Kalman Filtering by Minimax Criterion with Uncertain Noise Intensity Functions

The problem of minimax filtering is examined for linear continuous-time observation models with uncertain intensities of non-stationary white noises. For designing algorithms of minimax filtering, the method of dual optimization is used together with the techniques of the maximum principle. It is shown that the Kalman filter is a minimax one if its coefficients are defined by the least favorable noise intensity. The explicit form of the minimax filter is derived in the case of scalar state and observation processes with arbitrarily correlated disturbances. The results of numerical modeling are also presented.