A dynamic game approach to mixed H-infinity/H-2 estimation

A deterministic, two-person, zero-sum, linear quadratic estimation game, which is closely related to the mixed H-infinity/H-2 estimation problem, is introduced. The strategy of the estimator in this game must guarantee a prescribed H-infinity-performance level gamma. If the desired H-infinity-performance level is not achieved by an H-2-optimal estimator, the H-2-performance of the estimator must be degraded. An optimal estimator, in the sense of this game, minimizes the ratio between the resulting H-2-performance degradation, and the performance degradation that would have been obtained if one had used the standard H-infinity-central filter. Both the continuous and the discrete-time cases are treated.