Multiple-model multiple-hypothesis filter with Gaussian mixture reduction
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Universidade Federal de Minas Gerais
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We address the problem of state estimation for Markov jump nonlinear systems and present a modified version of the multiple-model and multiple-hypothesis (M3H) algorithm to suboptimally solve it. In such systems, the exact filter must track an exponentially increasing number of possible trajectories. Therefore, practical solutions must approximate the exact filter trading off filter precision for computational speed. In this contribution, we employ Gaussian mixture reduction methods in the merging of hypotheses of the original M3H. Thus, information from both the analog and digital states is used to merge the hypotheses, whereas only information from the digital state is employed in the original method. In our numerical results, we show that the proposed method outperforms the original M3H when increased precision constraints are imposed to the filter.
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Sistemas não lineares, Modelos matemáticos
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multiple hypotheses multiple models filter, Gaussian Mixture Reduction, stochastic hybrid systems, filtering and state estimation, we have considered the problem of state estimation for MJSs. In the M3H filter, the issue of the exponential growth of the number of possible trajectories is tackled by merging hypotheses with similar digital state trajectories. An alternative method for the merging step of the M3H algorithm was discussed and investigated in this paper. The proposed M3HR filter leverages techniques from the theory of Gaussian mixture reduction to reduce the approximation error in the merging step., Numerical results in a target tracking example suggest that the M3HR provides improvement in the accuracy of analog and digital state estimates. In particular, most of the improvement is due to the first of 3 steps of the proposed algorithm.
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https://onlinelibrary.wiley.com/doi/full/10.1002/acs.2841