基于机器学习与多光电二极管的可见光定位实验研究
1 引言
据统计[1],大多数人在室内环境中度过的时间超过80%,随着人们对室内定位服务的要求越来越高,在保证精度的前提下进行高速的室内定位引起了研究界的广泛关注,如商场、机场和地下停车场等大型室内环境中的导航。全球定位系统(Global positioning system,GPS)是常用的室外定位系统,然而GPS无法在室内可靠地工作[2-3]。文献[4]中报道了大量的室内定位方案,如无线保真(Wireless fidelity,Wi-Fi)[5-6]、射频识别(Radio frequency identification,RFID)[7]、蓝牙[8],和ZigBee[9]等无线技术目前已广泛地应用于室内定位系统(Indoor positioning system,IPS)。然而,这些基于射频通信(Radio frequency communication,RFC)的定位技术会受到噪声和多径效应等因素的影响,使其定位精度只能达到米级别。超声波定位[10]可以非常精确,但其需要额外部署大量的基础设施。激光雷达[11]和基于相机的场景分析[12]技术提供了毫米级别的误差,但成本高昂,需要较高的计算能力。随着发光二极管(Light-emitting diode,LED)逐渐取代传统光源,出现了一种新的基于可见光通信(Visible light communication,VLC)的室内定位方法,即可见光定位(Visible light positioning,VLP)[13]。VLP的优点:1)其频率远高于射频信号,不易受到RFC的干扰[14],这意味着VLP技术可以实现更高的定位精度;2)在一些特殊环境中,如医院和飞机场,RFC是被禁止的,VLP因不会产生射频干扰而非常适用;3)只要存在照明基础设施,VLP技术就可以提供定位服务,从而使硬件成本最小化[15]。VLP从接收信号特征角度主要分为:接收信号强度(Received signal strength,RSS)[16],到达角度(Angle of arrival,AOA)[17]和到达时间(Time of arrival,TOA)[18]。AOA的实现通常需要不止一个光电二极管(Photodiode,PD)或专用光学器件[19]。基于TOA的系统需要硬件高度同步,从而增加了实施成本[20]。RSS使用PD直接接收,且不需要硬件时钟的同步,从而降低了成本和复杂性[21],综合考虑室内定位的成本、难度和精度,基于RSS的VLP成为首选。由于RSS与发射器和接收器之间的距离相关,还与发射器的辐射角和接收器的入射角相关,文献中提出了使用3个[22-26]或更多[16,27-29]PD的三维VLP系统,其可以减轻单个PD系统的倾斜问题[30],同时多PD布局的角度和位置差异可以创造新的定位方法[26-27,31]。虽然该系统在接收端需要更多的PD,但其对发射器没有任何的特殊要求[32-33],并且已经显示出减少LED数量的潜力[34],这也比较适合真实的室内环境。大多数办公室的LED分布非常稀疏,而单个PD的VLP系统至少需要3个LED才能完成有效定位,这意味着在现有的照明条件下需要添加额外的LED,而多PD的VLP系统则没有这个问题[35]。
VLP定位技术可分为三大类:邻近技术、指纹技术和基于几何的技术[36]。邻近技术部署简单,但精度不高。基于几何的技术是通过RSS特征向量和光的衰减模型估算目标与每个LED的距离,然后使用三边测量或三角测量算法确定目标相对于LED的位置[37-38]。众所周知,RSS受到许多模型参数的影响,例如辐射角和入射角、模型阶数、模型类型、探测器物理面积、滤光片增益以及LED与PD之间的距离等[39],因此,很难通过模型准确地估计LED与目标之间的距离,这使得基于三边测量的几何技术在VLP场景的适用性不如指纹技术。指纹技术的指纹点由PD测量到的RSS特征向量组成,该向量唯一地标识目标所在的空间位置,以此完成指纹数据库的构建,再结合分类算法实现可见光定位,因其不存在距离的计算,所以不依赖于模型参数,甚至可以在LED位置未知的情况下进行定位,这些对RSS的误差和波动具有良好的鲁棒性,文献[13,40-45]报道了该VLP系统的开发以及一些初步结果,因此本文采用基于RSS的指纹定位技术。