Self-Calibration Kalman Filter with Linearly-Varying Unknown Input

State estimation for stochastic systems with unknown inputs has been a research hotspot in recent years. Many research results including the augmented state Kalman filter, the two-stage Kalman filter, the optimal two-stage Kalman filter and the robust two-stage Kalman filter (RTSKF) have been developed by various researchers. Considering that unknown inputs sometimes vary linearly in practical engineering, this paper addresses the problem of state estimation for linear systems with linearly-varying unknown inputs. A self-calibration Kalman filter with linearly-varying unknown input (SCKF-LVUI) is proposed where the unknown input is estimated by exploring the information from the state equation and state estimates at previous steps. The derivation of the SCKF-LVUI is given and the state estimate are calculated as well as the corresponding covariance matrix. Furthermore, a simulation example is conducted and demonstrates that the presented SCKF-LVUI has high estimation accuracy and can be conveniently applied in engineering applications.