Set-valued observers for constrained state estimation of discrete-time systems with quantized measurements

We describe a recursive set-valued observer for discrete-time linear systems with quantized measurements. The observer is aimed at obtaining the smallest set-valued state estimate at every sampling instant. We limit computational complexity by deploying a block moving horizon strategy. Starting with a simple case, we incrementally enhance the observer design in order to improve performance in the presence of measurement noise, model inaccuracy and disturbances. We also implement a simple observer/controller strategy and demonstrate its performance by means of a simulation example.