We consider the problem of controlling the precision of the multiple-model multiple-hypothesis filter with Gaussian mixture reduction. The controller adaptively chooses the number of hypotheses kept by the filter to (sub)optimally seek a tradeoff between filter precision and computational effort. In order to quantify the approximation error due to hypotheses truncation, the controller employs probability divergence measures such as f-divergences and the Wasserstein divergence. The proposed solution is tested on the problem of estimating the states of a networked control system with packet drops on the controller-actuator channel. Theoretical results demonstrate that our strategy leads to a divergence between the true Bayes posterior and the truncated one that remains bounded over time. Numerical results show a good improvement with respect to truncation with a constant number of hypotheses, specially as the number of modes increases and so does the problem dimensionality.

中文翻译：

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马尔可夫跳跃系统中的简约贝叶斯过滤及其在网络控制中的应用


我们考虑用高斯混合约简控制多模型多假设滤波器的精度问题。控制器自适应地选择滤波器保留的假设数量，以（次）最优地寻求滤波器精度和计算量之间的权衡。为了量化由于假设截断而产生的近似误差，控制器采用概率散度度量，例如 f 散度和 Wasserstein 散度。所提出的解决方案在控制器-执行器通道上存在丢包的网络控制系统状态估计问题上进行了测试。理论结果表明，我们的策略导致真实贝叶斯后验和截断贝叶斯后验之间存在分歧，并且随着时间的推移仍然有界。数值结果表明，在假设数量恒定的情况下，截断有良好的改进，特别是随着模式数量的增加以及问题维度的增加。