指纹定位技术在很大程度上依赖于训练指纹数据库的信号分类算法,如K最近邻(K-nearst neighbor,KNN)[46-48],加权K最近邻(Weighted K-nearest neighbor,WKNN)[40,49],随机森林(Random forest,RF)[50],支持向量机(Support vector machine,SVM)[51],人工神经网络(Artificial neural networks,ANN)[39,52-54]和极限学习机(Extreme learning machine,ELM)[53,55-56]等,这些机器学习算法(Machine learning algorithm,MLA)已经被报道用于室内的VLP,但多PD接收方案的文献比较少,而且文献中通常显示的是基于仿真的结果[57]。因此,本文搭建实验平台,同时通过实验与仿真详细分析了4种具有代表性的MLA在基于多PD和RSS指纹匹配的VLP系统中的定位性能,同时详细地分析了LED个数M、PD个数N和LED发射功率Pt对定位精度的影响。在LED分布密度较低的场景下,为VLP系统的设计提供新的理论支持与实际应用参考价值,以及为MLA在多PD接收的VLP系统研究中提供应用参考。
2 系统概述
2.1 系统的硬件组成
为了实验验证MLA在多PD的VLP系统中的定位性能,搭建了一个真实的LED定位场景。前期工作表明[49],在单个PD接收环境中,当LED的个数M从3增加到8时,各MLA均可以实现较低的定位误差,因此采用了4个LED作为发射器。该系统由一个100 cm×100 cm×150 cm的铝制框架,4个LED和一个可在地板上自由移动的光接收器构成,其中光接收器包括4个型号为QIAS TSL2561的PD,光接收器分别在地面,以及距离地面10 cm和20 cm的3个平面内移动,4个PD的输出分别发送到STM32 MCU的AD引脚。为了精准化指纹点和测试点,将实际定位范围为65 cm×70 cm的平面划分为5 cm×5 cm尺寸的单元格,每个单元格至少都选取一个指纹点和测试点,因此每个平面分别都选取了210个指纹点和测试点[46]。在整个采集过程中,4个LED固定在同一高度,其发射面与地面平面,光接收面与发射面平行且都在4个LED的有限视场(Field of view,FOV)范围内,以确保获得稳定的RSS特征向量。实验区是在框架里面,因此实验区内没有障碍物,这样可以减少多径反射的负面影响,搭建的实验平台如
图 1. 多光电二极管接收器的VLP系统实验装置
Fig. 1. Experimental setup of the VLP system with a multi-PD receiver
表 1. 实验参数
Table 1. Experimental parameter
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2.2 RSS指纹矩阵构造
光接收器放置在指定的F个指纹位置,N个PD分别采集来自第m个LED的RSS特征值,为了减小RSS波动造成的误差,提高指纹矩阵的精度,每个PD都循环采集100次,并去尾求平均值,以提高抗噪性能,由其构成一个RSS特征矩阵
式中:向量
M个RSS特征矩阵
3 定位算法
3.1 算法概述
考虑监督学习算法中性能较佳的非线性学习(Nonlinear learning,NL)和集成学习模型(Ensemble learning,EL)。NL方法中最经典的是KNN和以快速著称的ELM。而EL方法大致可分为两大类:一类是Boosting,最流行的版本是AdaBoost;另一类是Bagging,较先进的版本是RF。综上,本文选择了4种典型的分类器:KNN、ELM、RF和AdaBoost。
KNN[46-48]是通过比较测试点与每个指纹点的RSS向量之间的差异以确定目标位置。一般采用欧氏距离作为RSS向量之间的相似性指标,通过相似性从大到小排序得到前
式中:
ELM[63]是依据广义逆(Moore-Penrose)矩阵理论提出的一类性能优良的新型单隐层前馈神经网络,设有
式中:
图 3. L个隐藏神经元的单隐层前馈神经网络
Fig. 3. Single-hidden layer feedforward network with L hidden neurons
AdaBoost[64-65]基本原理是将多个弱分类器整合成一个强分类器。首先,给全部的指纹点数据赋予相同的权值,训练出一个弱分类器并计算该分类器的错误率
式中:p为分错的指纹点数量;q为全部的指纹点数量。
