Inverse k-visibility for RSSI-based Indoor Geometric Mapping

TL;DR

This work tackles indoor mapping with WiFi RSSI by introducing Structure from WiFi (SfW) based on inverse $k$-visibility. It develops both dense and sparse variants to recover geometry from RSSI-derived $k$-values, using multiple routers and occupancy-grid maps, and validates the approach against LiDAR ground truth in simulated and real environments. Key findings include $k$-value accuracy around 82–96% and IOU ~0.83–0.96, with multi-router configurations offering substantial improvements and real-time processing capabilities. The method provides a viable alternative for WiFi-based geometric mapping, enabling planning and navigation without relying on cameras or LiDAR, and highlights future directions in multipath modeling and active exploration.

Abstract

In recent years, the increased availability of WiFi in indoor environments has gained interest in the robotics community to utilize WiFi signals for indoor simultaneous localization and mapping algorithms. This paper discusses the challenges of achieving high-accuracy geometric map building using WiFi signals. The paper introduces the concept of inverse k-visibility, developed from the k-visibility algorithm, to identify free space in an unknown environment, used for planning, navigation, and obstacle avoidance. Comprehensive experiments, including those utilizing single and multiple RSSI signals, were conducted in both simulated and real-world environments to demonstrate the robustness of the proposed algorithm. Additionally, a detailed analysis comparing the resulting maps with ground-truth LiDAR-based maps is provided to highlight the algorithm's accuracy and reliability.

Figures (13)

• Figure 1: The concept of $k$-visibility is demonstrated where different $k$-values are shown: $k=0$ (red), $k=1$ (green), $k=2$ (black) and $k=3$ (yellow). Based on a straight-line measure from a reference point such as a router (shown in dark black) to a desired location, $k$-visibility is a metric on how many times the line traverses through a wall/obstacle.
• Figure 2: Diagram illustrating the ray-drawing principle fundamental to the inverse $k$-visibility algorithm. The wall is located where two consecutive $k$-value regions intersect along a ray projected from the router point. Only the region within the $k=1$ area is displayed.
• Figure 3: Ray-drawing for an arbitrary trajectory coordinates $T_i$ with an associated $k$-value $k_i$. According to the definition of $k$-visibility, the ray $\overline{RT_i}$ must intersect exactly $k_i$ walls along its path.
• Figure 4: Analysis of received power (left) and propagation paths (right) based on $k$-values using Remcom Wireless InSite remcom2024
• Figure 5: Visual demonstration of the geometric rules for areas with $k=0$ and $k=1$. Rule 1, depicting the robot's trajectory, was omitted from the legend for clarity.