Solving Nonlinear Filtering Problems Using a Tensor Train Decomposition Method

• 成果类型: Article
• 署名作者: Li, Sijing; Wang, Zhongjian; Yau, Stephen S. -T.; Zhang, Zhiwen
• 署名单位: University of Hong Kong; University of Chicago; Tsinghua University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3223319
• 发表日期: 2023
• 页码: 4405-4412
• 关键词: Duncan-Mortensen-Zakai (DMZ) equation; forward Kolmogorov equations (FKEs); nonlinear filtering (NLF) problems; real-time algorithm; tensor train (TT) decomposition method

摘要

In this article, we propose an efficient numerical method to solve nonlinear filtering (NLF) problems. Specifically, we use the tensor train decomposition method to solve the forward Kolmogorov equation (FKE) arising from the NLF problem. Our method consists of offline and online stages. In the offline stage, we use the finite difference method to discretize the partial differential operators involved in the FKE and extract low-dimensional structures in the solution tensor using the tensor train decomposition method. In the online stage using the precomputed low-rank approximation tensors, we can quickly solve the FKE given new observation data. Therefore, we can solve the NLF problem in a real-time manner. Finally, we present numerical results to show the efficiency and accuracy of the proposed method in solving up to six-dimensional NLF problems.