Maximum a Posteriori Based Fundamental Frequency and Order Estimation in Impulsive Noise

In this article, we present a maximum
a posteriori
(MAP) based framework to deal with the challenging problem of joint fundamental frequency and order estimation for harmonic signal corrupted by impulsive noise, which is modeled as Gaussian noise contaminated by outliers. In the proposed method, parameters including the fundamental frequency (subject to possible scaling), noise variance, signal waveform and precision parameters of the outliers are firstly jointly estimated through maximizing the posterior probability density function (PDF). To tackle the consequent problem, the expectation-maximization (EM) algorithm is employed and an alternating optimization method is developed to solve the multi-variable optimization problem in the maximization step. Based on the estimated parameters, the order of the harmonic signal is determined according to the MAP criterion. Moreover, the scaling of fundamental frequency is resolved according to the order estimate and selected harmonic components. Simulation results demonstrate the superiorities of the proposed approach in comparison with existing schemes.