Probabilistic Occupancy Grid for Radio-Based SLAM

TL;DR

A probabilistic occupancy grid framework for radio-based simultaneous localization and mapping (SLAM) is presented, jointly reconstructing geometric structures and their radio-related properties and simulation results demonstrate accurate reconstruction of geometry and material properties, as well as high-accuracy localization.

Abstract

Sensing is an integral part of 6G and beyond systems, providing exceptional environmental perception along with communication. RF-based sensing often relies on simplified geometric assumptions (e.g., point scatterers or planar surfaces) to model specular multipath and keep inference tractable. However, such representations are not physically informative and fail to accurately capture extended objects with complex shapes and properties. This paper presents a probabilistic occupancy grid framework for radio-based simultaneous localization and mapping (SLAM), jointly reconstructing geometric structures and their radio-related properties. The proposed occupancy grid map representation is integrated into a multipath-based SLAM (MP-SLAM) formulation to enable simultaneous mobile-agent localization and environment mapping using multipath measurements. To connect RF measurements with the grid map, a surface model is employed to describe candidate reflection paths, while occupancy grid cell states capture measurement uncertainties and fine--grained geometric details. Object RF-related properties are modeled via reflection coefficients. The proposed framework offers a principled, proof-of-concept approach to physically interpretable radio-based mapping, and simulation results demonstrate accurate reconstruction of geometry and material properties, as well as high-accuracy localization. In addition, the results highlight the potential to use prior occupancy maps obtained from other radio devices or complementary sensors for subsequent map extension and refinement.

Figures (4)

• Figure 1: (a) Geometrical depiction of a distributed mimo radio propagation environment consisting of three reflective surfaces, two pa and a mobile agent. (b) Illustration of the interaction between grid cells and the rf double-bounce path (cyan) from pa $1$ at position $\bm{p}_{\mathrm{pa}}^{(1)}$ to the mobile agent at $\bm{p}_{n}$, accounting for measurement and agent position uncertainties. The resulting occupancy probability profile is also shown, where transversal cells converge toward free occupancy, surface-hit cells toward occupied, and all other cells remain in an unknown (unexplored) state.
• Figure 2: Factor graph representation of the joint posterior pdf \ref{['eq:JointPosteriorPDF']}. (a) shows the message propagation between the subgraphs, as well as iterations over time and pa. The black square and circle symbols denote factor nodes and variable nodes, respectively. Dashed arrows indicate messages propagated forward in time. As an example, (b) shows the variable nodes, factor nodes, and messages for a single-bounce path. The following short notations are used: $S \triangleq S_{n}^{(j)}$, $M \triangleq M_{n}^{(j)}$, $f_{\mathrm{x}} \triangleq f(\bm{x}_{n}|\bm{x}_{n-1})$, $f_{\mathrm{o}} \triangleq f(o_{i,n}|o_{i,n-1})$, $\underline{q}_{\mathrm{P}}^{(j)}$, $\underline{q}_{\mathrm{S},s}^{(j)}$, $\underline{q}_{\mathrm{D},\space s\space s'}^{(j)}$ and $\overline{q}_{\mathrm{N},m}^{(j)}$ represent the pseudo lhf of the los paths \ref{['eq:LHFPA']}, single-bounce paths \ref{['eq:LHFSpath']}, double-bounce paths \ref{['eq:LHFDpath']} and new paths \ref{['eq:LHFNew']}, respectively.
• Figure 3: Performance results using synthetic dmimo measurements. (a) Geometrical depiction of the simulation environment and setup. (b) and (d) show the localization and mapping results for agent $1$. (c) and (e) present the results for agent $2$ using the established occupancy grid map from agent $1$ in (d) as prior for $p(\bm{o}_{0})$.
• Figure 4: Results of a simulation run for agent $1$. The estimated surfaces, propagation paths and agent track are shown for time $n=173$. The estimated surfaces are computed using the mmse estimates of the detected sfv. Estimated propagation paths are obtained by connecting the mmse estimates of the agent position, interaction points on the estimated surfaces and pa, and compared with the true visible paths. The color of each estimated path represents its snr estimates, i.e., the square of norm amplitude estimates.