Outlier probability of generalized chirpogram-based estimators for multicomponent polynomial-phase signals

Outliers are often encountered by estimators that have a nonlinear nature. In this paper, the probability of outliers is derived concerning the generalized chirpogram (GC)-based estimators for polynomial-phase signals (PPS). To derive the approximate theoretical expressions, we develop an approach that is based on the extrema theory of complex Gaussian envelope and the asymptotic Poisson model. The semi-aliasing effect of PPS is also considered in order to predict the outliers more accurately. Then expressions of the probability of outliers are presented for several typical cases of PPS, including single-tone and chirp signals and their two-component versions. The GC with the Hamming windowing is also incorporated. Numerical examples of computer simulations are also provided to show the accuracy of the theoretical expressions.