中国激光, 2021, 48 (3): 0306004, 网络出版: 2021-02-02   

基于粒子群优化压缩感知的可见光定位算法 下载: 922次

Visible Light Positioning Algorithm Based on Particle Swarm Optimization Compressed Sensing
徐世武 1,2,3,4吴怡 1,2,3,*王徐芳 1,2,3
作者单位
1 福建师范大学光电与信息工程学院医学光电科学与技术教育部重点实验室, 福建 福州 350007
2 福建师范大学协和学院, 福建 福州 350117
3 福建师范大学光电与信息工程学院福建省光子技术重点实验室, 福建 福州 350007
4 福建师范大学光电与信息工程学院福建省光电传感应用工程技术研究中心, 福建 福州 350007
摘要
目前,基于压缩感知的可见光定位采用线性最小二乘法重构信号,容易陷入局部最优解,且需要高密度的发光二极管布局。针对这些问题,提出了一种基于粒子群优化压缩感知的可见光定位算法。首先,建立一种基于重构接收信号强度残差的适应度函数;其次,将指纹定位的权重求解问题转换为稀疏矩阵的重构问题;最后,采用粒子群优化重构信号。仿真结果表明,所提算法的时间复杂度较低、鲁棒性好,即使在低密度的发光二极管布局下,定位误差依然很小。当信噪比为10 dB、网格间距为50 cm时,所提算法定位误差的平均值为3.67 cm,显著低于现有的10种同类算法。还详细分析了不同参数对所提算法定位误差的影响,所得结果可为实际可见光定位系统的设计提供有益的参考。
Abstract

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.

徐世武, 吴怡, 王徐芳. 基于粒子群优化压缩感知的可见光定位算法[J]. 中国激光, 2021, 48(3): 0306004. Shiwu Xu, Yi Wu, Xufang Wang. Visible Light Positioning Algorithm Based on Particle Swarm Optimization Compressed Sensing[J]. Chinese Journal of Lasers, 2021, 48(3): 0306004.

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