Tobit Kalman filter with time-correlated multiplicative measurement noise

Kalman filters for discrete-time linear systems with censored measurements have been developed, of which the Tobit Kalman filter has been shown an effective candidate. In this study, the authors expand the Tobit Kalman filter to discrete-time linear systems with time-correlated multiplicative measurement noise. By introducing several new terms including the estimates for the products of multiplicative measurement noise and the state as well as their error covariance matrices, the proposed filter can be implemented in a recursive manner. A numerical example involving radar tracking is provided to show the effectiveness of the proposed filter.