基于学习算法的无线传感器网络定位问题研究
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摘要
随着无线通信、集成电路、传感器以及微电子机械系统等技术的飞速发展和日益成熟,使得低成本、低功耗、大规模的无线传感器网络的产生与发展成为可能。在传感器网络中,节点位置信息对整个网络的监测活动至关重要,在其诸多应用中扮演着不可或缺的重要角色。如何设计高效率、高精度、低能耗的定位算法一直都是传感器网络研究中的热点问题。
本文针对节点定位问题,以核方法和流形学习为研究手段,以减少定位过程中使用的信标节点的数目和降低测量误差对定位精度的影响为目标,对节点定位技术进行了深入的研究。本文的主要研究内容和创新点包括以下几个方面:
1.本文综述了无线传感器网络中节点定位技术的相关研究,并以算法复杂度、信标节点比例、定位误差等作为综合指标对现有的定位算法进行了综合分析,并归纳出现有定位算法的不足以及尚待解决的问题。
2.考虑基于邻近节点间信号强度的定位问题,为了降低测量误差对定位精度的影响,本文通过研究邻近节点间的拓扑结构,将定位问题转换成无向图上的非线性降维问题,并提出了基于核函数局部保持映射(KLPP)的定位算法。该算法的基本思想是利用高斯核函数度量节点间的相似性,并在定位过程中尽可能地保持邻近节点间的相似性。仿真结果表明,基于KLPP的定位算法受信标节点数目的影响较小,当信标节点的比例较低时,依然可以获得较高的定位精度。而且,与基于核函数主成份分析(KPCA)的定位算法、MDS-MAP定位算法等同类方法相比,该算法受测量误差的影响也较小。
3.考虑基于邻近节点间信号强度的定位问题,本文以降低算法复杂度为目标,在基于KLPP的定位算法的基础上,提出了基于核函数谱回归(KSR)的定位算法。该算法的基本思想是通过非线性逼近的方法,将图上的非线性降维问题转换成正则化核函数最小二乘回归问题。理论分析和仿真结果表明,基于KSR的定位算法很好地保留了基于KLPP的定位算法的优点,在保证定位精度的同时,极大地降低了算法的复杂度。
4.考虑基于邻近节点间信号强度或测量距离的定位问题,为了降低信标节点数目对定位精度的影响,本文通过观测节点分布的流形,将定位问题放在半监督框架下进行研究,并提出了基于半监督拉普拉斯最小二乘的定位算法。该算法在训练预测模型阶段,通过引入非信标节点的测量信息来提高预测模型的泛化能力,进而降低信标节点数目对定位精度的影响。另外,本文还给出了定位问题中基于Alignment准则的核函数学习算法。仿真结果表明,与基于正则化核函数最小二乘(RKLS)的定位算法、基于核函数矩阵回归(KMR)的定位算法等同类方法相比,该算法能够获得较高的定位精度,并且适当地减小节点的通信半径能够降低平均定位误差。
5.考虑基于邻近节点间测距的定位问题,为了解决基于Ⅰsomap的定位算法对参数敏感和坐标变换矩阵依赖信标节点的问题,本文提出了一种改进的基于Ⅰsomap的定位算法(Ⅱsomap)。该算法主要包括三个部分:基于信标节点的Ⅰsomap参数选择、基于Ⅰsomap的相对坐标估计和基于最小二乘或流形回归的绝对坐标估计。其中,流形回归法能够获得较高的定位精度,但算法复杂度较大。仿真结果表明,无论网络的拓扑结构如何,在测距误差较大、信标节点数目较少时,与同类的基于欧式距离的定位算法相比,Ⅱsomap定位算法都能获得较高的定位精度。而且,节点的平均定位误差基本上随着通信半径的增大而逐渐增加。因此,在基于测距的定位机制设计中,Ⅱsomap定位算法使得减小节点的发射功率和提高节点的定位精度同时满足成为可能。
本文将核方法和流形学习的思想引入到无线传感器网络定位问题中,为该领域的研究拓展了新的思路,并提出了四种节点定位算法。在本文的最后,还分析了本文提出的算法中有待改进的地方,并对进一步的研究工作进行了展望。
Recent advances in wireless communication, integrated circuit, sensor technology and MEMS have made it possible to deploy large scale wireless sensor networks (WSNs) by using low-cost and low-power sensor nodes. In emerging WSNs applications, it is necessary to accurately position the nodes where their reported data are geographically meaningful. In WSNs, how to design a fast converging and low-cost method to accurately estimate the locations of the nodes, is always an active area.
The dissertation targets at the localization problem in WSNs and focuses on decreasing the number of anchors and alleviating the influence of the measurement error. It presents indepth study in the localization problem by using kernel-based and manifold learning methods. The main contributions of the dissertation are as follows:
1. We survey the localization problem, and analyze the existing localization methods in terms of computing complexity, number of anchors and localization accuracy. Furthermore, we also summarize the drawbacks and disadvantages of the existing localization methods, and point out the unsolved problems.
