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.

中文翻译：

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具有自适应删失限制的改进 Tobit Kalman 滤波器

本文讨论了测量相关和删失时的托比特卡尔曼滤波 (TKF) 过程。考虑区间删失的情况，即测量值属于具有给定删失限制的某个区间的情况。提出了标准 TKF 过程的两项改进，以估计隐藏状态向量。首先，通过考虑删失限制来计算删失测量的精确协方差矩阵。其次，通过考虑卡尔曼残差来计算潜在（正态分布）测量属于或超出未经审查区域的概率。使用合成数据集和真实数据集对设计的算法进行测试。真实数据集包括由 Microsoft Kinect II 传感器捕获的人体骨骼关节坐标。为了应对导致人体骨骼跟踪问题的某些现实情况，例如（自我）遮挡、密切交互的人等，在提议的 TKF 过程中使用了自适应审查限制。实验表明，所提出的方法在最小化合成和真实数据集的整体均方根误差 (RMSE) 方面优于其他过滤过程。