Approximate least squares estimators of a two-dimensional chirp model and their asymptotic properties

An efficient methodology to estimate the parameters of a two-dimensional chirp signal model

“…However, this replacement simplifies the estimation process to a great extent as the evaluation of periodogram-type functions does not involve matrix inversion. This relationship is analogous to the one that was first proposed by Walker [2] for the sinusoidal model and later Grover et al [17,18] extended the same for 1-D and 2-D chirp models. The estimators obtained by maximising a periodogram function [2] or a periodogram-type function [17,18] are called the approximate least squares estimators (ALSEs).…”

“…This relationship is analogous to the one that was first proposed by Walker [2] for the sinusoidal model and later Grover et al [17,18] extended the same for 1-D and 2-D chirp models. The estimators obtained by maximising a periodogram function [2] or a periodogram-type function [17,18] are called the approximate least squares estimators (ALSEs). In fact, Grover et al [17,18] showed that the ALSEs are strongly consistent and asymptotically equivalent to the corresponding LSEs.…”

“…The estimators obtained by maximising a periodogram function [2] or a periodogram-type function [17,18] are called the approximate least squares estimators (ALSEs). In fact, Grover et al [17,18] showed that the ALSEs are strongly consistent and asymptotically equivalent to the corresponding LSEs. Furthermore, they showed that the ALSEs have two distinctive and noteworthy aspects− (a) their consistency is obtained under slightly less restrictive assumptions on the linear parameters than those required for the LSEs and (b) their computation is faster as compared to the LSEs due to absence of a matrix inversion in the former case.…”

“…Parameter estimation of a 2-D chirp signal is an important statistical signal processing problem. Recently Zhang et al [8], Lahiri et al [11] and Grover et al [18] proposed some estimation methods of note. For instance, Zhang et al [8] proposed an algorithm based on the product cubic phase function for the estimation of the frequency rates of the 2-D chirp signals under low signal to noise ratio and the assumption of stationary errors.…”

“…The rates of convergence of the amplitude estimates were observed to be M −1/2 N −1/2 , of the frequencies estimates, they are M −3/2 N −1/2 and M −1/2 N −3/2 and of the frequency rate estimates, they are M −5/2 N −1/2 and M −1/2 N −5/2 . Grover et al [18] proposed the approximate least squares estimators (ALSEs), obtained by maximising a periodogram-type function and under the same stationary error assumptions, they observed that ALSEs are strongly consistent and asymptotically equivalent to the LSEs.…”