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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.08684 |
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| _version_ | 1866912846747533312 |
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| author | Seo, Min-Won Kia, Solmaz S. |
| author_facet | Seo, Min-Won Kia, Solmaz S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08684 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Computationally Efficient Maximum A Posteriori Sequence Estimation via Stein Variational Inference Seo, Min-Won Kia, Solmaz S. Robotics 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. |
| title | A Computationally Efficient Maximum A Posteriori Sequence Estimation via Stein Variational Inference |
| topic | Robotics |
| url | https://arxiv.org/abs/2312.08684 |