Estimating Parameters in Multichannel Sinusoidal Model

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.

Automated summary

This paper investigates the problem of estimating parameters in a multichannel sinusoidal model. Two estimation methods, the minimization of the sum of residual sum of squares and the use of more efficient generalized least squares estimators, are proposed and compared through simulation experiments. The results show that the variances of the generalized least squares estimators reach the Cramer-Rao lower bound, and the computational complexity does not significantly increase with the number of channels.