Game theory approach to state estimation of linear discrete-time processes and its relation toH∞-optimal estimation

A game theory approach to constrained minimax state estimation

“…This paper generalizes the results of [30] so that minimax state estimation can be performed while satisfying equality constraints on the state estimate. The major contribution of this paper is the development of a minimax state estimator for linear systems that enforces equality constraints on the state estimate.…”

“…We will assume that , and are mutually uncorrelated unity-variance white noise sequences that are uncorrelated with . This form of the adversary's input is not intuitive because it uses the state estimation error, but this form is taken because the solution of the resulting problem results in a state estimator that bounds the infinity norm of the transfer function from the random noise terms to the state estimation error [30]. [This is discussed further following (15).…”

“…The noise in (1) is introduced by an adversary that has the goal of maximizing the estimation error. Similar to [30], we will assume that our adversary's input to the system is given by (6) where is a gain to be determined, is a given matrix, and is a noise sequence. We will assume that , and are mutually uncorrelated unity-variance white noise sequences that are uncorrelated with .…”

“…Motivated by [30], we define the objective function as (15) where is any positive definite weighting matrix. The differential game is for the filter designer to find a gain sequence that minimizes , and for the adversary to find a gain sequence that maximizes .…”

“…The major contribution of this paper is the development of a minimax state estimator for linear systems that enforces equality constraints on the state estimate. We formulate the problem as a particular game which was shown in [30] to be equivalent to an state estimation problem. We then derive the estimator gain and adversary gain that yields a saddle point for the constrained estimation problem.…”