Mean likelihood frequency estimation

Estimation of signals with nonlinear as well as linear parameters in noise is studied. Maximum likelihood estimation has been shown to perform the best among all the methods. In such problems, joint maximum likelihood estimation of the unknown parameters reduces to a separable optimization problem, where first, the nonlinear parameters are estimated via a grid search, and then, the nonlinear parameter estimates are used to estimate the linear parameters. We show that a grid search can be avoided by using the mean likelihood estimator for estimating the unknown nonlinear parameters and how its performance can be made equivalent to that of the maximum likelihood estimator (MLE). The mean likelihood estimator requires computation of a multidimensional integral. However, using the concepts of importance sampling, we obtain the mean likelihood estimate without using integration. The technique is computationally far less burdensome than the direct maximum likelihood method but performs just as well. Simulation examples for estimating frequencies of multiple sinusoids in noise are given. The general technique can be applied to a large class of nonlinear regression problems.