# TensorMap: Lidar-Based Topological Mapping and Localization via Tensor Decompositions

## TL;DR

TensorMap leverages tensor decompositions to create efficient, accurate topological maps from Lidar data, enabling real-time vehicle localization with high compression and robustness to noise.

## Contribution

The paper introduces TensorMap, a novel method using orthogonal Tucker3 tensor decomposition for Lidar-based topological mapping and localization, improving speed and accuracy.

## Key findings

- Achieves high data compression compared to full Lidar data
- Accurately detects vehicle position in topological maps
- Demonstrates robustness to Gaussian and translational noise

## Abstract

We propose a technique to develop (and localize in) topological maps from light detection and ranging (Lidar) data. Localizing an autonomous 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, $\textit{TensorMap}$, also accurately detects the position of the vehicle in a graph-based representation of a map. We also analyze the robustness of the proposed technique to Gaussian and translational noise, thus initiating explorations into potential applications of tensor decompositions in Lidar data analysis.