Multi-sensor information fusion estimators for stochastic uncertain systems with correlated noises

•Correlated multiplicative noises and correlated additive noises are considered.•The LMV optimal centralized fusion filter, predictor and smoother are proposed.•A distributed fusion filter weighted by matrices is proposed in the LMV sense.•The filtering error cross-covariance matrix between any two local filters is derived.•A CI fusion filter is proposed to avoid the calculation of cross-covariance matrices.

The information fusion estimation problems are investigated for multi-sensor stochastic uncertain systems with correlated noises. The stochastic uncertainties caused by correlated multiplicative noises exist in the state and observation matrices. The process noise and the observation noises are one-step auto-correlated and two-step cross-correlated, respectively. While the observation noises of different sensors are one-step cross-correlated. The optimal centralized fusion filter, predictor and smoother are proposed in the linear minimum variance sense via an innovative analysis approach. To enhance the robustness and flexibility, a distributed fusion filter is put forward, which requires the calculation of filtering error cross-covariance matrices between any two local filters. To avoid the calculation of cross-covariance matrices, another distributed fusion filter is also presented by using the covariance intersection (CI) fusion algorithm, which can reduce the computational cost. A simulation example is given to show the effectiveness of the proposed algorithms.