Objective Over the past few years, the large-scale popularization of smart terminal devices has introduced a wide range of services, including indoor positioning. Indoor positioning systems that are based on visible light communication have four advantages over indoor positioning systems that are based on radio-frequency communication technology: 1) Centimeter-level positioning accuracy can be achieved; 2) They have high bandwidth and support high-speed data transmission; 3) There is no electromagnetic wave radiation, so they can be used directly in gas stations, operating rooms, and other places where electromagnetic radiation is prohibited; 4) They use mainly line-of-sight communication. Because of these advantages, indoor positioning based on visible light communication has gradually become a research hotspot. Currently, fingerprint positioning based on compressed sensing has two problems: 1) Using the linear least squares method to reconstruct the signal can easily fall into the local optimal solution, resulting in large positioning errors; 2) Large observation values are required to improve the accuracy of reconstructed signals, that is, a high-density light emitting diode (LED) layout is required. To solve the two abovementioned problems, a visible light positioning algorithm based on particle swarm optimization compressed sensing (PSO-CS) is proposed that aims to provide a high-precision positioning method under low-density LED layout.
Methods The research methods for visible light positioning propose in this paper are mainly based on compressed sensing and particle swarm optimization. First, based on the reconstructed and measured received signal strength (RSS) values, a fitness function based on the matched RSS residual is established. Second, based on the sparsity of the location fingerprints, the problem of solving the weight of fingerprint positioning is transformed into the problem of reconstructing the sparse matrix. Third, based on the inner product of the measurement matrix and the observation vector, the energy of the inner product is arranged from high to low to obtain the four fingerprint points with the highest energy value. Finally, combined with particle swarm optimization, the weight vector of four fingerprint points close to the target is reconstructed and the coordinates of the target are calculated.
Results and Discussion The simulation results show that the average positioning error of the PSO-CS algorithm is significantly lower than that of K-nearest neighbor (KNN), extreme learning machine (ELM), random forests (RF), artificial neural network (ANN), weighted K-nearest neighbor (WKNN), orthogonal matching pursuit (OMP), reweighted l1-norm minimization (RWl1M), and basis pursuit (BP) algorithms. In the low signal-to-noise ratio (SNR) range (5 dB-20 dB), even if the grid spacing is 50 cm, the average positioning error of the PSO-CS algorithm is still better than that of the Newton-Raphson (NR) and linear least square (LLS) positioning algorithms (Fig. 3). When the SNR is between 10 dB and 20 dB, the cumulative distribution of positioning errors made by the PSO-CS algorithm is significantly better than that of the other 10 algorithms (Fig. 4). Even in the low-density LED layout, the average positioning error based on the PSO-CS algorithm is still low (Fig. 8). The PSO-CS algorithm has good robustness. Even if the grid spacing is 50 cm and the fingerprint sampling rate is only 50%, the average positioning error curve fluctuation is still small, even after execution is repeated 50 times. When the SNR is 10 dB, the variance is 2.54 cm, and when the SNR is 20 dB, the variance is 1.38 cm. The variance in both cases is very small (Fig. 9 and Fig. 10). When the grid spacing is 50 cm and the SNR is 10 dB, compared with KNN, ELM, RF, ANN, WKNN, OMP, RWl1M, BP, NR, and LLS algorithms, the average positioning errors of PSO-CS algorithm are reduced by 75.88%, 89.15%, 85.44%, 90.25%, 58.05%, 80.82%, 86.29%, 80.01%, 73.57%, and 76.56%, respectively (Table 2). When its positioning accuracy is similar to that of the PSO-CS algorithm, the WKNN algorithm requires 34.3 times more fingerprints than the PSO-CS algorithm, and WKNN’s average calculation time is 2.5 times higher than PSO-CS’s (Table 3).
Conclusion In this paper, a novel particle swarm optimization compressed sensing algorithm is proposed and successfully applied to visible light positioning based on location fingerprints. Because only four neighbor fingerprints are required to participate in positioning, the dimension value of the swarm search is 4. The weight value of the fingerprint points is between 0 and 1; that is, the search space of the swarm is between 0 and 1. The dimensions and space are very small, so the time complexity of the proposed algorithm is low. This allows it to meet real-time positioning requirements. The simulation results show that even in the low signal-to-noise ratio and low-density LED layout, the average positioning error of the proposed algorithm is still low, and it remains significantly lower than that of similar algorithms. This paper also analyzes the influence of grid spacing, swarm size, sparsity, number of LEDs, and fingerprint sampling rate on positioning errors in the PSO-CS algorithm. The results obtained can provide a useful reference for the design of a practical visible light positioning system.
