参数化多维标度定位方法研究
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摘要
随着物联网概念的兴起，位置感知服务在民用和军事领域都将扮演重要的角色，而传统依赖定位卫星或蜂窝网络提供的位置感知服务不能满足复杂环境下定位或高精度定位的需求。
本论文正是针对上述问题，以基于ZigBee技术的无线自组织网络（WirelessADHoc Networks）为硬件平台，以基于距离测量的多维标度（Multidimensional Scaling,MDS）算法为主要研究对象，在深入分析室内环境的信道传输特性基础上，对室内环境中的定位问题作了创新性和探索性研究。主要内容为：
1.详细研究了现有MDS定位算法的统一求解框架及其通解，针对现有MDS定位算法进行移动站位置估计时，需要进行特征值分解或求逆运算，而由此导致算法运算量偏大，不能满足移动站连续跟踪定位需求的问题，提出了基于矩阵分解和拉格朗日约束函数的MDS快速定位算法。所提方法由于有效的避开了现有MDS方法中的特征值分解问题，从而简化运算量。
2.详细研究了信号估计中的无偏估计性质与克拉美罗下界（Cram′er-Rao lowerbound, CRLB）特性，采用与二步加权最小二乘（Two-step Weighted Least Squares,TWLS）方法类似的思想，提出了基于到达时间（Time of Arrival, TOA）测量的加权MDS快速定位算法，结果表明加权MDS快速定位算法的定位估计性能与统一框架下的加权MDS方法类似，都接近于CRLB，在中等信噪比水平下是最优的。
3.针对经典MDS定位算法在低信噪比条件下的不稳健特性，将最小二乘算法引入到对MDS定位算法的噪声向量约束之中，提出了一种基于数据矩阵分解的MDS噪声向量最小二乘解。该算法在低信噪比和较少基站个数条件下，相较于经典MDS定位算法和子空间MDS定位算法均表现出了更稳健的定位估计性能。
4.针对在到达角度（Angle of Arrival, AOA）测量中，传统最小二乘定位算法性能较低，无法满足实际定位需求的问题，将基于数据矩阵的MDS定位方法推广到了AOA测量之中，提出了基于AOA测量的MDS定位算法无偏估计量。结果表明，所提估计量在信噪比和基站个数变化时，其定位性能均优于传统的最小二乘估计量。
5.研究了复数表示在MDS定位算法中的应用，针对传统MDS定位方法中，数据矩阵信息量不够丰富的特点，提出了基于复数数据矩阵的MDS定位算法。所提方法由于在复数数据矩阵各元素的虚部涵盖了与估计位置相关的距离信息，使得定位性能接近CRLB，优于传统MDS定位算法。
6.详细分析了在对数正态模型条件下的位置估计量，研究了基于ZigBee技术的无线自组织网络硬件平台，并基于此平台，利用MATLAB GUI搭建了一套室内定位算法仿真与实测定位系统软件，在软件中分析了最大似然估计结合最速梯度下降法的定位性能，并实现了移动站的室内定位，定位精度优于现有室内定位硬件引擎。
With the rise of the concept about Internet of Things, location-aware services incivil and military fields will play an important role, while the traditionallocation-aware services rely on positioning satellite or cellular networks, cannot meetthe needs of positioning in a complex environment or high-precision positioning.
This dissertation is to address this problem. Based on an in-depth analysis ofchannel transmission characteristics in the indoor environment, and a hardwareplatform on ZigBee technology for wireless self-organizing network (Wireless AD HocNetworks), a detailed study of multidimensional scaling (MDS) localization algorithmhas been conducted. The dissertation in the field of indoor environment localizationwas innovative and exploratory research. The main contents are:
1. Detailed study of existing MDS location algorithms for the unified solutionframework and its general solution. The traditional MDS localization framework usingeigenvalue decomposition or inverse operation, cannot meet the need of continuouslymobile station track. To address this issue, a fast localization algorithm is introduced.The proposed method which based on the MDS matrix decomposition and Lagrangeconstraint functions, is effective to avoid the eigenvalue decomposition existed inMDS methods, and simplifies the computational complexity.
2. Detailed study of the characteristics of unbiased estimate, as well as theCramer-Rao Lower Bound (CRLB). Draws on the two-step weighted least squares(TWLS) method, a weighted MDS fast localization algorithm based on time of arrival(TOA) measurements is proposed. The results showed that the localizationperformance of the weighted MDS fast localization algorithm is close to the CRLB inthe medium SNR level, and unified under the framework of weighted MDS.
3. For the low robust problem of classic MDS localization algorithm in low SNRconditions, the noise vector least square solution based on MDS localization algorithmis proposed. The algorithm showed a more robust performance in low signal to noiseratio (SNR) and fewer base stations, compared with the classical MDS localization algorithm and subspace MDS localization algorithm.
4. MDS localization method is innovatively introduced into the arrival of angle(AOA) measurements. Compared with the traditional least squares location algorithm,the proposed estimator is superior in the condition of changed SNR and base station(BS).
5. Complex representation is firstly introduced into MDS algorithm. Theimaginary part informative rich distance features about location of mobile station (MS).Through simulation analysis, we can find that the proposed method which is close toCRLB, covers more distance information in the complex data matrix, and itslocalization performance is superior to the traditional MDS localization algorithm.
6. Detailed analysis of the lognormal model conditional estimators and wirelessZigBee technology-based AD Hoc Networks platform is introduced. Rely onMATLAB GUI, we build an indoor localization software system with the measurementof received signal strength (RSS). Maximum likelihood estimation combined with thesteepest gradient descent positioning algorithm is the key to position estimation. In theindoor environment, the positioning accuracy is better than existed indoor positioninghardware engine.
