Enhanced passive acoustic localization with an array of non-identical sensors using blind Gauss-Markov estimate

For a stationary radiating source, the optimum time-delay vector estimation at a receiving sensor array is realized using the Generalized Cross Correlation (GCC) function. The estimates are combined with the correlator error matrix, expressed in terms of the sensor signal spectra and background noise spectra, to obtain a linear minimum variance unbiased estimate of the time delay vector, known as the Gauss-Markov estimate. In this estimation procedure, the signal power spectral density (PSD) is assumed to be the same at the different sensors which will be approximately true for distant sources. This PSD is replaced in practice by the a priori known source PSD. In the absence of a priori information, the PSD is required to be estimated at the sensors of the receiver array. This modified algorithm has been called the “blind” Gauss-Markov estimation algorithm. It provides better estimates of inter-sensor time delay, source range and bearing compared to the respective estimates obtained with the classical correlator system in terms of mean square error (MSE) measure. For a wide-aperture array, the use of PSD estimation based Gauss-Markov algorithm has been proposed earlier by the authors through two algorithms. In the first algorithm, the signal spectrum estimate at the closest sensor is used, while in the second algorithm, the signal spectra estimates at individual sensors are used. These proposed algorithms improve the estimates obtained from the correlator system in MSE terms. For a wide aperture array, the individual sensor PSD based Gauss-Markov estimate is more accurate than the closest sensor PSD based Gauss-Markov estimate as it utilizes the signal amplitude gradient information across the sensors of the array. This paper investigates the use of arrays with non-identical sensors along with the second algorithm in which the signal spectrum estimation is done at the individual sensors. Analytic explanation of the same shall be presented. The algorithm has been implemented and studied for an underwater acoustic experiment based on a three-element, non-uniform, perturbed linear array. It is found to give enhanced parameter estimation compared to the classical Gauss-Markov algorithm that uses constant PSD across the sensors. The proposed algorithm can be useful in providing more accurate localization of radiating underwater sources in applications like underwater robotics, diver guidance system, underwater object handling, and tracking of maneuvering vessels.