Multiple-model multiple-hypothesis filter with Gaussian mixture reduction

We address the problem of state estimation for Markov jump nonlinear systems and present a modified version of the multiple-model and multiple-hypothesis ((MH)-H-3) 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 (MH)-H-3. 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 (MH)-H-3 when increased precision constraints are imposed to the filter.