Towards hypotheses disambiguation in retrospective

Robust autonomous perception is a key required capability in robotics and AI when dealing with scenarios and environments that exhibit some level of ambiguity and perceptual aliasing. In such scenarios one has to maintain multiple (data association) hypotheses, each with a corresponding inference solution, e.g. maintain a Gaussian mixture model (GMM), as resorting to a single but incorrect hypothesis may lead to catastrophic results. In this work we consider such a setting and contribute a framework that enables to update probabilities of externally-defined hypotheses from some time in the past with new information (e.g. image measurements) that has been accumulated until current time. In particular, we show appropriately updating probabilities of past hypotheses within this smoothing perspective potentially enables to disambiguate these hypotheses even when there is no full disambiguation of the mixture distribution at the current time. Furthermore, we first derive a baseline approach that updates probabilities of past hypotheses by performing re-calculation for each time step until current time. We then develop an approach that re-uses previous calculations, thereby reducing computational complexity by an order of magnitude.