In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable as it involves integrals of general nonlinear functions and the filtered and smoothed state distributions lack closed-form solutions. As such, it is common to approximate the state estimation problem. In this paper, we develop an assumed Gaussian solution based on variational inference, which offers the key advantage of a flexible, but principled, mechanism for approximating the required distributions. Our main contribution lies in a new formulation of the state estimation problem as an optimisation problem, which can then be solved using standard optimisation routines that employ exact first- and second-order derivatives. The resulting state estimation approach involves a minimal number of assumptions and applies directly to nonlinear systems with both Gaussian and non-Gaussian probabilistic models. The performance of our approach is demonstrated on several examples; a challenging scalar system, a model of a simple robotic system, and a target tracking problem using a von Mises-Fisher distribution and outperforms alternative assumed Gaussian approaches to state estimation.

中文翻译：

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非线性状态空间模型的高斯变分状态估计


在本文中，考虑了非线性状态空间模型在滤波和平滑背景下的状态估计问题。由于模型的非线性性质，状态估计问题通常很棘手，因为它涉及一般非线性函数的积分，并且滤波和平滑的状态分布缺乏闭式解。因此，近似状态估计问题是很常见的。在本文中，我们开发了一种基于变分推理的假设高斯解决方案，它提供了一种灵活但有原则的机制来近似所需分布的关键优势。我们的主要贡献在于将状态估计问题作为优化问题的新表述，然后可以使用采用精确一阶和二阶导数的标准优化例程来解决。由此产生的状态估计方法涉及最少数量的假设，并直接适用于具有高斯和非高斯概率模型的非线性系统。我们的方法的性能通过几个例子得到了证明；具有挑战性的标量系统、简单机器人系统的模型以及使用 von Mises-Fisher 分布的目标跟踪问题，并且优于替代假设的高斯状态估计方法。