Simultaneous input and state estimation of linear discrete-time stochastic systems with input aggregate information

In this paper, we present filtering algorithms for simultaneous input and state estimation of linear discrete-time stochastic systems when the unknown inputs are partially known, i.e., when some aggregate information of the unknown inputs is available as linear equality or inequality constraints. The stability and optimality properties of the filters are presented and proven using two complementary perspectives. Specifically, we confirm the intuition that the partial input information improves the performance of the filters when a linear input equality constraint is given. On the other hand, given a linear inequality constraint, we show that the estimate error covariance is decreased but the estimates may be biased.