A Reduced Complexity Tensor Approach for Order Selection and Frequency Estimation

Abstract

This paper presents a reduced complexity tensor approach for order selection and subspace-based frequency estimation. The proposed covariance tensor based order selection algorithm, termed as CT-OS, uses singular values of the covariance tensor formed from the 1D noisy observations of multiple complex sinusoids. Experimental results show that the CT-OS algorithm is capable of providing accurate order selection under short observations and is robust under medium to high signal-to-noise ratios. The proposed covariance tensor based frequency estimator, termed as CT-FE, utilizes a singular vector matrix in the higher-order singular value decomposition of the covariance tensor. Experimental results show that the CT-FE outperforms the subspace alignment and separation algorithm (SAS-Est) and a recent two-stage order and frequency estimation algorithm. Furthermore, both theoretical analysis and experimental results demonstrate reduced computational complexity and time for the proposed CT-OS against the recent covariance tensor based order estimation algorithm CTB-OE. The CT-FE algorithm is also shown to enjoy reduced computational complexity and time when compared with the frequency estimator SAS-Est.

Keywords

• Covariance tensor
• frequency estimation
• generalized Kullback-Leibler divergence
• high order singular value decomposition
• order selection
• subspace alignment and separation algorithm