Sinusoidal Order Estimation using the Subspace Orthogonality and Shift-Invariance Properties

In this paper, we study and compare a number of subspace-based methods for determining the the number of sinusoids in noise. These are based on the subspace orthogonality and and shift-invariance properties that are known from the MUSIC (multiple signal classification) and ESPRIT frequency estimators. The method based on the orthogonality property has not previously appeared in the literature. We compare, in simulations, the various sub-space methods. These show that the subspace methods can estimate the correct order with a high probability for sufficiently high SNRs and number of observations with MUSIC performing the best. Also, unlike the commonly used statistical methods, the subspace methods do not depend on the probability density function of the noise being known.