Sensitivity considerations in state-space model-based harmonic retrieval methods

State-space models are considered for estimating the frequencies of multiple sinusoids, and robust coordinate systems for frequency estimation are identified. It is shown that the ideal parameter set from a parameter sensitivity point of view involves estimating a unitary state transition matrix and then computing its eigenvalues to obtain an estimate of the frequencies. Procedures to estimate such matrices from covariance and time-series data are examined. It is shown that two state-space methods, the Toeplitz approximation method and direct data approximation, estimate robust state transition matrices