Robust state estimation for uncertain linear systems with random parametric uncertainties

In this paper, we investigate state estimations of a dynamical system with random parametric uncertainties which may arbitrarily affect a plant state-space model. A robust estimator is derived based on expectation minimization of estimation errors. An analytic solution similar to that of the well-known Kalman filter is derived for this new robust estimator which can be realized recursively with a comparable computational complexity. Under some weak assumptions, it is proved that this estimator converges to a stable system, the covariance matrix of estimation errors is bounded, and the estimation is asymptotically unbiased. Numerical simulations show that the obtained robust filter has an estimation accuracy comparable to other robust estimators and can be applied in a wider range.