To localize ourselves in an environment for spatial navigation, we rely on vision and self-motion inputs, which only provide noisy and partial information. It is unknown how the resulting uncertainty affects navigation behavior and neural representations. Here we show that spatial uncertainty underlies key effects of environmental geometry on navigation behavior and grid field deformations. We develop an ideal observer model, which continually updates probabilistic beliefs about its allocentric location by optimally combining noisy egocentric visual and self-motion inputs via Bayesian filtering. This model directly yields predictions for navigation behavior and also predicts neural responses under population coding of location uncertainty. We simulate this model numerically under manipulations of a major source of uncertainty, environmental geometry, and support our simulations by analytic derivations for its most salient qualitative features. We show that our model correctly predicts a wide range of experimentally observed effects of the environmental geometry and its change on homing response distribution and grid field deformation. Thus, our model provides a unifying, normative account for the dependence of homing behavior and grid fields on environmental geometry, and identifies the unavoidable uncertainty in navigation as a key factor underlying these diverse phenomena.

Environmental boundaries anchor cognitive maps that support memory. However, trapezoidal boundary geometry distorts the regular firing patterns of entorhinal grid cells proposedly providing a metric for cognitive maps. Here, we test the impact of trapezoidal boundary geometry on human spatial memory using immersive virtual reality. Consistent with reduced regularity of grid patterns in rodents and a grid-cell model based on the eigenvectors of the successor representation, human positional memory was degraded in a trapezoid compared to a square environment; an effect particularly pronounced in the trapezoid’s narrow part. Congruent with spatial frequency changes of eigenvector grid patterns, distance estimates between remembered positions were persistently biased; revealing distorted memory maps that explained behavior better than the objective maps. Our findings demonstrate that environmental geometry affects human spatial memory similarly to rodent grid cell activity — thus strengthening the putative link between grid cells and behavior along with their cognitive functions beyond navigation.