State estimation for nonlinear systems with unknown inputs using SDC factorization

This paper considers the unknown input filtering (UIF) problem of nonlinear stochastic systems with arbitrary unknown inputs. A possible solution to solve this more general UIF problem is to apply the recently proposed unified framework of unknown inputs decoupled nonlinear estimator designs, by which a specific derivative-based estimator (DBE) can be obtained to achieve the goal. However, the DBE may not work well due to the fact that the obtained Jacobians of the nonlinearities in the system dynamics and measurements may have large errors. In this paper, a system reformation using the state-dependent coefficient (SDC) factorization technique is further proposed to remedy the aforementioned filtering degradation problem. In the sequel, the addressed nonlinear UIF problem can be easily solved by using the well-known linear UIF algorithm. An illustrative example is given to show the usefulness of the proposed results.