The robust generalized least-squares estimator

Abstract

This paper addresses the problem of robust linear estimations of systems perturbed by noise with a wide sense stationary process (WSS). The noise spectral density is known only to be in a neighborhood of some specified spectral density. Additionally the system's impulse response function is assumed to be a random process. A generalized least-squares estimator (GLS) in the frequency domain is considered and it is demonstrated that where the Fourier transform is applied to the observed data, robust estimation occurs. The experiment shows that the sample maximum variance depends on noise contamination for large data segments and depends on the upper bound of the robust method for short data segments. The proposed approach is simple to implement and can be very effective in several practical applications.