Sinusoidal Parameter Estimation Using Roots of an Algebraic Equation

Abstract

An algorithm for estimating sinusoidal parameters is presented. In this paper, it is assumed that an observed signal is a single sinusoidal signal contaminated by white Gaussian noise. Based on this assumption, the sinusoidal parameters can be found by minimizing a cost function using the mean squared error (MSE) between the observed signal and a sinusoidal signal with arbitrary sinusoidal parameters. Because the cost function is nonlinear and not convex, it has undesirable local minima. To solve the minimization problem, we propose to use the roots of an algebraic equation. The algebraic equation is derived straightforwardly from the cost function. We show that the global solution is formulated by using the roots of the algebraic equation.