Distributed Kalman Filter With Fuzzy Noises Over Multiagent Systems

In this article, we propose a novel distributed Kalman filter based on the possibilistic framework to deal with the fuzzy noises over multiagent systems. To describe the fuzzy uncertainty, the noises are modeled as fuzzy random variables with trapezoidal probability distributions instead of Gaussian distributions. In the possibilistic framework, we define the consistency of a fuzzy variable and propose a novel fuzzy information fusion (FIF) algorithm, which fuses fuzzy random variables by linear weighted summation to guarantee the consistency of the fusion results. Then, a distributed fuzzy information filter (DFIF) for the linear system is derived by embedding the FIF algorithm in distributed sensor networks, wherein each agent fuses local fuzzy information with fuzzy information from the neighbors based on the FIF algorithm. Moreover, under standard observability and connectivity assumptions, it is proved that the DFIF guarantees stability regardless of consensus steps. Finally, we illustrate the effectiveness of the proposed estimation algorithm by a target tracking problem.