Set Membership State Estimation with Quantized Measurements and Optimal Threshold Selection

The problem of state estimation with quantized measurements is addressed in the set membership estimation setting. The main contribution concerns the optimal selection of the quantizer thresholds in order to minimize the worst-case radius of the feasible state set. This allows one to design adaptive quantizers reducing the uncertainty associated to the state estimates. The proposed solution is applied to several outer approximations of the feasible sets, based on parallelotopes, zonotopes and constrained zonotopes. The benefits of the threshold selection mechanism are assessed on a numerical example, highlighting the trade off between computational burden and uncertainty reduction.