Robust Filtering Based on Probabilistic Descriptions of Model Errors

A new approach to robust estimation of signals and prediction of time{series is considered. Signal and system parameter deviations are represented as random variables, with known covariances. A robust design is obtained by minimizing the squared estimation error, averaged both with respect to model errors and noise. A polynomial solution, based on averaged spectral factor-izations and averaged Diophantine equations, is derived. The robust estimator is called a cautious Wiener lter. It turns out to be no more complicated to design than an ordinary Wiener lter.