On approximate least squares estimators of parameters on one-dimensional\n chirp signal

Chirp signals are quite common in many natural and man-made systems like\naudio signals, sonar, radar etc. Estimation of the unknown parameters of a\nsignal is a fundamental problem in statistical signal processing. Recently,\nKundu and Nandi \\cite{2008} studied the asymptotic properties of least squares\nestimators of the unknown parameters of a simple chirp signal model under the\nassumption of stationary noise. In this paper, we propose periodogram-type\nestimators called the approximate least squares estimators to estimate the\nunknown parameters and study the asymptotic properties of these estimators\nunder the same error assumptions. It is observed that the approximate least\nsquares estimators are strongly consistent and asymptotically equivalent to the\nleast squares estimators. Similar to the periodogram estimators, these\nestimators can also be used as initial guesses to find the least squares\nestimators of the unknown parameters. We perform some numerical simulations to\nsee the performance of the proposed estimators and compare them with the least\nsquares estimators and the estimators proposed by Lahiri et al., \\cite{2013}.\nWe have analysed two real data sets for illustrative purposes.\n