In this paper, visible light-based positioning (VLP) is studied. VLP is greatly challenging because (i) it is essentially a non-convex optimization problem since the visible-light received signal strength (RSS) is nonlinear with the user equipment (UE) position; and (ii) in addition to the UE location, the visible light RSS also depends on the UE orientation and small-scale channel gains, which are unknown in practice. This complicates the VLP problem due to the enlarged searching space. To address these challenges, we propose a location-domain grid sampling scheme. Specifically, the location-domain grid sampling can potentially partition the location space into small cells, and hence the non-convexity challenge of RSS-based VLP is mitigated. In addition, using the location-domain grid sampling, we transform VLP into a sparse recovery problem. A novel group sparse learning (GSL) algorithm with self-adaptive location-domain grids is proposed to achieve an efficient RSS-based VLP solution, via exploring the inherent sparse structure. The convergence of our GSL algorithm is established. Thanks to the adaptivity of dynamic location-domain grids, the required number of location-domain grids can be significantly reduced, compared with conventional fixed-grid-based GSL solutions. Moreover, the proposed GSL-based VLP method jointly learns the UE location, orientation and channel gain, thus achieving a robust RSS-based VLP solution against parameter uncertainties. Finally, our simulation result verifies the large performance gain of the proposed RSS-based VLP solution over state-of-the-art VLP baselines, thanks to our self-adaptive grid sampling and problem-specific group sparse learning.

中文翻译：

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使用自适应位置域网格采样的基于可见光的用户位置、方向和信道估计

本文研究了基于可见光的定位（VLP）。VLP 极具挑战性，因为 (i) 它本质上是一个非凸优化问题，因为可见光接收信号强度 (RSS) 与用户设备 (UE) 位置呈非线性关系；(ii) 除了 UE 位置，可见光 RSS 还取决于 UE 方向和小规模信道增益，这在实践中是未知的。由于扩大的搜索空间，这使 VLP 问题变得复杂。为了应对这些挑战，我们提出了一种位置域网格采样方案。具体来说，位置域网格采样可以潜在地将位置空间划分为小单元格，因此减轻了基于 RSS 的 VLP 的非凸性挑战。此外，使用位置域网格采样，我们将 VLP 转换为稀疏恢复问题。通过探索固有的稀疏结构，提出了一种具有自适应位置域网格的新型群稀疏学习 (GSL) 算法，以实现有效的基于 RSS 的 VLP 解决方案。我们的 GSL 算法的收敛性已经建立。由于动态位置域网格的适应性，与传统的基于固定网格的 GSL 解决方案相比，所需的位置域网格数量可以显着减少。此外，所提出的基于 GSL 的 VLP 方法联合学习了 UE 的位置、方向和信道增益，从而实现了针对参数不确定性的稳健的基于 RSS 的 VLP 解决方案。最后，由于我们的自适应网格采样和特定问题的组稀疏学习，我们的仿真结果验证了所提出的基于 RSS 的 VLP 解决方案在最先进的 VLP 基线上的巨大性能增益。