A game theoretic approach to linear dynamic estimation

he state estimation problem of a linear dynamic system, in a deterministic as well as a stochastic framework, is addressed. In the deterministic scenario, the disturbances are assumed as finite energy processes of an unknown spectrum. The measure of performance is in the form of a disturbance attenuation function and resembles an induced norm. An optimal estimate bounds the attenuation function from above. The disturbance attenuation function is converted to a performance measure for a zero-sum linear-quadratic (LQ) game and the exogenous inputs--the disturbances and the initial state--are viewed as adversaries to the estimator. Adopting a variational procedure, optimal strategies of each player in the game are determined. These optimal strategies are shown to satisfy a saddle point condition. Satisfaction of the saddle inequality helps establish the bound on the disturbance attenuation function. The optimal estimator, restricted to a class of functions of the measurement alone, is both unbiased and linear in structure. With a few mild assumptions, the results are extended to a linear time-invariant system on an infinite horizon and the optimal estimator obtained is shown to impose an upper bound on the ;In the stochastic framework, the disturbances are assumed to be white Gaussian processes and the measure of performance chosen is the expected value of an exponential function of the estimation error. If the statistical parameters are viewed as deterministic weighting functions in the attenuation function, the optimal statistical estimator obtained by minimizing the exponential cost is identical to the deterministic estimator. The worst-case...