Parameter estimation of multi-component chirp signals based on discrete chirp Fourier transform and population Monte Carlo

Abstract

In this paper, a parameter estimation method for multi-component chirp signals with white Gaussian noise is proposed based on the modified discrete chirp Fourier transform (MDCFT) and the population Monte Carlo (PMC) methodology, in which the model order is unknown. By utilizing the integrability of linear parameters in the Bayesian model, this paper considers the posterior distribution of nonlinear parameters. MDCFT was adopted to calculate the chirpogram of the observed data, and clear peaks can be detected in the discrete chirp Fourier transform domain. The importance function (IF) was constructed according to the peaks, and the PMC algorithm was employed to evaluate the posterior distribution. The proposed method cannot only use the selected IF to generate the sample fitting target function in the parameter region of interest, but can also utilize samples and importance weights to update the IF adaptively. The simulation results indicated that the proposed method can realize joint Bayesian model selection and parameter estimation of multi-component chirp signals. Compared with the two existing methods based on Monte Carlo methodology, the proposed method exhibits improved performance.