Statistical analysis of state-covariance subspace-estimation methods

We present a statistical analysis of subspace-based methods for the retrieval of sinusoids, in the style of [3], applied to the general framework introduced in [1,2]. The formalism in [1,2] encompasses the modern nonlinear methods of MUSIC and ESPRIT and yields methods of even higher resolution. These rely on eigen decomposition of state-covariances of linear systems, as opposed to eigen decomposition of Toeplitz matrices (originating from antenna arrays or tapped delay-lines and treated, e.g., in [3]). We focus on the variability of estimates when the theory is applied to sampled covariances obtained from finite observation records, and in particular, we provide an expression for the variance of the angle operator between estimated and exact signal subspaces.