A statistically efficient algorithm for estimating the parameters of a chirp signal model with time-varying amplitude

Parameter estimation of chirp signal model with time-varying amplitude and additive noise is a critical problem in statistical signal processing. A statistically efficient algorithm is proposed to estimate the nonlinear parameters of frequency rate (FR) and initial frequency (IF). Initial estimates are first deduced from the ambiguity function (AF) and then refined through a statistics-based iterative procedure that improves their convergence rates from O-p(N-1) and O-p(N-2) to O-p(N-3/2) and O-p(N-5/2), respectively. It is worth noting that the convergence rates of FR and IF double while being controlled by each other at each iteration, causing the convergence rates of FR and IF to jump up and down before the algorithm converges. Four iterative processes are considered involving crossovers between two types of initial estimators and two types of iterative coefficients. The asymptotic distribution of the refined estimators is obtained and demonstrated to be bivariate normal, and the Cramer-Rao lower bound (CRLB) is derived for each. Monte Carlo simulations were performed to verify the effectiveness of the proposed algorithm.