Convex Optimization for Frequency Estimation and Related Problems

Description

Estimation of the frequencies of sinusoidal signals from a finite number of noisy discrete-time measurements has been an active research area to date because of its wide applications in science and engineering. Although the maximum likelihood estimator, nonlinear least squares technique and periodogram can provide optimum frequency estimation performance, the cost functions of all these methods are multimodal and two steps are typically involved in the estimation procedure: suboptimal initial parameter estimates are first obtained and then a refinement is made through an iterative optimization of the cost functions. As a result, sufficiently accurate initial estimates are critical to achieve the globally optimum solutions. In this research, the researchers propose to approximate these estimators using convex optimization technique so that high-performance global solutions can be obtained. Related signal processing problems, namely, parameter estimation of polynomial-phase signals, system identification and polynomial root finding, will also be investigated in the convex optimization framework.