In this study, a distributed fuzzy filter is proposed for a non-linear state estimation problem on the possibilistic framework. Firstly, instead of Gaussian distribution on the probability framework, the process and observation noises are modelled as fuzzy random variables with trapezoidal possibility distributions. Secondly, a novel square root fuzzy cubature information filtering (SRFCIF) algorithm is proposed to deal with non-linear state estimation with fuzzy noise; a fuzzy variable fusion (FVF) algorithm is used for fuzzy random variables fusion. Consequently, a distributed square root fuzzy cubature information filter (DSRFCIF) is proposed by embedding SRFCF and FVF into the consensus frame. Finally, consistency analysis and simulation demonstration are executed for the proposed filter.

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