RF[46,50]基本原理也是通过训练多个弱分类器整合成一个强分类器。但不同于AdaBoost,RF每次都是随机且有放回地从所有指纹点数据库中抽取部分指纹点数据作为训练集,即每个弱分类器的训练集因随机抽取而不同,因有放回而同一个训练集里包含相同的指纹点数据;同时,RF最后为每个弱分类器分配的是相同的权重,即输入测试点数据时,RF的每个弱分类器都会判断该测试点的分类结果,最后对各预测结果进行投票判决,票数多的一类即为预测的最终结果。由于随机性的引入,该算法不容易过拟合且抗噪声性能好,但处理时间和计算复杂度随着迭代次数的增加而增加。
3.2 参数设置
文献[49]和[57]的研究表明,KNN的最佳邻域数K为3或4,本文K取为3;考虑到ELM中随机设置的输入隐藏权值
表 2. 4种机器学习算法的参数
Table 2. Parameter of the four machine learning algorithms
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3.3 系统模型
实验环境如
图 4. 定位系统示意图。(a)二维定位;(b)三维定位
Fig. 4. Conceptual architecture of positioning system. (a) 2-D positioning; (b) 3-D positioning
由于在可见光定位中视距(Line of sight,LOS)通信占据主要成分,因此后续的仿真结果中,为了不失一般性,同样采用LOS传输的Lambertian辐射模型[68-70],即
式中:Pr为PD的接收功率;
在典型的室内可见光通信中,噪声通常包括散粒噪声和热噪声[14,49],其公式如下。
式中:
噪声模型的参数设置如下[14,49]:TK=295 K,G0=10,gm=30 mS,Γ=1.5,B=100 MHz,I2=0.562,I3=0.0868,RPD=0.54 A/W,η=112 pF/cm2,Ibg=5100 µA。
4 仿真与实验结果分析
在以下的仿真与实验结果分析中,S-KNN、S-ELM、S-RF和S-AdaBoost表示仿真的结果,KNN、ELM、RF和AdaBoost表示实验的结果。为了不失一般性,同样采用定位误差的累积分布函数(Cumulative distribution function,CDF),平均定位误差(Average positioning error,APE)以及平均定位时间(Average positioning time,APT)参数分析仿真和实验结果,其中APE[71]为
式中:
4.1 各机器学习算法的定位性能
1)定位误差的CDF
分别在二维和三维定位中分析了各MLA对目标的定位性能,展示了多PD的VLP系统定位精度,各MLA定位误差的CDF如
图 6. 各算法的定位误差的CDF。(a)二维定位;(b)三维定位
Fig. 6. CDF of positioning error for different algorithms. (a) 2-D positioning; (b) 3-D positioning
在二维定位时,S-KNN、S-ELM、S-RF和S-AdaBoost的定位误差小于2 cm的概率分别为100%、93.81%、99.52%和29.52%,KNN、ELM、RF和AdaBoost的定位误差小于2 cm的概率分别为96.67%、48.57%、67.14%和15.24%;在三维定位时,S-KNN、S-ELM、S-RF和S-AdaBoost的定位误差小于2 cm的概率分别为100%、95.59%、99.29%和16.19%,KNN、ELM、RF和AdaBoost的定位误差小于2 cm的概率分别为74.52%、38.81%、59.76%和6.43%。因此无论二维或三维定位,KNN的定位性能均优于ELM、RF和AdaBoost。为了仿真和实验的测试点数据同步化,仿真和实验设置的测试点离指纹点的距离均为固定值1.414 cm,而指纹定位是把测试点匹配到最近邻的指纹点,然后以指纹点的位置坐标作为测试点坐标,所以KNN实际上实现了大多数测试点的正确分类。
2)APE
各MLA在二维和三维定位中的APE如
图 7. 各算法的APE。(a)二维定位;(b)三维定位
Fig. 7. APE of different algorithms. (a) 2-D positioning; (b) 3-D positioning
3)APT
各MLA在二维和三维中的APT如
表 3. 不同算法的APT
Table 3. APT of different algorithms
