Robust 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 this work we consider such a setting and contribute a framework that enables to update probabilities of externally-defined data association hypotheses from some past time with new information 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. Further, we develop an incremental algorithm that re-uses hypotheses’ weight calculations from previous steps, thereby reducing computational complexity. In addition we show how our approach can be used to enhance current-time hypotheses pruning, by discarding corresponding branches in the hypotheses tree. We demonstrate our approach in simulation, considering an extremely aliased environment setting.