Coloured Tobit Kalman Filter

TL;DR

This paper introduces an improved Tobit Kalman Filter that accounts for coloured noises and accurately computes censored measurement moments, enhancing filtering performance in real-world scenarios.

Contribution

The paper proposes a novel Tobit Kalman Filter that incorporates coloured noises and exact moment calculations for censored data, advancing existing filtering techniques.

Findings

Outperforms existing methods in RMSE reduction

Effective in handling coloured noises in censored measurements

Validated through simulation experiments

Abstract

This paper deals with the Tobit Kalman filtering (TKF) process when the one-dimensional measurements are censored and the noises of the state-space model are coloured. 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, coloured 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.