Adaptive Multipath-Based SLAM for Distributed MIMO Systems

Abstract

Localizing users and mapping the environment using radio signals is a key task in emerging applications such as low-latency communications and safety-critical navigation. Recently introduced multipath-based SLAM methods can jointly localize a mobile agent and map reflective surfaces in radio frequency (RF) environments. Most existing methods assume that map features and their corresponding RF propagation paths are statistically independent. This assumption neglects inherent dependencies that arise when a single reflective surface contributes to multiple propagation paths or when an agent communicates with multiple base stations. Existing approaches that aim to fuse information across propagation paths are further limited by their inability to perform ray tracing in RF environments with nonconvex geometries. In this paper, we propose a Bayesian multipath-based SLAM method for distributed MIMO systems that addresses these limitations. We exploit amplitude statistics to establish adaptive, time-varying detection probabilities. Based on the resulting 'soft' ray-tracing strategy, the proposed method can fuse information across propagation paths in RF environments with nonconvex geometries. A Bayesian estimation framework for the joint estimation of map features and agent state is developed by applying the message passing rules of the sum-product algorithm to a factor graph representation of the proposed statistical model. We further introduce a new initialization procedure for reflective surfaces that enables the introduction of new surface states even when measurements arise solely from double-bounce paths. The proposed method is validated using both synthetic and real RF measurements obtained in challenging scenarios with nonconvex geometries and OLoS conditions. The results demonstrate that it provides accurate localization and mapping performance and approaches the posterior CRLBs.

Figures (9)

• Figure 1: Exemplary dmimo rf propagation scenario with five reflective surfaces $s \in \{1,\dots,5\}$, two pa $\bm{p}_{\mathrm{pa}}^{(j)}$, and one mobile agent $\bm{p}_{n}$. Reflective surfaces are represented by mva $\bm{p}_{s,\mathrm{{sfv}}}$, i.e., mirror images of a common origin $(0,0)$ with respect to the surfaces. Reflected paths are modeled by va $\bm{p}_{ss',\mathrm{va}}^{(j)}$. The intersection point of each path with the first reflective surface is denoted by $\bm{p}_{\mathrm{{IP}}ss',n}^{(j)}$. This intersection point determines the aod. Array orientations, aod, and aoa at pa $1$ and the agent, respectively, are shown on the left side of the figure. The red dashed line indicates the infinite extent of surface $5$ as assumed in previously proposed methods, e.g., LeiVenTeaMey:TSP2023. In the absence of surface extent information, such an environmental model may introduce nonexistent paths such as path $1$, while failing to account for existing paths such as paths $2$ and $3$, since the infinite extent of surface $5$ would block these paths.
• Figure 2: Factor graph representation of the joint posterior pdf in \ref{['eq:jointPDF']}. The black square and circle symbols denote factor nodes and variable nodes, respectively, while the colored boxes represent subgraphs formed by subsets of nodes and edges. The block diagram in (a) illustrates message propagation between the subgraphs, as well as iterations over time and pa. Detailed views of the variable nodes, factor nodes, and messages related to (b) pa and los pva, (c) legacy pmva and single-bounce pva, (d) double-bounce pva, and (e) new pmva and new pva are shown in the corresponding zoomed-in plots. The following shorthand notation is used: $S \triangleq S_{n}^{(j)}$, $M \triangleq M_{n}^{(j)}$, $f_{\mathrm{x}} \triangleq f(\bm{x}_{n}|\bm{x}_{n-1})$, $f_{s}^{(j)} \triangleq f(\underline{\bm{y}}_{s,n}^{(j)}|\bm{y}_{s,n-1}^{(j)})$, $f_{s\space s'}^{(j)} \triangleq f(\underline{\bm{\beta}}_{ss',n}^{(j)} | \bm{\beta}_{ss',n-1}^{(j)})$ with $(s\space,\space s') \in \tilde{\mathcal{D}}_{n}^{(j)}$, and $\underline{q}_{\mathrm{P}}^{(j)}$, $\underline{q}_{\mathrm{S},s}^{(j)}$, $\underline{q}_{\mathrm{D},\space s\space s'}^{(j)}$, and $\overline{q}_{\mathrm{N},m}^{(j)}$ denote 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. For a detailed factor graph representation of the da component, the reader is referred to LeiVenTeaMey:TSP2023. In (e), new pmva states are connected to the legacy pmva states, reflecting the use of predicted legacy pmva states for constructing the proposal pdf of new pmva supported by double-bounce paths, as detailed in Section \ref{['subsec:ImpAsp']} .
• Figure 3: Results of a simulation run of prop for Experiment $1$, showing the true and estimated reflective surfaces, propagation paths, and agent positions at time steps $n = 18$ in (a), (b) and $n = 307$ in (c), (d), respectively. In (a), the surfaces are labeled in the same order as in Fig. \ref{['fig:GraphicalOverview_MVADemo']}. The line representations of the estimated surfaces are computed from the mmse estimates of the detected mva. Estimated propagation paths are obtained by connecting the mmse estimate of the agent position, the interaction points on the estimated surfaces, and the pa, and are compared with the true visible paths at each time step. The color of each estimated path represents its estimated snr, i.e., the square of the normalized amplitude mmse estimate.
• Figure 4: Performance results of "soft" ray tracing using prop for Experiment $1$. (a) For each pa, the true number of visible paths, the number of detected paths, and the sum of the estimated existence probabilities of the detected paths are shown. (b) mospa errors of the estimated va, obtained by geometric transformation of the mva estimates at each pa. (c) mospa errors of the estimated mva, including a comparison with the meb(DB), averaged over all surfaces. All values are averaged over all simulation runs at each time step.
• Figure 5: Performance results of prop for Experiment $1$. For each surface labeled as $s \in \{1,\dots,5\}$ in Figs. \ref{['fig:GraphicalOverview_MVADemo']} and \ref{['subfig:synResultPA1fig1']}, (a)–(e) show the meb and the corresponding true numbers of single- and double-bounce paths over time, while (f)–(j) show the rmse of the mva position estimates. The shaded bands around the mean rmse indicate the variability of the error samples, corresponding to central $80\%$ quantile intervals DeutschmannAsilomar25.