Detecting Changes in the Environment Based on Full Posterior Distributions Over Real-Valued Grid Maps

To detect changes in an environment, one has to decide whether a set of recent observations is incompatible with a set of previous observations. For binary, lidar-based grid maps, this is essentially the case when the laser beam traverses a voxel that has been observed as occupied, or when the beam is reflected by a voxel that has been observed as empty. However, in real-world environments, some voxels are neither completely occupied nor completely free. These voxels have to be modeled by real-valued variables, whose estimation is an inherently statistical process. Thus, it is nontrivial to decide whether two sets of observations emerge from the same underlying true map values, and hence from an unchanged environment. Our main idea is to account for the statistical nature of the estimation by leveraging the full map posteriors instead of only the most likely maps. Closed-form solutions of posteriors over real-valued grid maps have been introduced recently. We leverage a similarity measure on these posteriors to score each point in time according to the probability that it constitutes a change in the hidden map value. While the proposed approach works for any type of real-valued grid map that allows the computation of the full posterior, we provide all formulas for the well-known reflection maps and the recently introduced decay-rate maps. We introduce and compare different similarity measures and show that our method significantly outperforms baseline approaches in simulated and real-world experiments.