Estimating the parameters of multiple chirp signals

Chirp signals occur naturally in different areas of signal processing. Recently, Kundu and Nandi (2008) considered the least squares estimators of the unknown parameters of a chirp signal model and established their consistency and asymptotic normality properties. It is observed that the dispersion matrix of the asymptotic distribution of the least squares estimators is quite complicated. The aim of this paper is twofold. First, using a number theoretic result of Vinogradov (1954), we present a simplified form of the above mentioned dispersion matrix. Secondly, using the orthogonal structure of the different chirp components, we propose a step by step sequential estimation procedure of the unknown parameters of the model. Under the proposed sequential procedure, the problem of estimation of the parameters of a multiple chirp signal model reduces to solving only a two dimensional optimization problem at each step. It is observed that the estimators obtained by the proposed method are strongly consistent. Due to the complicated nature of the model, we could not establish the asymptotic distribution of the proposed sequential estimators. We perform some simulation experiments to compare the performance of the proposed and least squares estimators for small sample sizes, and for different parameter values. It is observed that the mean squared errors of the proposed estimators are very close to the corresponding mean squared errors of the least squares estimators. Two real data sets have been analyzed for illustrative purposes.