Researchers use environmental PDEs for GPS-free robot localization

A team of roboticists led by Jose Fuentes, Abdullah Al Redwan Newaz, Ana Cavalcanti, and Leonardo Bobadilla has developed a localization method that uses environmental physics as a GPS replacement. Their framework, detailed in arXiv:2608.00272 and accepted to IROS 2026, exploits spatiotemporal fields modeled by partial differential equations (PDEs)—specifically the shallow water equations for coastal and riverine flows, and the advection-diffusion equation for scalar transport like heat and salinity. A numerical PDE solver predicts field values across the region, which are then treated as multimodal measurements for a robot to estimate its position.

The core algorithmic contribution is a Rao-Blackwellized particle filter (RBPF) that splits the state into a nonlinear position component sampled by particles and a linear sensor bias component tracked analytically using per-particle Kalman filters. This factorization dramatically reduces the number of particles needed while still accounting for realistic sensor drift. In simulations of both PDE scenarios, the RBPF consistently beat a standard particle filter in 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 confirmed that these natural fields provide enough spatial variability for practical, drift-free localization. The research opens a path toward robust navigation in underwater, coastal, and other GPS-denied settings where cameras and lidar fail.