In view of the situation that system state equations are influenced by unknown inputs (such as environmental influence

improper selection of models or parameters

and etc.)

a nonlinear self-calibration filtering recursive method for state equations with unknown inputs was proposed based on two nonlinear Kalman filtering methods

the self-calibration rank filter (SRF) and the self-calibration unscented Kalman filter (SUKF) were discussed respectively. According to numerous numerical simulation results and engineering applications

by estimating and compensating the unknown inputs in state equations automatically

the proposed algorithm can improve the filtering effect of the system under the influence of unknown inputs

and the estimation accuracy increased by 80% when compared with the unscented Kalman filtering method (UKF). Moreover

the calculation was simple and convenient for engineering applications.