Eigenstructure-based algorithms for time varying array

Abstract

This study considers the problem of finding the directions of narrow-band signals using a time-varying array whose elements move during the observation interval in an arbitrary but known way. The emphasis is on the case where the shape of the array changes significantly during the observation interval. The motivation for this study are problems involving direction finding systems employing more than one platform such as a spatially referenced synthetic aperture sonar. Assuming that the signal is uncorrelated from snapshot to snap-shot, two eignestructure based algorithms for this problem were derived. These algorithms are modifications of techniques developed originally for time invariant arrays. The first uses array interpolation, and the second uses the ideal of focusing matrices. Like other eigenstructure methods, these algorithms require a modest amount of computations in comparison with the maximum likelihood estimator. The performance of the algorithms is evaluated by Monte-Carlo simulations and compared to the performance of the time-varying beamformer and to the Cramer–Rao bound. Although both techniques were successful for wideband array processing with time invariant arrays, it was found that only the interpolated array algorithm is useful for direction finding with time varying arrays.