2025/12/15 by Razavi, Hassan, Ángel F. García‐Fernández, Simo Särkkä +2
Computer Science · Engineering · Physics and Astronomy · #62-08 #68W10 #93E11 #Computation (stat.CO) #Control Systems and Identification #Distributed #FOS: Computer and information sciences #FOS: Electrical engineering #Model Reduction and Neural Networks #Parallel #Signal Processing (eess.SP) #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #and Cluster Computing (cs.DC) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2512.13319
openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28
This paper proposes a parallel-in-time method for computing continuous-time maximum-a-posteriori (MAP) trajectory estimates of the states of partially observed stochastic differential equations (SDEs), with the goal of improving computational speed on parallel architectures. The MAP estimation problem is reformulated as a continuous-time optimal control problem based on the Onsager-Machlup functional. This reformulation enables the use of a previously proposed parallel-in-time solution for optimal control problems, which we adapt to the current problem. The structure of the resulting optimal control problem admits a parallel solution based on parallel associative scan algorithms. In the linear Gaussian special case, it yields a parallel Kalman-Bucy filter and a parallel continuous-time Rauch-Tung-Striebel smoother. These linear computational methods are further extended to nonlinear continuous-time state-space models through Taylor expansions. We also present the corresponding parallel two-filter smoother. The graphics processing unit (GPU) experiments on linear and nonlinear models demonstrate that the proposed framework achieves a significant speedup in computations while maintaining the accuracy of sequential algorithms.