2. We consider the location estimation problem using signal strength in WSNs. In order to alleviate the influence of measurement errors between nodes, by analyzing the neighborhood topological structure, we formulate the localization problem as a nonlinear graph embedding problem, and propose a KLPP-based localization method. The main idea is to measure the similarities between nodes by a Gaussian kernel function and optimally preserving the neighborhood similarities in the localization procedure. The simulation results show that the KLPP-based localization method is not significantly sensitive to the number of anchors, i.e., when the number of anchors is small, the localization accuracy is still high. Compared with the related localization methods, e.g., KPCA-based localization method, MDS-MAP, our KLPP-based localization method is less sensitive to the measurement error.
3. To reduce the complexity of KLPP-based localization method, we formulate the nonlinear graph embedding problem as regularized kernel least-squares regression problem, and propose a KSR-based localization method. Both theoretical analysis and simulation results show that KSR-based localization method optimally preserves the advantages of the KLPP-based localization method. Besides, the former achieves lower computing complexity with a little decrease of the localization accuracy than the latter.
4. When the measurements are signal strengths or pair-wise distances, in order to reduce the influence of the number of anchors, we propose a semi-supervised Laplacian regularized least squares (S~2LapRLS) method for the localization problem. The main idea is that when nodes are close in their location space, their localization feature vectors will be similar. We first propose a solution to choose an appropriate kernel function based upon alignment criterion. Then, we construct a mapping between the measurement space and the location space under semi-supervised framework. The location of non-anchors can be estimated based upon the mapping. Compared with the related methods, e.g., RKLS-based localization method, KMR-based localization method, the simulation results show that S~2LapRLS method can obtain a higher localization accuracy. By relatively reducing the maximum communication range of nodes, the localization accuracy can be further improved.
5. When the measurements are pair-wise distances, in the purpose of reducing parameter influence of the Isomap and the transformation matrix dependence on the anchors, we propose improved Isomap-based localization approach(IIsomap), which is composed of three factors: Isomap parameter selection based upon the locations of the anchors, relative location estimation with Isomap, and absolute location estimation by using the least squares (LS) method and the manifold regression (MR) method. Simulations show that MR can achieve relatively higher localization accuracy, but at the expense of spending more time than LS. For any topological sensor network, when the number of anchors is small and the measurements are error-prone, IIsomap method achieves higher localization accuracy than the Euclidean-based localization methods. Especially, the average location error increases with the increase of the communication range, Thus, IIsomap method makes it possible to simultaneously reduce the transmitting power and improve the localization accuracy.
In this dissertation, we introduce the kernel-based approach and the manifold learning method into the localization problem, which bring new ideas into this area, and propose four location estimation methods. In the end of this dissertation, we point out several aspects waiting for improvement in our localization methods, and introduce our future work.
本文针对节点定位问题,以核方法和流形学习为研究手段,以减少定位过程中使用的信标节点的数目和降低测量误差对定位精度的影响为目标,对节点定位技术进行了深入的研究。本文的主要研究内容和创新点包括以下几个方面:
1.本文综述了无线传感器网络中节点定位技术的相关研究,并以算法复杂度、信标节点比例、定位误差等作为综合指标对现有的定位算法进行了综合分析,并归纳出现有定位算法的不足以及尚待解决的问题。
2.考虑基于邻近节点间信号强度的定位问题,为了降低测量误差对定位精度的影响,本文通过研究邻近节点间的拓扑结构,将定位问题转换成无向图上的非线性降维问题,并提出了基于核函数局部保持映射(KLPP)的定位算法。该算法的基本思想是利用高斯核函数度量节点间的相似性,并在定位过程中尽可能地保持邻近节点间的相似性。仿真结果表明,基于KLPP的定位算法受信标节点数目的影响较小,当信标节点的比例较低时,依然可以获得较高的定位精度。而且,与基于核函数主成份分析(KPCA)的定位算法、MDS-MAP定位算法等同类方法相比,该算法受测量误差的影响也较小。
3.考虑基于邻近节点间信号强度的定位问题,本文以降低算法复杂度为目标,在基于KLPP的定位算法的基础上,提出了基于核函数谱回归(KSR)的定位算法。该算法的基本思想是通过非线性逼近的方法,将图上的非线性降维问题转换成正则化核函数最小二乘回归问题。理论分析和仿真结果表明,基于KSR的定位算法很好地保留了基于KLPP的定位算法的优点,在保证定位精度的同时,极大地降低了算法的复杂度。
4.考虑基于邻近节点间信号强度或测量距离的定位问题,为了降低信标节点数目对定位精度的影响,本文通过观测节点分布的流形,将定位问题放在半监督框架下进行研究,并提出了基于半监督拉普拉斯最小二乘的定位算法。该算法在训练预测模型阶段,通过引入非信标节点的测量信息来提高预测模型的泛化能力,进而降低信标节点数目对定位精度的影响。另外,本文还给出了定位问题中基于Alignment准则的核函数学习算法。仿真结果表明,与基于正则化核函数最小二乘(RKLS)的定位算法、基于核函数矩阵回归(KMR)的定位算法等同类方法相比,该算法能够获得较高的定位精度,并且适当地减小节点的通信半径能够降低平均定位误差。
5.考虑基于邻近节点间测距的定位问题,为了解决基于Ⅰsomap的定位算法对参数敏感和坐标变换矩阵依赖信标节点的问题,本文提出了一种改进的基于Ⅰsomap的定位算法(Ⅱsomap)。该算法主要包括三个部分:基于信标节点的Ⅰsomap参数选择、基于Ⅰsomap的相对坐标估计和基于最小二乘或流形回归的绝对坐标估计。其中,流形回归法能够获得较高的定位精度,但算法复杂度较大。仿真结果表明,无论网络的拓扑结构如何,在测距误差较大、信标节点数目较少时,与同类的基于欧式距离的定位算法相比,Ⅱsomap定位算法都能获得较高的定位精度。而且,节点的平均定位误差基本上随着通信半径的增大而逐渐增加。因此,在基于测距的定位机制设计中,Ⅱsomap定位算法使得减小节点的发射功率和提高节点的定位精度同时满足成为可能。
