Estimation of the Number of Sources by Using an MMSE-Based MDL Criterion without Eigendecomposition

A new computationally simple MDL approach is addressed in this paper. Unlike the eigenvalue-based MDL methods, the proposed method suggests to use the minimum mean square errors (MMSEs) of the multi-stage Wiener filter (MSWF) to calculate the description length required to encode the observed data. As a result, the proposed method is more robust to the no uniform noise than the eigenvalue-based MDL methods. On the other hand, since the proposed method does not involve the estimation of the observed covariance matrix and its eigendecomposition, its computational complexity can be significantly reduced. Numerical results are presented to illustrate the consistency and robustness of the proposed method.