Estimation of mixed spectrum using genetic algorithm

This paper proposes a method for estimating the mixed spectrum which is composed of line and continuous spectra, the latter of which is characterized by an AR or ARMA noise model. Line spectrum is represented by multiple sinusoids. In order to avoid simultaneous minimization of a prediction error criterion with respect to all unknown parameters, we give an efficient iterative algorithm for estimating the frequencies of the sinusoids and other parameters separately. By adopting the genetic algorithm in choice of initial values of the AR or ARMA parameters in the iterative estimation, we can attain a globally optimal estimates of unknown parameters. The frequency estimate is given by a modified Toeplitz approximation method using a shifted correlation matrix of observed signals. The effectiveness of the proposed algorithm is validated in numerical simulations.