: HMM Observation Probability

Distribution for the Boat Noise

The system has been tested for the classification capability and correct recognition has been obtained for the assumed set of underwater noise source waveforms. The observation probability variations shown in Figures 3 and 4 can be utilized in HMM recognition phase. By the proper extraction of DST features, various unknown underwater noise sources can be assigned to known classes of targets, leading to the generation of classification clues. From simulation results, it can be seen that the DST based features of the underwater signals provide excellent performance with respect to the classification performance of the HMM based system. They exhibit robustness and compatibility with the classifier architecture which are essential for the training and recognition phases of the system. The different target signals possess unique features which are characteristic of the noise generating sources. They are being extracted by the system which will form functions of input data for the proposed classifier.

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HM

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Fig. 4: HMM Observation Probability Distribution for Dolphin Noise

4. Conclusions The proposed system makes use of Discrete Sine Transform based spectral features for the classi- fication of underwater signal sources. The Hidden Markov Model based classifier utilizing the desired features, has to be trained using a set of underwater target signals and correct recognition has been obtained for the assumed source signals. The system performance has also been analyzed for the effect of white Gaussian noise. For the underwater target signals corrupted by moderate levels of white Gaussian noise, the proposed system gives unambiguous recognition for the set of inputs, except for Beluga and Blue-Grunt noises. The system can be augmented by utilizing DST features along with other suitable characteristics and will form a robust underwater target classification archi- tecture.

Acknowledgments The authors gratefully acknowledge the Depart- ment of Electronics, Cochin University of Science and Technology, Kochi, for providing the necessary facilities for carrying out this work.

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