State estimation for nonlinear systems with unknown inputs

This paper describes an unknown input filtering framework for the state estimation of nonlinear systems with arbitrary unknown inputs. It is known that the celebrated extended Kalman filter (EKF) may have poor performance due to the lack of the true dynamics of the unknown input. A possible remedy to improve the performance is to apply an EKF-like nonlinear version of the recently developed ERTSF (NERTSF), which however may encounter implementation problem because it may be prohibitively difficult or impossible to obtain all the Jacobians and Hessians of complex nonlinear systems. In this paper, a general derivative-free version of the NERTSF is further proposed to avoid the need for the calculation of model partial derivatives. Simulation results illustrate that this new nonlinear filter may have comparable performance to the NERTSF.