A Bernoulli Optimal Kalman Filter for a Multi-sensor System with Random Data Packet Dropouts and Delays

A distributed filtering method is proposed to solve the packet dropouts and delays in a multi-sensor wireless sensor network. For an asynchronous multi-sensor system with sensors of different working frequencies, a distributed Bernoulli optimal Kalman filter (BOKF) is constructed to decrease the dropouts and delays with random multistep states. In the BOKF algorithm, a wireless Bernoulli transmission output model is established and applied to solve random multi-step delays between the sensor nodes and the local processors. Moreover, the paper presents the concept of data arrival probability p and corresponding simulations analyze the influence of the data arrival probability p to the filtering accuracy. The effectiveness of the methodology is verified by a system including two types of sensors, which can be represented by a linear time-varying system and a linear time invariant one. It is shown that the Bernoulli transmission output model and the BOKF have decent performance in the two types of system, the data arrival probability p is changing oppositely with the filtering accuracy.