State estimation poses substantial challenges in robotics, often involving encounters with multimodality in real-world scenarios. To address these challenges, it is essential to calculate Maximum a posteriori (MAP) sequences from joint probability distributions of latent states and observations over time. However, it generally involves a trade-off between approximation errors and computational complexity. In this article, we propose a new method for MAP sequence estimation called Stein-MAP, which effectively manages multimodality with fewer approximation errors while significantly reducing computational and memory burdens. Our key contribution lies in the introduction of a sequential variational inference framework designed to handle temporal dependencies among transition states within dynamical system models. The framework integrates Stein's identity from probability theory and reproducing kernel Hilbert space (RKHS) theory, enabling computationally efficient MAP sequence estimation. As a MAP sequence estimator, Stein-MAP boasts a computational complexity of O(N), where N is the number of particles, in contrast to the O(N^2) complexity of the Viterbi algorithm. The proposed method is empirically validated through real-world experiments focused on range-only (wireless) localization. The results demonstrate a substantial enhancement in state estimation compared to existing methods. A remarkable feature of Stein-MAP is that it can attain improved state estimation with only 40 to 50 particles, as opposed to the 1000 particles that the particle filter or its variants require.

翻译：状态估计在机器人领域面临重大挑战，实际场景中常涉及多模态问题。为应对这些挑战，需要从潜在状态与观测的联合概率分布中计算最大后验（MAP）序列。然而，这通常需要在近似误差与计算复杂度之间进行权衡。本文提出一种名为Stein-MAP的MAP序列估计新方法，该方法能在显著降低计算与内存负担的同时，以更小的近似误差有效处理多模态问题。我们的核心贡献在于引入了一种专为动态系统模型中转移状态时间依赖性设计的序列变分推断框架。该框架整合了概率论中的斯坦因恒等式与再生核希尔伯特空间（RKHS）理论，实现了计算高效的MAP序列估计。作为MAP序列估计器，Stein-MAP的计算复杂度为O(N)（N为粒子数），而维特比算法的复杂度为O(N²)。通过基于距离（无线）定位的真实世界实验，该方法得到实证验证。结果表明，相较于现有方法，状态估计性能显著提升。Stein-MAP的一大显著特点是仅需40至50个粒子即可获得更优的状态估计，而粒子滤波器及其变体则需要1000个粒子。