Estimation of the Number of Sources in Unbalanced Arrays via Information Theoretic Criteria

TL;DR

This paper introduces a robust, low-complexity MDL-based estimator for determining the number of sources in unbalanced sensor arrays, addressing real-world deviations from ideal assumptions.

Contribution

It proposes a new MDL-type estimator that remains consistent despite unequal noise levels and offers a computationally efficient implementation avoiding multi-dimensional searches.

Findings

The estimator is robust against deviations from equal noise assumptions.

The proposed method is computationally efficient and suitable for practical applications.

Consistency of the estimator is theoretically proven.

Abstract

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 non-robust 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 multi-dimensional searches. In this paper, 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 multi-dimensional searches is presented as well, making this estimator a favorable choice for practical applications.