A Fast Algorithm for Estimating the Parameters of a Quadratic FM Signal

Abstract

Abstract—This paper describes a fast algorithm that can be used for estimating the parameters of a quadratic frequency modulated (FM) signal. The proposed algorithm is fast in that it requires only one-dimensional (1-D) maximizations. The optimal maximum likelihood method, by contrast, requires a three-dimensional (3-D) maximization, which can only be realized with an exhaustive 3-D grid search. Asymptotic statistical results are derived for all the estimated parameters. The amplitude estimate is seen to be optimal, whereas the phase parameters are, in general, suboptimal. Of the four phase parameter esitmates, two approach optimality as the signal-to-noise ratio (SNR) tends to infinity. The other two have mean-square errors that are within 50 % of the theoretical lower bounds for high SNR. Simulations are provided to support the theoretical results. Extensions to multiple components and higher order FM signals are also discussed. Index Terms—Cubic phase function, parameter estimation, polynomial phase signals, statistical signal processing. I.