本论文正是针对上述问题，以基于ZigBee技术的无线自组织网络（WirelessADHoc Networks）为硬件平台，以基于距离测量的多维标度（Multidimensional Scaling,MDS）算法为主要研究对象，在深入分析室内环境的信道传输特性基础上，对室内环境中的定位问题作了创新性和探索性研究。主要内容为：
1.详细研究了现有MDS定位算法的统一求解框架及其通解，针对现有MDS定位算法进行移动站位置估计时，需要进行特征值分解或求逆运算，而由此导致算法运算量偏大，不能满足移动站连续跟踪定位需求的问题，提出了基于矩阵分解和拉格朗日约束函数的MDS快速定位算法。所提方法由于有效的避开了现有MDS方法中的特征值分解问题，从而简化运算量。
2.详细研究了信号估计中的无偏估计性质与克拉美罗下界（Cram′er-Rao lowerbound, CRLB）特性，采用与二步加权最小二乘（Two-step Weighted Least Squares,TWLS）方法类似的思想，提出了基于到达时间（Time of Arrival, TOA）测量的加权MDS快速定位算法，结果表明加权MDS快速定位算法的定位估计性能与统一框架下的加权MDS方法类似，都接近于CRLB，在中等信噪比水平下是最优的。
3.针对经典MDS定位算法在低信噪比条件下的不稳健特性，将最小二乘算法引入到对MDS定位算法的噪声向量约束之中，提出了一种基于数据矩阵分解的MDS噪声向量最小二乘解。该算法在低信噪比和较少基站个数条件下，相较于经典MDS定位算法和子空间MDS定位算法均表现出了更稳健的定位估计性能。
4.针对在到达角度（Angle of Arrival, AOA）测量中，传统最小二乘定位算法性能较低，无法满足实际定位需求的问题，将基于数据矩阵的MDS定位方法推广到了AOA测量之中，提出了基于AOA测量的MDS定位算法无偏估计量。结果表明，所提估计量在信噪比和基站个数变化时，其定位性能均优于传统的最小二乘估计量。
5.研究了复数表示在MDS定位算法中的应用，针对传统MDS定位方法中，数据矩阵信息量不够丰富的特点，提出了基于复数数据矩阵的MDS定位算法。所提方法由于在复数数据矩阵各元素的虚部涵盖了与估计位置相关的距离信息，使得定位性能接近CRLB，优于传统MDS定位算法。
6.详细分析了在对数正态模型条件下的位置估计量，研究了基于ZigBee技术的无线自组织网络硬件平台，并基于此平台，利用MATLAB GUI搭建了一套室内定位算法仿真与实测定位系统软件，在软件中分析了最大似然估计结合最速梯度下降法的定位性能，并实现了移动站的室内定位，定位精度优于现有室内定位硬件引擎。
With the rise of the concept about Internet of Things, location-aware services incivil and military fields will play an important role, while the traditionallocation-aware services rely on positioning satellite or cellular networks, cannot meetthe needs of positioning in a complex environment or high-precision positioning.
This dissertation is to address this problem. Based on an in-depth analysis ofchannel transmission characteristics in the indoor environment, and a hardwareplatform on ZigBee technology for wireless self-organizing network (Wireless AD HocNetworks), a detailed study of multidimensional scaling (MDS) localization algorithmhas been conducted. The dissertation in the field of indoor environment localizationwas innovative and exploratory research. The main contents are:
1. Detailed study of existing MDS location algorithms for the unified solutionframework and its general solution. The traditional MDS localization framework usingeigenvalue decomposition or inverse operation, cannot meet the need of continuouslymobile station track. To address this issue, a fast localization algorithm is introduced.The proposed method which based on the MDS matrix decomposition and Lagrangeconstraint functions, is effective to avoid the eigenvalue decomposition existed inMDS methods, and simplifies the computational complexity.
2. Detailed study of the characteristics of unbiased estimate, as well as theCramer-Rao Lower Bound (CRLB). Draws on the two-step weighted least squares(TWLS) method, a weighted MDS fast localization algorithm based on time of arrival(TOA) measurements is proposed. The results showed that the localizationperformance of the weighted MDS fast localization algorithm is close to the CRLB inthe medium SNR level, and unified under the framework of weighted MDS.
3. For the low robust problem of classic MDS localization algorithm in low SNRconditions, the noise vector least square solution based on MDS localization algorithmis proposed. The algorithm showed a more robust performance in low signal to noiseratio (SNR) and fewer base stations, compared with the classical MDS localization algorithm and subspace MDS localization algorithm.
4. MDS localization method is innovatively introduced into the arrival of angle(AOA) measurements. Compared with the traditional least squares location algorithm,the proposed estimator is superior in the condition of changed SNR and base station(BS).
5. Complex representation is firstly introduced into MDS algorithm. Theimaginary part informative rich distance features about location of mobile station (MS).Through simulation analysis, we can find that the proposed method which is close toCRLB, covers more distance information in the complex data matrix, and itslocalization performance is superior to the traditional MDS localization algorithm.
6. Detailed analysis of the lognormal model conditional estimators and wirelessZigBee technology-based AD Hoc Networks platform is introduced. Rely onMATLAB GUI, we build an indoor localization software system with the measurementof received signal strength (RSS). Maximum likelihood estimation combined with thesteepest gradient descent positioning algorithm is the key to position estimation. In theindoor environment, the positioning accuracy is better than existed indoor positioninghardware engine.
引文
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