DETERMINATION OF NUMBER OF SIGNALS BASED ON MINIMUM MSE

A criterion based on the minimum MSE (mean square error) is given to d etermine the number of signals mixed with white Gaussian noise in orde r to estimate their frequencies based on the modified minimum square e rror method using a higher-order linear prediction model (CLS). Being different from the usual autoregression (AR) model of linear predictio n, the method has the advantage of iterative reduction of noise by sub traction of noise variances from diagonal elements of the correlation matrix of observed signal disturbed by noise at the instance of taking an inversion. But it needs precise estimation of both the rank of the correlation matrix and variances of noise by using only observed sign als. In this paper, the following three points are made: (1) the analy tic method to determine the order of eigenvalues which minimizes MSE c riterion derived from eigenvalue analysis; (2) the formula which must be satisfied by noise variances; and (3) the iterative algorithm which gives simultaneous solution for rank order determination of the corre lation matrix and estimation of noise variances. Finally, numerical ex amples are given to show the usefulness and correctness of the propose d MSE criterion, and some comparisons with other methods are made. (C) 1998 Scripta Technica.