本文将核方法和流形学习的思想引入到无线传感器网络定位问题中,为该领域的研究拓展了新的思路,并提出了四种节点定位算法。在本文的最后,还分析了本文提出的算法中有待改进的地方,并对进一步的研究工作进行了展望。
Recent advances in wireless communication, integrated circuit, sensor technology and MEMS have made it possible to deploy large scale wireless sensor networks (WSNs) by using low-cost and low-power sensor nodes. In emerging WSNs applications, it is necessary to accurately position the nodes where their reported data are geographically meaningful. In WSNs, how to design a fast converging and low-cost method to accurately estimate the locations of the nodes, is always an active area.
The dissertation targets at the localization problem in WSNs and focuses on decreasing the number of anchors and alleviating the influence of the measurement error. It presents indepth study in the localization problem by using kernel-based and manifold learning methods. The main contributions of the dissertation are as follows:
1. We survey the localization problem, and analyze the existing localization methods in terms of computing complexity, number of anchors and localization accuracy. Furthermore, we also summarize the drawbacks and disadvantages of the existing localization methods, and point out the unsolved problems.
2. We consider the location estimation problem using signal strength in WSNs. In order to alleviate the influence of measurement errors between nodes, by analyzing the neighborhood topological structure, we formulate the localization problem as a nonlinear graph embedding problem, and propose a KLPP-based localization method. The main idea is to measure the similarities between nodes by a Gaussian kernel function and optimally preserving the neighborhood similarities in the localization procedure. The simulation results show that the KLPP-based localization method is not significantly sensitive to the number of anchors, i.e., when the number of anchors is small, the localization accuracy is still high. Compared with the related localization methods, e.g., KPCA-based localization method, MDS-MAP, our KLPP-based localization method is less sensitive to the measurement error.
3. To reduce the complexity of KLPP-based localization method, we formulate the nonlinear graph embedding problem as regularized kernel least-squares regression problem, and propose a KSR-based localization method. Both theoretical analysis and simulation results show that KSR-based localization method optimally preserves the advantages of the KLPP-based localization method. Besides, the former achieves lower computing complexity with a little decrease of the localization accuracy than the latter.
4. When the measurements are signal strengths or pair-wise distances, in order to reduce the influence of the number of anchors, we propose a semi-supervised Laplacian regularized least squares (S~2LapRLS) method for the localization problem. The main idea is that when nodes are close in their location space, their localization feature vectors will be similar. We first propose a solution to choose an appropriate kernel function based upon alignment criterion. Then, we construct a mapping between the measurement space and the location space under semi-supervised framework. The location of non-anchors can be estimated based upon the mapping. Compared with the related methods, e.g., RKLS-based localization method, KMR-based localization method, the simulation results show that S~2LapRLS method can obtain a higher localization accuracy. By relatively reducing the maximum communication range of nodes, the localization accuracy can be further improved.
5. When the measurements are pair-wise distances, in the purpose of reducing parameter influence of the Isomap and the transformation matrix dependence on the anchors, we propose improved Isomap-based localization approach(IIsomap), which is composed of three factors: Isomap parameter selection based upon the locations of the anchors, relative location estimation with Isomap, and absolute location estimation by using the least squares (LS) method and the manifold regression (MR) method. Simulations show that MR can achieve relatively higher localization accuracy, but at the expense of spending more time than LS. For any topological sensor network, when the number of anchors is small and the measurements are error-prone, IIsomap method achieves higher localization accuracy than the Euclidean-based localization methods. Especially, the average location error increases with the increase of the communication range, Thus, IIsomap method makes it possible to simultaneously reduce the transmitting power and improve the localization accuracy.
In this dissertation, we introduce the kernel-based approach and the manifold learning method into the localization problem, which bring new ideas into this area, and propose four location estimation methods. In the end of this dissertation, we point out several aspects waiting for improvement in our localization methods, and introduce our future work.
引文
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