Parameter estimation of harmonic linear chirps

We address the problem of estimating the initial frequency and frequency rate of a linear chirp with harmonic components given time samples of the observed signal. As an alternative to the maximum likelihood estimator, which requires an exhaustive search in the initial frequency-frequency rate space, we present a two-step estimation method. First, the signal is separated into its harmonic components. Then, the two parameters of the fundamental component are jointly estimated using a least squares approach given the estimated time-varying phase of each separated component. This method is compared to the maximum likelihood and to a modified high-order ambiguity function based method. Simulations results and a real data example demonstrate the performance of the proposed method. In particular, it is shown that the estimates achieve the Cramer-Rao lower bound at high signal-to-noise ratio and that the two-step method outperforms the high-order ambiguity function based method.