Robust H 2 Estimation

This paper considers the design of robust, nite-horizon and innnite-horizon H 2 estima-tors based on multliplier theory (which is intimately related to the mixed structured singular value). Speciically, the Popov-Tsypkin multiplier is used to develop a novel upper bound on a nite-horizon, cost function for the assumed uncertainty set. The results are then applied to develop design equations for robust H 2 estimation which collapse to the standard Kalman lter design equations if the uncertainty is absent. The robust design equations are complex and possible solution approaches are discussed. Robust estimation using the Popov-Tsypkin multiplier is illustrated by using a parameter optimization approach (in particular, a zero-prediction, continuation algorithm) to design a robust lter for an innnite-horizon H 2 cost function.