Colored Tobit Kalman filter

Abstract

This article deals with the Tobit Kalman filtering (TKF) process when the one-dimensional measurements are censored and the noises of the state-space model are colored. Two improvements of the standard TKF process are proposed. Firstly, the exact moments of the censored measurements are calculated via the moment generating function of the censored measurements. Secondly, colored noises are considered in the proposed method in order to tackle real-life problems, where the white noises are not common. The designed process is evaluated using two experiments-simulations. The results show that the proposed method outperforms other methods in minimizing the Root Mean Square Error (RMSE) in both experiments.

Keywords:

• Censored data
• moment generating function
• Kalman filtering
• colored noise

Acknowledgement

I would like to thank Prof. George Tsaklidis, (Department of Mathematics, Aristotle University of Thessaloniki, Greece) for his useful remarks and indications in writing this article.