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 Cramér–Rao lower bounds (CRLB’s). 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.