Zhang Licheng, Zhang Wence, Bao Xu
Opt Express. 2023 Jul 3;31(14):22885-22902. doi: 10.1364/OE.492628.
Visible light communication(VLC) is a new method of indoor communication. It can provide an effective solution for indoor positioning. Fingerprint-based visible light positioning(VLP) has been widely studied for its feasibility and high accuracy. The acquisition of 'fingerprint database' is crucial for accurate VLP. However, sparse sensors such as photodiode(PD) can only be arranged because of the space-limited scenario and high costs. Correspondingly, it results in the loss of the fingerprint database. Therefore, it is indispensable to solve the problem of how to effectively and accurately recover the fingerprint database from measurements of sparsely arranged sensors. In this paper, we propose a spatio-temporal constraint tensor completion (SCTC) algorithm based on CANDECOMP/PARAFAC (CP) decomposition to recover the fingerprint database from measurements of sparsely arranged sensors. Specifically, we model the measurements from the spatial and temporal dimensions as a tensor, and formulate the optimization problem based on the low-rank feature of the tensor. To improve the recovery accuracy, spatial and temporal constraint matrices are introduced to effectively constrain the optimization direction when completing the tensor. Spatial constraint matrices are constructed by utilizing the mode-n expansion matrix of the tensor based on the undirected graph theory. Accordingly, the Toeplitz matrix is used as the temporal constraint matrix to excavate the temporal correlation of the tensor. Since the optimization problem is non-convex and difficult to solve, we introduce CP decomposition to decompose the tensor into several factor matrices. By solving the factor matrices, the original tensor is reconstructed. The performance of the proposed SCTC algorithm is confirmed via experimental measured data.
可见光通信（VLC）是一种新型的室内通信方式。它能够为室内定位提供有效的解决方案。基于指纹的可见光定位（VLP）因其可行性和高精度而受到广泛研究。“指纹数据库”的获取对于精确的VLP至关重要。然而，由于空间受限场景和高成本，只能布置诸如光电二极管（PD）之类的稀疏传感器。相应地，这导致了指纹数据库的丢失。因此，解决如何从稀疏布置的传感器测量值中有效且准确地恢复指纹数据库的问题是必不可少的。在本文中，我们提出了一种基于CANDECOMP/PARAFAC（CP）分解的时空约束张量完备化（SCTC）算法，用于从稀疏布置的传感器测量值中恢复指纹数据库。具体而言，我们将来自空间和时间维度的测量值建模为一个张量，并基于张量的低秩特性制定优化问题。为了提高恢复精度，引入了空间和时间约束矩阵，以便在完成张量时有效地约束优化方向。利用基于无向图理论的张量的n模展开矩阵构建空间约束矩阵。相应地，使用托普利兹矩阵作为时间约束矩阵来挖掘张量的时间相关性。由于优化问题是非凸的且难以求解，我们引入CP分解将张量分解为几个因子矩阵。通过求解因子矩阵，重建原始张量。通过实验测量数据验证了所提出的SCTC算法的性能。
