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On estimating random amplitude chirp signals

This paper considers the problem of estimating the parameters of chirp signals with randomly time-varying amplitude. Two methods for solving this problem are presented. First, a nonlinear least-squares approach (NLS) is proposed. It is shown that by minimizing the NLS criterion with respect to all samples of the time-varying amplitude, the problem reduces to a two-dimensional maximization problem. A theoretical analysis of the NLS estimator is presented and an expression for its asymptotic variance is derived. It is shown that the NLS estimator has a variance very close to the Cramer-Rao bound. The second approach combines the principles behind the high-order ambiguity function (HAF) and the NLS approach. It provides a computationally simpler but suboptimum estimator. A statistical analysis of this estimator is also carried out. Numerical examples attest to the validity of the theoretical analysis and establish a comparison between the two proposed methods.