Robust Wiener filtering based on probabilistic descriptions of model errors

A new approach to robust estimation of signals and prediction of time{ series is considered. Possible modelling errors are described by sets of systems , parametrized by 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 factorizations 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. The methodology can be applied to any open loop ltering or control problem.