Underwater Noise Modeling and Direction-Finding Based on Heteroscedastic Time Series
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Research Article Underwater Noise Modeling and Direction-Finding Based on Heteroscedastic Time Series Hadi Amiri,1 Hamidreza Amindavar,1 and Mahmoud Kamarei2 1 Department 2 Department
of Electrical Engineering, Amirkabir University of Technology, P.O. Box 15914, Tehran, Iran of Electrical and Computer Engineering, University of Tehran, P.O. Box 14395-515, Tehran, Iran
Received 8 November 2005; Revised 29 April 2006; Accepted 29 June 2006 Recommended by Douglas Williams We propose a new method for practical non-Gaussian and nonstationary underwater noise modeling. This model is very useful for passive sonar in shallow waters. In this application, measurement of additive noise in natural environment and exhibits shows that noise can sometimes be significantly non-Gaussian and a time-varying feature especially in the variance. Therefore, signal processing algorithms such as direction-finding that is optimized for Gaussian noise may degrade significantly in this environment. Generalized autoregressive conditional heteroscedasticity (GARCH) models are suitable for heavy tailed PDFs and time-varying variances of stochastic process. We use a more realistic GARCH-based noise model in the maximum-likelihood approach for the estimation of direction-of-arrivals (DOAs) of impinging sources onto a linear array, and demonstrate using measured noise that this approach is feasible for the additive noise and direction finding in an underwater environment. Copyright © 2007 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
A passive sonar generally employs array processing techniques to resolve problems such as localization of targets [1, 2]. As a matter of fact, all the DOA estimation methods make a crucial assumption for the noise model, that have a great impact on the performance of DOA estimation. In the underwater environment, the measurements of additive noise show that we have non-Gaussian process [3–5]. Natural and manmade sources such as reverberation and industrial noise that cause additive noise distribution exhibit performances far away from the Gaussian model. These factors are more in coastal and shallow waters. Thus, the algorithms that are optimized for Gaussian distribution will degrade in actual experiments. All this mentioned factors give a stochastic and time-varying nature to the background noise. Thus, a proper model presentation which could best and simply describe the different features of the realistic background noise affecting the desired signal is an important part of a sonar signal processing. In the last decade, after the seminal works by Engle [6] and Bullerslev [7] there has been a growing interest in time series modeling of changing variance or heteroscedasticity. These models have found a great number of applications in nonstationary time series such as financial records. Generalized autoregressive conditional heteroscedasticity; for example, GARCH [7], is a time
series modeling technique that uses past variances and the past variance forecasts to forecast future variances. GAR
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