Separable estimation of discrete and continuous spectra based on genetic algorithm

This paper is concerned with a method for separately estimating line and continuous spectra of signals which are composed of multiple sinusoids and an autoregressive (AR) noise. The whitening filter approach is proposed in which the frequency estimates are obtained by applying the Toeplitz approximation method to the output of the whitening filter. The filter coefficients which correspond to the AR parameters are iteratively calculated so as to minimize the squared prediction error criterion, however, the solution is a local minimum. By employing the genetic algorithm in the choice of initial values of the iterative AR parameter estimation, we can attain a globally optimal solution. The decision rule for deciding the number of sinusoids and the order of the AR model is also investigated. The validity of the proposed algorithm is examined in numerical simulations including a benchmark example.