The Tobit Kalman Filter: An Estimator for Censored Measurements
Tobit model censored data arise in multiple engineering applications through saturating sensors, limit of detection effects, and image frame effects. In this brief, we introduce a novel formulation of the Kalman filter for Tobit Type 1 censored measurements. Our proposed formulation, called the Tobit Kalman filter, is identical to the standard Kalman filter in the no censoring case. At or near the censored region, the Tobit Kalman filter utilizes a local approximation of the probability of censoring in order to provide a fully recursive estimate of the state and state error covariance. The additional computational burden of the method compared with the standard Kalman filter is limited to the calculation of m normal probability density functions and m normal cumulative density functions per update, where m is the number of measurements.
IEEE Transactions on Control Systems Technology