Estimation of saturated data using the Tobit Kalman filter

Saturated, clipped or censored data arises in multiple engineering applications including sensors systems and image based tracking. The saturation limits of a measurement consist of an upper limit and lower limit on the measurements. When a measurement is near a saturated region or in saturated region a standard Kalman filter will be biased and unable to track the true states. In this paper, we use a novel formulation of the Kalman filter for Tobit Type 1 censored measurements. The proposed formulation, called the Tobit Kalman filter for saturated data, converges to the standard Kalman filter in the no-censoring case. A motivating example is presented to demonstrate the usefulness of an estimator for censored data.