Estimating Parameters in Multichannel Sinusoidal Model

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Research Article

Publication Title

Circuits, Systems, and Signal Processing


In this paper, we study the problem of estimation of parameters of multichannel sinusoidal model. In multichannel sinusoidal model, the inherent frequencies from distinct channels are same with different amplitudes. It is assumed that the errors in individual channel are independently and identically distributed, whereas the signal from different channels is correlated. We first propose to minimize the sum of residual sum of squares to estimate the unknown parameters, and they can be easily obtained. Next we propose to use more efficient generalized least squares estimators which become the maximum likelihood estimators also when the errors follow multivariate Gaussian distribution. Both the estimators are strongly consistent and asymptotically normally distributed. We have provided the implementation of the generalized least squares estimators. Simulation experiments have been performed to compare the performances of the least squares estimators and generalized least squares estimators. It is observed that the variances of the maximum likelihood estimators reach the Cramer–Rao lower bound even for moderate sample sizes. We have extended the methods of estimation and the associated results of the two-channel model to an arbitrary m-channel model. It is observed that the computational complexity does not increase significantly with the increase in number of channels.

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