Parameter estimation of superimposed sinusoids by data matrix subfactorization: Theory and algorithm

Abstract

Estimating parameters of a sum of complex exponentials in white noise is considered in this paper. A simplified maximum likelihood estimation algorithm based on subfactorization of a structured data matrix is proposed, and we show that parameterization of the data model in signal space allows to improve estimation accuracy at low signal-to noise ratio (SNR). The idea of solution of the normal equations is based on the singular value decomposition method of the data matrix, which allows one to simplify drastically the obtained equations. The geometric sence of the proposed solution is discussed.