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Distributed Adaptive Tobit Kalman Filter for Networked Systems Under Sensor Delays and Censored Measurements

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.