[Submitted on 31 Jul 2026]
Title:Localization in Spatiotemporal Fields via Environmental PDEs
View a PDF of the paper titled Localization in Spatiotemporal Fields via Environmental PDEs, by Jose Fuentes and 3 other authors
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Abstract:This paper proposes a localization framework that uses spatiotemporal fields governed by partial differential equations (PDEs) as localization signatures. Two PDE classes are considered: the shallow water equations, which describe free-surface flows in coastal and riverine environments, and the advection-diffusion equation, which models the transport and mixing of scalar quantities such as temperature, salinity, and dissolved oxygen. A numerical PDE solver provides predicted fields over the domain, and multiple field channels are fused as multimodal measurements to improve localization accuracy. We formulate the problem within a Rao-Blackwellized particle filter (RBPF) that partitions the vehicle state into a nonlinear component sampled by particles and a linear sensor bias component tracked analytically via per-particle Kalman filters. This factorization reduces the required number of particles compared to a standard particle filter while accounting for realistic sensor drift. Simulation studies on both PDE scenarios show that the RBPF consistently outperforms a standard particle filter in terms of final position error and Root Mean Square Error (RMSE) across varying particle counts. Field experiments with an autonomous surface vehicle measuring salinity, temperature, and dissolved oxygen validate that PDE-governed environmental fields provide sufficient spatial variability for practical localization. Related experimental videos are available at this https URL.
Comments: Accepted to the 2026 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2026)
Subjects:
Robotics (cs.RO)
Cite as: arXiv:2608.00272 [cs.RO]
(or arXiv:2608.00272v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2608.00272
arXiv-issued DOI via DataCite
Submission history
From: Abdullah Al Redwan Newaz [view email] [v1] Fri, 31 Jul 2026 20:25:53 UTC (14,780 KB)
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