Fusion of Monostatic and Bistatic Sensing for ISAC-Enabled Low-Altitude Environment Mapping

TL;DR

This paper presents the first Bayesian multipath-based environment mapping framework for ISAC that integrates monostatic and bistatic measurements under non-ideal surface propagation and establishes geometric relationships linking both sensing modes to a common reflective surface, enabling their association with the same physical feature for data-level fusion.

Abstract

Driven by the rapid growth of the low-altitude economy, integrated sensing and communication (ISAC) technologies are essential to meet the stringent demands for reliable connectivity and situational awareness. Within this context, multipath-based simultaneous localization and mapping has emerged as a promising approach by leveraging radio frequency (RF) multipath to reconstruct environment maps alongside agent localization. Nevertheless, existing studies largely confine themselves to bistatic non-line-of-sight links and assume purely specular reflections from smooth surfaces, overlooking the monostatic sensing capability inherent in ISAC systems and the diffuse scattering effects induced by non-ideal outdoor building facades. To address these limitations, this paper presents the first Bayesian multipath-based environment mapping framework for ISAC that integrates monostatic and bistatic measurements under non-ideal surface propagation. We establish geometric relationships linking both sensing modes to a common reflective surface, enabling their association with the same physical feature for data-level fusion. Building on this formulation, we design two complementary Bayesian frameworks with corresponding factor-graph representations, allowing flexible adaptation to different scene requirements. The effectiveness of the proposed approach is validated through synthetic RF data, demonstrating that the fusion of monostatic and bistatic links consistently yields environment maps with higher accuracy, greater robustness and faster convergence than single-link baselines.

Figures (8)

