Unbiased Spectral Estimation and System Identification Using Short-Time Spectral Analysis Methods

Abstract

The methods of system identification and spectral analysis are well documented in the literature. In this paper, we attempt to merge the methods of least-square system identification and short-time Fourier transform spectral estimation. Starting from the least-squares normal equations for a linear system identification problem and expanding the signals in short-time Fourier transforms, we derive a Toeplitz system of equations, the solution of which approximates the original least-squares equation solution. We then bound the error norm between the two solution methods and show the properties of the error by numerical methods. The resulting “spectral” estimation method is shown to completely remove the bias normally associated with previously proposed spectral estimation procedures. The method appears to be particularly useful when one is interested in linear system identification of very large systems (long impulses response) or for system identification in the presence of nonstationary (eg., hurst) noise. Extensive numerical results are included.