The distributed adaptive Tobit Kalman filter (DATKF) is derived in this article for the discrete time networked system with multiple sensors under sensor delays and censored measurements. In the modified measurement model, the phenomena of sensor delays and censored measurements are characterized by the random variables, which obey Bernoulli distribution. Then, based on measurement residual and modified probability density function (pdf) of measurement variables, an adaptive probability selection strategy is derived to eliminate the approximate error and initial error for censoring probability and time-delay probability, respectively. Next, based on weighted average consensus (WAC), the DATKF is provided for the discrete time networked system to obtain the fused state estimates. The adaptive Tobit Kalman filter (ATKF) is selected as the local state estimator, and the filtering error covariance of ATKF is acquired through searching its upper bound to eliminate the approximate error of the filtering gain. To enhance the precision of information fusion within limited consensus steps, the weighted rule is derived on the foundation of the measurement residual and censoring probability. Finally, the filtering accuracy and computation efficiency are verified for DATKF through several simulations.

中文翻译：

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传感器延迟和删失测量下网络系统的分布式自适应 Tobit Kalman 滤波器

本文推导了分布式自适应 Tobit Kalman 滤波器 (DATKF)，用于在传感器延迟和删失测量下具有多个传感器的离散时间网络系统。在改进的测量模型中，传感器延迟和删失测量的现象以随机变量为特征，随机变量服从伯努利分布。然后，基于测量变量的测量残差和修正的概率密度函数（pdf），导出了一种自适应概率选择策略，以分别消除删失概率和时延概率的近似误差和初始误差。接下来，基于加权平均共识（WAC），为离散时间网络系统提供DATKF以获得融合状态估计。选择自适应Tobit Kalman滤波器(ATKF)作为局部状态估计器，通过搜索其上界得到ATKF的滤波误差协方差，消除滤波增益的近似误差。为了在有限的共识步骤内提高信息融合的精度，加权规则是在测量残差和审查概率的基础上推导出来的。最后，通过多次仿真验证了DATKF的滤波精度和计算效率。