Estimation of saturated data using the Tobit Kalman filter

Abstract

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.