Spectral line tracking for nonstationary random processes

The harmonic decomposition of a random process into a sum of sinusoids in white noise is an important problem with applications in a number of different areas. As a result of the work of V.F. Pisarenko, it has been shown that the sinusoidal frequencies and the white noise power are determined by the minimum eigenvalue and the corresponding eigenvector of the autocorrelation matrix. Many authors have formulated adaptive versions of the Pisarenko solution for the purpose of spectral line tracking, but most have concentrated only on stationary sinusoids. In most of the interesting applications, however, the frequencies of the sinusoids change, thus they are nonstationary. In this paper we concentrate on the nonstationary case, and propose a novel fast iterative technique for real-time tracking of the time-varying frequencies. Simulation examples are given which compare the iterative method to other data-adaptive techniques. These examples show that the proposed method converges to good estimates of the frequencies much more quickly than the adaptive techniques as well as being able to perform better in tracking nonstationary sinusoids.