Filter design for linear discrete-time systems with unknown disturbances and quantized measurements

In this paper, an unknown input filter is proposed for discrete-time linear systems with quantized measurements. The approach uses a slightly modified model of the system to estimate both the system states and the unknown input simultaneously. Two well-known quantization methods, namely linear and logarithmic, are studied and a specific design procedure is derived for each case. For the linear case, the quantization error is modelled as measurement noise and for the logarithmic case, it is modelled as a norm-bounded uncertainty. In the end, simulation results are used to illustrate the effectiveness of the proposed filter.