Sampled-data minimum variance filtering

摘要

This paper deals with the optimal solution to the sampled-data minimum variance filtering problem for linear systems with noise in the states and in the measurements.The solution is derived in the time-domain by using a fast sampling zero-order hold input discretization of the continuous time systems together with a lifting technique.The original sampled-data system is transformed into an equivalent LTI discrete-time system with infinite-dimensional input-output space.However,the designed filter is finite-dimensional.We derive both the existence conditions and the explicit expression of the desired filter and provide an illustrative numerical example.