Constrained State Estimation for Nonlinear Systems with Unknown Input

This paper extends the problem of state estimation for linear discrete-time systems with unknown input to the nonlinear systems. Based on physical consideration, the constraints of state are also considered. And the constraints which can improve the quality of estimation are imposed on individual updated sigma points as well as the updated state. The advantage of algorithm is that it is able to deal with arbitrary constraints on the states during the estimation procedure, Least-squares unbiased estimation algorithm can be used to obtain unknown input, and the unknown input which can be any signal affects both the system and the outputs. The state estimation problem is transformed into a standard Unscented Kalman filter problem which can easily be solved. Simulations are provided to demonstrate the effectiveness of the theoretical results.