Robust adaptive Kalman filters for linear time-varying systems with stochastic parametric uncertainties

We present an adaptive robust Kalman filtering algorithm that addresses estimation problems that arise in linear time-varying systems with stochastic parametric uncertainties. The filter has the one-step predictor-corrector structure and minimizes the mean square estimation error at each step, with the minimization reduced to a convex optimization problem based on linear matrix inequalities. The algorithm is shown to converge when the system is mean square stable and the state-space matrices are time-invariant. A numerical example, consisting of equalizer design for a communication channel, demonstrates that our algorithm offers considerable improvement in performance when compared to standard Kalman filtering techniques.

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