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

Abstract

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.

An investigation of several typical model selection criteria for detecting the number of signals

“…Associated with this model, a key problem which has received much attention in signal processing literature (e.g., Refs. [1,17,18,20,21]) is to determine the number of source signals based on an observed sequence x(t), t = 1, 2, . .…”

“…[1] and followed by Refs. [17][18][19][20][21][22], AIC [245][246][247][248][249][250][251][252][253][254][255] and minimum description length (MDL) [23] were introduced to determine the number of signals with efforts on approximating the underestimation (or overestimation) probability and asymptotical consistency under an infinite N . Moreover, recent progress in random matrix theory demonstrates the existence of a phase transition threshold (for the eigenvalues of the covariance), below which the effective number of signals is reduced [10][11][12]22] under the limit N, n → ∞ with n/N → c, where n is the dimensionality of observations, and c > 0 is a constant.…”

Theoretical Analysis and Comparison of Several Criteria on Linear Model Dimension Reduction

“…It is a model selection problem in machine learning. Also, it is addressed as the problem of detecting the number of signals through a noisy channel in signal processing [4,5,6,7,8]. One conventional approach is hypothesis tests based on the likelihood ratio statistic [9] and a subjective threshold.…”

“…Following an early work [4] in signal processing literature, a framework was proposed in [5] for studying criteria such as AIC and MDL, with asymptotic bounds provided for overestimation and underestimation probabilities, which was further studied in [6,7]. Recently, the behaviors of AIC and MDL in a situation with high dimensional signals but relatively few samples were investigated in [8].…”

“…Recently, the behaviors of AIC and MDL in a situation with high dimensional signals but relatively few samples were investigated in [8]. In this track [4,5,6,7,8], FA is considered in its special case of PCA, and the studies are focused on asymptotic properties, such as consistency and asymptotic normality, and the results were shown to be robust for non-Gaussian sources empirically [7]. However, in practical the sample size is finite or even small, and it is intractable to get an exact selection accuracies of different criteria.…”