Robust Kalman Filter for Linear System With Convex Polytopic Uncertainties

This brief considers robust Kalman filtering problem for linear discrete-time systems with convex polytopic uncertain parameters. First, we characterize the uncertain parameter matrices as a combination of several vertex matrices. Then, based on the mean square stability and $\mathbf {H}_{2}$ and variance-constrained performance criteria, we design a variance-constrained based robust Kalman filter. The parametric matrices of the filter can be directly obtained by the variance-constrained optimization and MATLAB Toolbox. A classical instance is provided to verify the effectiveness of the proposed filter.