Array Processing: Underwater Acoustic Source Localization

Array processing is used in diverse areas such as radar, sonar, communications and seismic exploration. Usually the parameters of interest are the directions of arrival of the radiating sources. The High-Resolution subspace-based methods for direction-of-arrival (DOA) estimation have been a topic of great interest. The subspace-based methods well-developed so far require a fundamental assumption, which is that the background noise is uncorrelated from sensor to sensor, or known to within a multiplicative scalar. In practice this assumption is rarely fulfilled and the noise received by the array may be a combination of multiple noise sources such as flow noise, traffic noise, or ambient noise, which is often correlated along the array (Reilly & Wong, 1992; Wu & Wong, 1994). However, the spatial noise is estimated by measuring the spectrum of the received data when no signal is present. The data for parameter estimation is then pre-whitened using the measured noise. The problem with this method is that the actual noise covariance matrix varies as a function of time in many applications. At low signal-to-noise ratio (SNR) the deviations from the assumed noise characteristics are critical and the degradation may be severe for the localization result. In this chapter, we present an algorithm to estimate the noise with band covariance matrix. This algorithm is based on the noise subspace spanned by the eigenvectors associated with the smallest eigenvalues of the covariance matrix of the recorded data. The goal of this study is to investigate how perturbations in the assumed noise covariance matrix affect the accuracy of the narrow-band signal DOA estimates (Stoica et al., 1994). A maximum likelihood algorithm is presented in (Wax, 1991), where the spatial noise covariance is modeled as a function of certain unknown parameters. Also in (Ye & DeGroat, 1995) a maximum likelihood estimator is analyzed. The problem of incomplete pre-whitening or colored noise is circumvented by modeling the noise with a simple descriptive model. There are other approaches to the problem of spatially correlated noise: one is based on the assumption that the correlation structure of the noise field is invariant under a rotation or a translation of the array, while another is based on a certain linear transformation of the sensor output vectors (Zhang & Ye, 2008; Tayem et al., 2006). These methods do not require the estimation of the noise correlation function, but they may be quite sensitive to the deviations from the invariance assumption made, and they are not applicable when the signals also satisfy the invariance assumption.