Entropy-based subspace separation for multiple frequency estimation

Abstract

A subspace-based algorithm for estimating the order and the frequencies of multiple sinusoids embedded in noise is proposed. The new estimator (referred to as E-MUSIC) uses the entropy of a random variable related to the angles between the signal and noise subspaces as its objective function. Maximizing the entropy tends to achieve uniform angle distribution and thus leads to maximal subspace separation. The entropy-based objective function and the performance of the E-MUSIC algorithm is compared with some reference algorithms in the literature. Simulations which are performed in additive white and colored Gaussian noise show that the E-MUSIC offers an improvement for both model order and multiple frequency estimation. The improvement is more pronounced for high model orders and large SNR values. ► We propose a method to estimate model order and the frequencies of a mixture of sinusoids. ► The method employs a new cost function which is based on the entropy of the angles between subspaces. ► The results show considerable improvement over the existing methods of multiple frequency estimators.