Hybrid FM-polynomial phase signal modeling: parameter estimation and Cramer-Rao bounds

Parameter estimation for a class of nonstationary signal models is addressed. The class contains combination of a polynomial-phase signal (PPS) and a frequency-modulated (FM) component of the sinusoidal or hyperbolic type. Such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components. A novel approach is proposed that allows us to decouple estimation of the FM parameters from those of the PPS, relying on properties of the multilag high-order ambiguity function (ml-HAF). The accuracy achievable by any unbiased estimator of the hybrid FM-PPS parameters is investigated by means of the Cramer-Rao lower bounds (CRLBs). Both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on Monte Carlo simulations.