A game theory approach to the state-estimation of linear discrete-time systems is presented. The resulting state estimation suggests an alternative to the Kalman filter, in cases where the exact statistics of the input and the measurement noise processes is not known. It turns out that the game-theoretic filter provides anH∞-optimal estimation. Moreover, it is shown that the covariance matrix of the estimation error is bounded, from above, by the solution of a modified Riccati equation.