Humans navigate large, open-world environments not by maintaining a globally consistent metric map, but by forming cognitive maps—topological representations that support robust relocalization even under severe perceptual changes. This paradigm is inherently resilient to tracking failures, dynamic environments, and long-term appearance variations. A fundamental enabler of this robustness is sequential hypothesis testing (SHT), which humans implicitly perform to disambiguate perceptually aliased places over time.

Despite its importance, most robotic systems either (i) avoid aliasing through conservative data-association thresholds, or (ii) apply filtering only in a discrete place space constructed from keyframes. Such discretization restricts the hypothesis space, prevents reasoning in between stored views, and leads to brittle relocalization when observations do not perfectly overlap past frames.

We propose a pose-aware online topological mapping system that performs SHT directly in continuous SE(3) space. Our approach maintains and updates a multi-hypothesis belief over the robot pose and the map topology, allowing robust relocalization and loop closure without relying on global metric consistency. Addressing continuous-domain SHT introduces two major challenges: (1) how to represent and update distributions in SE(3) efficiently, and (2) how to manage map uncertainty—as each perceptual aliasing event can spawn multiple plausible map branches, whose number can grow rapidly if not controlled.

We introduce a Gaussian-mixture–based representation and a principled branch management strategy that together enable real-time inference, scalable map maintenance, and robust operation in dynamic, ambiguous, or previously unseen environments. This work provides the first practical continuous-space SHT framework for topological mapping, bringing robots closer to the reliability and flexibility of human navigation.