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4.2 LED个数M对定位精度的影响
各MLA的APE随着LED个数M的变化结果如
图 8. M对APE的影响。(a)二维定位;(b)三维定位
Fig. 8. Impact of M on APE. (a) 2-D positioning; (b) 3-D positioning
当M从4减少到3时,各MLA的定位精度下降很小;当M为2时,S-KNN的APE分别为1.35 cm和2.66 cm,KNN的APE分别为3.36 cm和3.95 cm,与文献[57]结论一样,2个LED所开发的多PD的VLP系统也可以达到相对精准的定位效果;即使只有单个LED也可以实现定位,其S-KNN的平均误差为4.26 cm和5.18 cm,KNN的平均误差为5.72 cm和7.49 cm,这意味着多PD的VLP系统有利于实际环境中LED个数比较少的情况。
4.3 PD个数N对定位精度的影响
考虑到实际环境中LED个数比较少的情况,所以选择探讨LED的个数为2时,PD个数N对定位精度的影响。
各MLA的APE随着N的变化结果如
图 9. N对APE的影响。(a)二维定位;(b)三维定位
Fig. 9. Impact of N on APE. (a) 2-D positioning; (b) 3-D positioning
同时在二维定位中发现,基于AdaBoost的实验结果在N为2时和基于ELM的仿真结果在N为3时定位性能存在轻微振荡的现象。前者是由于AdaBoost对异常指纹点敏感,实验数据类别较多而样本有限导致其鲁棒性受到影响[65];后者是由于ELM的输入隐藏权值
4.4 发射功率Pt对定位精度的影响
文献[49]从仿真角度分析了MLA在LED发射功率Pt为1~6 W范围内的APE,结果表明随着Pt的增大,APE减小,这是因为Pt的增大提高了信噪比,从而减小了APE。从仿真和实验角度均发现,当Pt从5 W增加到7 W时,各MLA的APE变化不大,这说明所搭建的多PD的VLP系统在Pt为5 W时,各MLA的APE已经接近收敛,因此即使在LED较低的发射功率Pt下,采用本文的实验方案依然可以实现较高的定位精度,具体如
图 10. Pt对APE的影响。(a)二维定位;(b)三维定位
Fig. 10. Impact of Pt on APE. (a) 2-D positioning; (b) 3-D positioning
5 结论
搭建了多PD的VLP实验平台,避免了单个PD的倾斜问题,同时采用RSS指纹定位技术代替几何技术,通过仿真与实验验证了现有的不同MLA的定位性能。结果发现:无论是二维或三维定位,基于KNN的指纹匹配定位的精度均优于RF、ELM和AdaBoost;而ELM在定位时间上有优势;RF比较稳定,但计算复杂度比较高。同时详细分析了LED个数,PD个数和LED发射功率对定位误差的影响,实验结果表明:无论是二维或三维定位,LED和PD个数的增加均有效地减小了定位误差,而且当LED的发射功率为5 W时即可实现定位误差的收敛,这是因为结合多PD接收技术,与单PD相比,接收端可以采集到更多的RSS信息,因此即使在LED低发射功率下,依然可以取得较高的定位精度,这为LED分布密度较低时VLP系统的设计提供新的理论支持和实际参考价值,以及为MLA在多PD接收的VLP系统研究提供应用参考。
鉴于ELM能快速定位的优势,而群体智能方法被证明是优化人工神经网络和模型参数的有效工具,因此可以结合群体智能方法以提高ELM的分类精度;同时对于MLA而言,指纹库的准确性和密集性非常重要,因此,开发一种自动且精准的室内位置指纹采集系统也是未来一个有趣的研究方向。
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Article Outline
魏芬, 吴怡, 徐世武. 基于机器学习与多光电二极管的可见光定位实验研究[J]. 激光与光电子学进展, 2023, 60(7): 0723002. Fen Wei, Yi Wu, Shiwu Xu. Experimental Research on Visible Light Positioning Using Machine Learning and Multi-Photodiode[J]. Laser & Optoelectronics Progress, 2023, 60(7): 0723002.