TensorMap: Lidar-based topological mapping and localization VIA tensor decompositions

We propose a technique to develop (and localize in) topological maps from light detection and ranging (Lidar) data. Localizing an au-tonomous vehicle with respect to a reference map in real-time is crucial for its safe operation. Owing to the rich information provided by Lidar sensors, these are emerging as a promising choice for this task. However, since a Lidar outputs a large amount of data every fraction of a second, it is progressively harder to process the information in real-time. Consequently, current systems have migrated towards faster alternatives at the expense of accuracy. To overcome this inherent trade-off between latency and accuracy, we propose a technique to develop topological maps from Lidar data using the orthogonal Tucker3 tensor decomposition. Our experimental evaluations demonstrate that in addition to achieving a high compression ratio as compared to full data, the proposed technique, TensorMap, also accurately detects the position of the vehicle in a graph-based representation of a map. We also analyze the robustness of the pro-posed technique to Gaussian and translational noise, thus initiating explorations into potential applications of tensor decompositions in Lidar data analysis.