State estimation in robotic systems presents significant challenges, particularly due to the prevalence of multimodal posterior distributions in real-world scenarios. One effective strategy for handling such complexity is to compute maximum a posteriori (MAP) sequences over a discretized or sampled state space, which enables a concise representation of the most likely state trajectory. However, this approach often incurs substantial computational costs, especially in high-dimensional settings. In this article, we propose a novel MAP sequence estimation method, Stein-MAP-Seq, which effectively addresses multimodality while substantially reducing computational and memory overhead. Our key contribution is a sequential variational inference framework that captures temporal dependencies in dynamical system models and integrates Stein variational gradient descent (SVGD) into a Viterbi-style dynamic programming algorithm, enabling computationally efficient MAP sequence estimation. This integration allows the method to focus computational effort on MAP-consistent modes rather than exhaustively exploring the entire state space. Stein-MAP-Seq inherits the parallelism and mode-seeking behavior of SVGD, allowing particle updates to be efficiently executed on parallel hardware and significantly reducing the number of trajectory candidates required for MAP-sequence recursion compared to conventional methods that rely on hundreds to thousands of particles. We validate the proposed approach on a range of highly multimodal scenarios, including nonlinear dynamics with ambiguous observations, unknown data association with outliers, range-only localization under temporary unobservability, and high-dimensional robotic manipulators. Experimental results demonstrate substantial improvements in estimation accuracy and robustness to multimodality over existing estimation methods.

翻译：机器人系统中的状态估计面临重大挑战，这主要源于现实场景中多峰后验分布的普遍存在。处理此类复杂性的一种有效策略是在离散化或采样的状态空间上计算最大后验序列，从而实现对最可能状态轨迹的简洁表示。然而，这种方法通常会产生巨大的计算成本，尤其是在高维场景中。本文提出了一种新颖的最大后验序列估计方法——Stein-MAP-Seq，该方法能有效处理多峰性，同时显著降低计算和内存开销。我们的核心贡献在于提出了一种序列变分推断框架，该框架能够捕捉动态系统模型中的时间依赖性，并将Stein变分梯度下降集成到Viterbi风格的动态规划算法中，从而实现计算高效的最大后验序列估计。这种集成使方法能够将计算资源集中于与最大后验一致的模态，而非穷举探索整个状态空间。Stein-MAP-Seq继承了SVGD的并行性和模态搜索特性，使得粒子更新能够在并行硬件上高效执行，并且与依赖数百至数千个粒子的传统方法相比，显著减少了最大后验序列递归所需的轨迹候选数量。我们在多种高度多峰场景中验证了所提方法的有效性，包括具有模糊观测的非线性动力学、存在异常值的未知数据关联、临时不可观测条件下的仅测距定位以及高维机器人操纵器。实验结果表明，相较于现有估计方法，该方法在估计精度和对多峰性的鲁棒性方面均有显著提升。