Distributed Federated Tobit Kalman Filter Fusion Over a Packet-Delaying Network: A Probabilistic Perspective

This paper investigates the distributed federated Tobit Kalman filter fusion problem for a class of discrete-time systems subject to measurement censoring and packet delays. The censored measurement is characterized by the Tobit measurement model and the packet delay obeys the Poisson distribution. At the input terminal of each local estimator, a censoring detection device and a buffer with finite length are exploited to tackle the censored/delayed measurements. The filtering fusion is carried out in two steps: in the first step, every sensor in the network collects and sends its measurements to the corresponding local estimator via an unreliable network with probabilistic packet delays and, in the second step, the estimates from local estimators are further collected by the fusion center to form a fused estimate. The local estimator runs a modified Tobit Kalman filtering algorithm, which is designed based on the modified Tobit regression model, while the fusion center performs a distributed federated modified Tobit Kalman filtering algorithm, which is devised on the basis of the federated Kalman fusion rule. Given the buffer length, the prescribed bound on the estimation error covariance and the probability distribution of the packet delay, the stability performance of the proposed filtering fusion algorithm is evaluated via a probabilistic approach. Simulation results are provided to show the feasibility of the proposed filter.