• Figure 1: Illustration of the environment mapping scenario with monostatic and bistatic links. VA1 and VA2 are the mirror-symmetric points of the BS about the non-ideal building facades S1 and S2, respectively, serving as their corresponding mapping features MF1 and MF2.
• Figure 2: Factor graph representing the factorization of the joint posterior PDF of the proposed schemes at time instant $n$. For readability, the time index $n$ is omitted from all variables in the graphs. (a) Factor graph of the joint posterior PDF for Scheme I in (\ref{['eq:F1']}). (b) Factor graph of the joint posterior PDF for Scheme II in (\ref{['eq:F2']}). The sub-graphs corresponding to individual BSs are indicated by white rounded rectangles. Factor nodes are depicted as rectangular boxes, while variable nodes are represented as circles. For the factor graph corresponding to BS $j$, the following shorthand notations are used: $\underline{K}\stackrel{\triangle}{=} \underline{K}^{(j)}_{n,\mathrm{bi}}$, $\tilde{\underline{K}}\stackrel{\triangle}{=} \underline{K}^{(j)}_{n,\mathrm{mo}}$, ${M}\stackrel{\triangle}{=} {M}^{(j)}_{n,\mathrm{bi}}$, $\tilde{{M}}\stackrel{\triangle}{=} {M}^{(j)}_{n,\mathrm{mo}}$, $b_m^{(j)}\stackrel{\triangle}{=} b_{m,n}^{(j)}$, $c_m^{(j)}\stackrel{\triangle}{=} c_{m,n}^{(j)}$, $\underline{q}_k^{(j)} \stackrel{\triangle}{=}\underline{q}\!(\underline{\boldsymbol{x}}_{k,n}^{(j)}, \underline{r}_{k,n}^{(j)} \mid \boldsymbol{x}_{k,n-1}^{(j)}, r_{k,n-1}^{(j)})$, $\tilde{\underline{q}}_k^{(j)} \stackrel{\triangle}{=} \tilde{\underline{q}}\!(\tilde{\underline{\boldsymbol{x}}}_{k,n}^{(j)}, \tilde{\underline{r}}_{k,n}^{(j)} \mid {\boldsymbol{x}}_{k,n}^{(j)}, \tilde{r}_{k,n}^{(j)})$, $\overset\smile{\underline{q}}_k^{(j)} \stackrel{\triangle}{=} {\underline{q}}\!({\underline{\boldsymbol{x}}}_{k,n}^{(j)}, {\underline{r}}_{k,n}^{(j)} \mid \tilde{\boldsymbol{x}}_{k,n-1}^{(j)}, \tilde{r}_{k,n-1}^{(j)})$, $\overline{q}_{m}^{(j)}\stackrel{\triangle}{=} \overline{q}\!(\overline{\boldsymbol{x}}_{k,n}^{(j)},\,\overline{r}_{k,n}^{(j)};\,\mathbf{u}_{n})$, $\overline{\tilde{q}}_{m}^{(j)}\stackrel{\triangle}{=} \overline{\tilde{q}}\!(\overline{\boldsymbol{\tilde{x}}}_{k,n}^{(j)},\,\overline{\tilde{r}}_{k,n}^{(j)};\,\mathbf{u}_{n})$, $g_{kk}^{(j)} \stackrel{\triangle}{=} g_{\underline{K}_{n}^{(j)}+k}\!( \overline{\boldsymbol{x}}_{k,n}^{(j)}, \overline{r}_{k,n}^{(j)},\, b_{k,n}^{(j)};\, \mathrm{z}_{k,n}^{(j)}, \mathbf{u}_{n} )$ where $\underline{K}_{n}^{(j)} \stackrel{\triangle}{=} \underline{K}^{(j)}_{n,\mathrm{bi}}$ in Fig.2 (a) and Fig.2 (b), $\tilde{g}_{kk}^{(j)} \stackrel{\triangle}{=} \tilde{g}_{\underline{K}_{n}^{(j)}+k}\!( \overline{\boldsymbol{\tilde{x}}}_{k,n}^{(j)}, \overline{\tilde{r}}_{k,n}^{(j)},\, c_{k,n}^{(j)};\, \tilde{\boldsymbol{z}}_{k,n}^{(j)}, \mathbf{u}_{n} )$, $h_{kl}^{(j)} \stackrel{\triangle}{=} h_{\underline{K}+k,l}^{(j)}\stackrel{\triangle}{=} h_k\!(\boldsymbol{x}_{k,n}^{(j)}, r_{k,n}^{(j)}, b_{l,n}^{(j)}; {z}_{l,n}^{(j)}, \mathbf{u}_n)$, $\tilde{h}_{kl}^{(j)} \stackrel{\triangle}{=} \tilde{h}_{\underline{K}+k,l}^{(j)}\stackrel{\triangle}{=} \tilde{h}_k\!(\boldsymbol{x}_{k,n}^{(j)}, r_{k,n}^{(j)}, b_{l,n}^{(j)}; \tilde{z}_{l,n}^{(j)}, \mathbf{u}_n)$.
• Figure 3: Scenario configuration. (a) 3D view, (b) 2D view.
• Figure 4: Comparison of environment map reconstruction results for different approaches. (a) Bistatic-only sensing Wielandner2023NonIdealSurfaces , (b) monostatic-only sensing, (c) proposed fusion 1, (d) proposed fusion 2, (e) proposed fusion 3, (f) proposed fusion 4, (g) fusion approach in Yang2022JSACHybridActivePassive.
• Figure 5: Mapping performance of BS1 for facades visible on both bistatic and monostatic links. (a) Ground-truth facade visibility versus time. S1 and S2 are encoded as ${0,1}$ and ${2,3}$, respectively, where 0/2 denote non-visible states and 1/3 denote visible states. Solid lines denote BS backscatter observations, and dashed lines denote BS--UAV bistatic observations. S1 is shown without markers, and S2 with square markers. (b) MOSPA error versus time for the four proposed fusion approaches, the bistatic-only scheme (Only UAV), the monostatic-only scheme (Only BS), and the baseline HybridAP method Yang2022JSACHybridActivePassive. Lower MOSPA indicates higher localization accuracy. (c) Enlarged view of (b) for a clearer comparison in the low-error region.