Estimation of the Elementary Chirp Model Parameters

In this article, we propose techniques for estimating elementary chirp model parameters, which are encountered in sonar, radar, acoustics, and other areas. We derive asymptotic theoretical properties of least squares estimators and approximate least squares estimators for the one component elementary chirp model. It is proved that the proposed estimators are strongly consistent and follow the normal distribution asymptotically. We also suggest how to obtain proper initial values for these methods. The problem of finding initial values is a difficult one when the number of components in the model is large, or when the signal-to-noise ratio is low, or when two frequency rates are close to each other. We propose sequential procedures to estimate multiple component elementary chirp model parameters. We prove that the theoretical properties of sequential least squares estimators and sequential approximate least squares estimators coincide with those of least squares estimators and approximate least squares estimators, respectively. Further, the asymptotic variances of the proposed estimators attain the Cramér–Rao lower bounds asymptotically when errors are normal random variables and independently and identically distributed. To evaluate the performance of the proposed estimators, numerical experiments are performed. It is observed that the proposed sequential estimators perform well even in situations where least squares estimators do not perform well. We illustrate the performance of the proposed sequential algorithm on bat data.