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.
翻译:本文涉及在测量结果相关和受审查时Tobit Kalman过滤(TKF)过程。 考虑的是间隙检查, 即属于特定检查限制的某一间隔的测量情况。 提出对标准TKF过程的两项改进, 以便估计隐藏的状态矢量。 首先, 检查的测量的精确共变矩阵是通过考虑到审查限度来计算的。 第二, 潜在( 通常分布的) 测量属于未审查区域的概率是通过考虑Kalman残余物来计算的。 设计的算法使用合成和真实的数据集进行测试。 真实的数据集包括微软 Kinect II传感器捕获的人类骨骼连接坐标。 为了应对某些在人体骨骼跟踪中造成问题的真实生活状况, 如( 自我) 隔离、 密切互动的人等, 在拟议的TKF 过程中使用了适应性检查限制。 实验表明, 拟议的方法在尽量减少整个根平方形的合成数据集中,, 所需的方法比其他过滤过程要优于其他过滤过程。