An Improved Tobit Kalman Filter with Adaptive Censoring Limits

TL;DR

This paper introduces an enhanced Tobit Kalman Filter that adaptively manages censored measurements with correlated noise, improving state estimation accuracy in real and synthetic data, including complex human skeleton tracking scenarios.

Contribution

The paper proposes two novel improvements to the standard TKF: exact covariance calculation considering censoring limits and probability estimation using Kalman residuals, with adaptive censoring limits for real-world applications.

Findings

Outperforms existing filters in reducing RMSE on synthetic data.

Effectively handles occlusions and interactions in human skeleton tracking.

Demonstrates robustness with both synthetic and real Kinect II data.

Abstract

This paper deals with the Tobit Kalman filtering (TKF) process when the measurements are correlated and censored. The case of interval censoring, i.e., the case of measurements which belong to some interval with given censoring limits, is considered. Two improvements of the standard TKF process are proposed, in order to estimate the hidden state vectors. Firstly, the exact covariance matrix of the censored measurements is calculated by taking into account the censoring limits. Secondly, the probability of a latent (normally distributed) measurement to belong in or out of the uncensored region is calculated by taking into account the Kalman residual. The designed algorithm is tested using both synthetic and real data sets. The real data set includes human skeleton joints' coordinates captured by the Microsoft Kinect II sensor. In order to cope with certain real-life situations that cause problems in human skeleton tracking, such as (self)-occlusions, closely interacting persons etc., adaptive censoring limits are used in the proposed TKF process. Experiments show that the proposed method outperforms other filtering processes in minimizing the overall Root Mean Square Error (RMSE) for synthetic and real data sets.