Estimation of the number of sources in unbalanced arrays via information theoretic criteria

Estimating the number of sources impinging on an array of sensors is a well-known and well-investigated problem. A common approach for solving this problem is to use an information theoretic criterion, such as Minimum Description Length (MDL) or the Akaike Information Criterion (AIC). The MDL estimator is known to be a consistent estimator, robust against deviations from the Gaussian assumption, and nonrobust against deviations from the point source and/or temporally or spatially white additive noise assumptions. Over the years, several alternative estimation algorithms have been proposed and tested. Usually, these algorithms are shown, using computer simulations, to have improved performance over the MDL estimator and to be robust against deviations from the assumed spatial model. Nevertheless, these robust algorithms have high computational complexity, requiring several multidimensional searches. In this paper, which is motivated by real-life problems, a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken. An MDL-type estimator that is robust against deviation from assumption of equal noise level across the array is studied. The consistency of this estimator, even when deviations from the equal noise level assumption occur, is proven. A novel low-complexity implementation method avoiding the need for multidimensional searches is presented as well, making this estimator a favorable choice for practical applications.