Stochastic Robust Kalman Filtering for Linear Time-Varying Systems with a Multiplicative Measurement Noise

In this paper, a stochastic robust Kalman filtering problem is investigated for timevarying linear systems with stochastic uncertainties in its measurement matrix. The influence of parametric uncertainties on the nominal Kalman filter estimate is analyzed in the sense of classical weighted least-squares criterion. Stochastic approximation of estimation errors due to uncertainties allows us to obtain a recursive stochastic robust Kalman filter. The procedure of the stochastic error compensation is interpreted as the optimization of an indefinite quadratic cost. Considering the single stage estimation problem, the stochastic robust Kalman filter recursion is derived. As well, its existence condition is recursively checked using the estimation error covariance. It is shown that the weighted estimation error of the suggested filter is zero mean, which is the distinct property compared to the previous robust filters.