Nonstationary spectral peak estimation by Monte Carlo filter

The aim of research is to estimate multiple peaks of the power spectrum that are varying with time. A model to estimate the time-varying peaks has been proposed by the author. The model is written in a state space representation composed of a system model and an observation model. The system model denotes smooth change of a state vector that consists of pairs of peak frequency and bandwidth. The observation model is an autoregressive model with time-varying coefficients that are nonlinearly parametrized by the state vector. The nonlinear parametrization is based on the fact that the pairs of frequency and bandwidth are roots of the characteristic equation of the autoregressive model. By estimating the state vector giving the observations results, the estimation of the frequency and bandwidth pairs results in a time-varying power spectrum. In state estimation, the nonlinear and non-Gaussian properties should be treated because of the nonlinear formulation of the model. As a method of state estimation, we have employed an approximation of non-Gaussian distribution and its realizations, called the Monte Carlo filter. Through numerical examples, the estimation precision of the peak frequency has been checked by comparison with a conventional model.