Objective With increasing demand for indoor localization services, indoor positioning technologies have gradually become a research hotspot. Visible light is harmless to the human body and can not interfere with electronic devices. In addition, the visible light signal is less affected by multi-path reflection; thus, it can be used as an information carrier for an indoor positioning system. Therefore, visible light has become an important indoor positioning technology. LED lights are often used in indoor positioning research due to their advantages, such as high cost performance, high broadband, long life. Model building of machine learning-based indoor visible light positioning currently relies on the photodiode and the number of fingerprints. To reduce the complexity of fingerprint acquisition and increase positioning accuracy, an indoor three-dimensional visible light positioning algorithm based on sparse reconstruction of fingerprint matrixes is proposed, and a localization algorithm with boundary correction is introduced. The proposed algorithm can effectively reduce the sampling rate of fingerprints and improve the global positioning speed and precision. We hope that our concepts and algorithms will facilitate the design of fingerprint acquisition and understanding of the relationship between singular value decomposition and fingerprint reconstruction.
Methods First, the proposed algorithm uses extreme learning machine to train sparse sampling nodes and is applied to learn the nonlinear mapping relationships between the received signal strength and location at the receiving end, which only considers the line-of-sight propagation and first-order reflection of visible light. In addition, singular value decomposition and the alternating direction multiplier method are combined to solve the reconstruction problem of sparse fingerprint matrixes, and we get the good sparse samples from the 64 sampling nodes through multiple simulation selection of samples. Second, due to the impact of multi-path reflection of visible light and other factors, the boundary positioning error of the positioning area is greater than the internal positioning error. A localization algorithm with boundary correction is introduced. This algorithm improves the extreme learning machine training weight of the positioning regional boundary by adding virtual boundary nodes to increase the number of fingerprints, reduce the generalization error of boundary targets, and reduce boundary positioning error significantly.
Results and Discussions At heights of 0 m, 0.3 m, 0.6 m, and 0.9 m, the average positioning error of less than 7 cm can be obtained. As the height of positioning targets increases, which leads to increased multi-path reflection gain of visible light, the boundary positioning error and overall positioning error increases (Fig. 4). It is observed that using 48 or 56 sparse samples for positioning provides good performance with sparse reconstruction. Here, the average positioning error is 2.74 cm with 48 sparse samples and 1.88 cm under 56 sparse samples by adding four virtual nodes (Fig. 7). By adding eight virtual nodes, the average positioning error is 1.59 cm with 48 sparse samples and 1.2 cm with 56 sparse samples (Fig. 8). The extreme learning machine has better positioning effect than the k-nearest neighbor, backpropagation, random forest algorithms (Fig. 10). The proposed algorithm has the shortest positioning time and lowest positioning error. The average positioning time is 0.0205 s, the average positioning error is 1.593 cm, and the average minimum error is 0.243 cm (Table 2). It is found that 48 and 56 sparse samples demonstrate good performance with sparse reconstruction, and the average positioning error is 7.29 cm with 48 sparse samples and 3.3 cm with 56 sparse samples (Fig. 13). By introducing the localization algorithm with boundary correction into an experimental scene with 48 and 56 sparse samples, we conclude that the proposed algorithm works well relative to reducing the positioning error and number of fingerprints. By adding eight virtual nodes, the average positioning error is 2.95 cm with 48 sparse samples and 2.49 cm with 56 sparse samples (Fig. 14).
Conclusions An indoor three-dimensional visible light localization algorithm based on sparse reconstruction of fingerprint matrixes is proposed. The proposed algorithm reduces the number of fingerprints required by traditional machine learning training significantly and improves the average positioning error and positioning speed compared to the KNN, BP, RF, and ELM algorithms. In addition, a localization algorithm with boundary correction is introduced to reduce the boundary positioning error of the positioning area. The simulation results demonstrate that the proposed algorithm has an average positioning time of 0.0205 s, average positioning error of 1.593 cm, and average minimum positioning error of 0.243 cm. With 48 samples, the experimental results demonstrate that the average positioning error is 2.95 cm, and the minimum average positioning error is 0.22 cm. With 64 sparse training nodes, the number of fingerprints can be reduced further using the singular value algorithm, and the global positioning speed and precision can be improved. Simulation and experimental results demonstrate that the proposed algorithm has better localization speed and accuracy while reducing the number of fingerprints compared to traditional machine learning algorithms.
