Robust filtering by fictitious noises

In this paper, a new approach is presented for robust filtering of a linear discrete-time signal by applying fictitious noise. Modeling errors, in both the numerator and denominator of the transfer functions, are parameterized by using random variables with zero mean and known covariance. The robust performance is obtained by minimizing the mean square estimation error over all of the random parameter and noise. To derive a robust estimator, the uncertainties in the model are incorporated into two mutually uncorrelated fictitious noises with zero means. The covariances of the fictitious noises are computed by using two formulas that are presented in this paper. An illustrative example shows the effectiveness of our approach.