Robust filter design for uncertain systems defined by both hard and soft bounds

A new approach to robust linear filter design is described that attempts to combine the advantages of H_∞ robust linear synthesis with a probabilistic method of system and noise modeling. The signal and measurement noise model parameters are assumed to be subject to perturbations represented by random variables with known covariances. The system is represented in polynomial form, and the uncertainty can be described by both soft and hard bounds. An H_∞ cost-function is minimized and averaged with respect to model errors in signal and noise descriptions. The polynomial solution is no more complicated than the usual H_∞ optimal filter and involves averaged spectral factorizations and linear equations. Both usual and deconvolution filtering problems are considered