To successfully navigate their habitats, many mammals use a combination of two mechanisms, path integration and calibration using landmarks, which together enable them to estimate their location and orientation, or pose. In large natural environments, both these mechanisms are characterized by uncertainty: the path integration process is subject to the accumulation of error, while landmark calibration is limited by perceptual ambiguity. It remains unclear how animals form coherent spatial representations in the presence of such uncertainty. Navigation research using robots has determined that uncertainty can be effectively addressed by maintaining multiple probabilistic estimates of a robot's pose. Here we show how conjunctive grid cells in dorsocaudal medial entorhinal cortex (dMEC) may maintain multiple estimates of pose using a brain-based robot navigation system known as RatSLAM. Based both on rodent spatially-responsive cells and functional engineering principles, the cells at the core of the RatSLAM computational model have similar characteristics to rodent grid cells, which we demonstrate by replicating the seminal Moser experiments. We apply the RatSLAM model to a new experimental paradigm designed to examine the responses of a robot or animal in the presence of perceptual ambiguity. Our computational approach enables us to observe short-term population coding of multiple location hypotheses, a phenomenon which would not be easily observable in rodent recordings. We present behavioral and neural evidence demonstrating that the conjunctive grid cells maintain and propagate multiple estimates of pose, enabling the correct pose estimate to be resolved over time even without uniquely identifying cues. While recent research has focused on the grid-like firing characteristics, accuracy and representational capacity of grid cells, our results identify a possible critical and unique role for conjunctive grid cells in filtering sensory uncertainty. We anticipate our study to be a starting point for animal experiments that test navigation in perceptually ambiguous environments.