Robust state estimation for linear systems with parametric uncertainties and quantised measurements

In this paper, the problem of state estimation for linear systems with bounded parametric uncertainties and quantised measurements is addressed. The quantised measurements are random variables of which the probability density functions (PDF) are closely related to the uncertain system parameters. Thus the statistical information of the quantised measurements and the deterministic bounds of the parametric uncertainties need to be incorporated in the design. Based on this, a robust estimator is proposed to minimise the worst-case expectation of the regularised residual norm over all possible parametric uncertainties. An iterative algorithm is presented to obtain the optimal solution. Simulation results are provided to show the effectiveness of the proposed estimator.