In this paper, a distributed cubature Gaussian mixture filter (DCGMF) based on an iterative diffusion strategy (DCGMF-ID) is proposed for multisensor estimation and information fusion. The uncertainties are represented as Gaussian mixtures at each sensor node. A high-degree cubature Kalman filter provides accurate estimation of each Gaussian mixture component. An iterative diffusion scheme is utilized to fuse the mean and covariance of each Gaussian component obtained from each sensor node. The DCGMF-ID extends the conventional diffusion-based fusion strategy by using multiple iterative information exchanges among neighboring sensor nodes. The convergence property of the iterative diffusion is analyzed. In addition, it is shown that the convergence of the iterative diffusion can be interpreted from the information-theoretic perspective as minimization of the Kullback–Leibler divergence. The performance of the DCGMF-ID is compared with the DCGMF based on the average consensus (DCGMF-AC) and the DCGMF based on the iterative covariance intersection (DCGMF-ICI) via a maneuvering target-tracking problem using multiple sensors. The simulation results show that the DCGMF-ID has better performance than the DCGMF based on noniterative diffusion, which validates the benefit of iterative information exchanges. In addition, the DCGMF-ID outperforms the DCGMF-ICI and DCGMF-AC when the number of iterations is limited.
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