On a Chirp-Like Model and Its Parameter Estimation Using Periodogram-Type Estimators

Parametric modelling of physical phenomena has received a great deal of attention in the signal processing literature. Different models like ARMA models, sinusoidal models, harmonic models, models with amplitude modulation, models with frequency modulation and their different versions and combinations have been used to describe natural and synthetic signals in a wide range of applications. Two of the classical models that were considered by Professor C. R. Rao were one-dimensional superimposed exponential model and two-dimensional superimposed exponential model. In this paper, we consider parameter estimation of a newly introduced but related model, called a chirp-like model. This model was devised as an alternative to the more popular chirp model. A chirp-like model overcomes the problem of computational difficulty involved in fitting a chirp model to data to a large extent and at the same time provides visually indistinguishable results. We search the peaks of a periodogram-type function to estimate the frequencies and chirp rates of a chirp-like model. The obtained estimators are called approximate least squares estimators (ALSEs). We also put forward a sequential algorithm for the parameter estimation problem which reduces the computational load of finding the ALSEs significantly. Large-sample properties of the proposed estimators are investigated and the results indicate strong consistency and asymptotic normality of the ALSEs as well as the sequential ALSEs. The performance of the estimators is analysed in an extensive manner both on synthetic as well as real world signals and the results indicate that the proposed methods of estimation provide reasonably accurate estimates of frequencies and frequency rates.