On subspace based sinusoidal frequency estimation

Subspace based methods for frequency estimation rely on a low-rank system model that is obtained by collecting the observed scalar valued data samples into vectors. Estimators such as MUSIC and ESPRIT have for some time been applied to this vector model. Also, a statistically attractive Markov-like procedure for this class of methods has been proposed in the literature. Herein, the Markov estimator is re-investigated. Several results regarding rank, performance, and structure are given in a compact manner. The results are used to establish the large sample equivalence of the Markov estimator and the approximate maximum likelihood (AML) algorithm proposed by Stoica et al. (see Automatica, vol.30, no.1, p.131-45, 1994)