无线传感网信号被动定位关键技术研究
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摘要
近年来，基于无线传感器网络（Wireless Sensor Networks，WSNs）的信号被动定位（Passive Source Localization，PSL）技术受到了国内外众多学者关注，它在民用与军事方面均具有广阔的应用前景。PSL-WSNs技术无论在基于定位数据处理的定位关联度量估计方面，还是在基于定位关联度量信息与传感器阵列信息的度量融合定位方面，均存在众多问题尚待解决，本文对其中几个关键技术进行了系统的研究，所取得的主要研究成果为：
（1）当WSNs节点接收噪声强度不同，或无线传输信道存在阴影慢衰落效应时，对目标信号到达距离比（RROA）定位关联度量估计方法，以及被动定位算法进行了研究。将特征值分解技术引入到RROA定位关联度量估计中，通过接收信号协方差矩阵特征值分解估计各节点所接收噪声强度；通过WSNs中参考节点的轮换与特征值分解方法消除阴影衰落效应所引入的定位误差，实现RROA关联度量的可靠估计；最后给出了基于RROA关联度量以及WSNs节点位置信息的最小二乘定位算法，该方法可较好的消除由于节点接收噪声强度不同以及阴影慢衰落效应等因素所带来的定位性能恶化。
（2）对WSNs中基于TDOA与GROA的信号被动定位BFGS拟牛顿算法进行了研究。为满足实际应用中高精度与实时性的要求，将变尺度（BFGS）拟牛顿算法引入到加性测量误差模型下非线性定位方程求解应用中给出了基于TDOA与GROA的BFGS拟牛顿定位算法，该算法克服了基本牛顿法目标函数海瑟矩阵非正定问题，并且在给予较好初始值条件下，对比经典的两步WLS算法具有更优的性能，在适当的信噪比条件下算法收敛于真实值并且无论对远场源还是近场源均可以达到CRLB，对比基本牛顿法与WLS算法，该算法同时具有更低的计算复杂度且易于系统实现。
（3）对WSNs节点位置模糊条件下基于TDOA与到达增益比GROA的多目标联合被动定位算法进行了研究。提出了该条件下多目标联合被动定位的代数闭式解算法，该算法联合估计未知信号源位置与带误差感知节点位置，利用TDOA与GROA所包含的相同感知节点位置误差信息提升定位精度，并推导得到基于TDOA与GROA多目标联合定位的克拉美罗下界（CRLB），仿真结果表明所提算法能较好的达到CRLB，并验证了GROA信息的引入给多目标定位精度所带来的性能提升量。
（4）对基于TDOA与GROA信号源被动定位代数闭式解的偏差消除算法进行了研究。首先对经典代数闭式解算法的偏差进行了推导，然后给出BiasRed与BiasSub两种偏差消减算法，BiasSub法从原始代数闭式解中直接减去期望偏差，BiasRed法通过分析误差表达方程并引入二次约束来提升定位估计精度；分析表明两种方法均可针对远距离信号源，在较小高斯误差情况下有效消减定位偏差，BiasRed法可将偏差降低到最大似然估计（MLE）算法的水平。
（5）对WSNs节点存在位置误差与速度误差情况下，基于TDOA与到达频率差FDOA的多目标联合被动定位算法进行了研究。给出了该条件下多目标联合被动定位以及节点位置与速度误差同步修正的代数闭式解算法，该算法将待估计的定位目标位置与速度信息，以及节点位置与速度信息同时作为被估计变量，对前人所提出的两步加权最小二乘（WLS）算法进行了优化，多个被定位目标与感知节点阵列的位置及速度可同时较好地达到CRLB。
In recent years, passive source localization based on wireless sensor networks(PSL-WSNs) has been paid comprehensive attention from domestic and alien scholars.It is widely used both in civil and military realms, and also it has been the hotspot to bestudied and developed in the world. But there are still many problems to be solved,which are related to the “Association Metrics Estimation (AME)” phase based onprocessing the received signals at the sensors and the “Metrics Fusion Localization(MFL)” phase by using association metrics and WSNs sensor positions. Thisdissertation is mainly concerned with the research on several key technologies to solvethese problems. The author’s major contributions are outlined as follows:
(1) When WSNs sensors have different received noise intensities or the wirelesstransmission channel has the shadow fading effect, it is studied that the associationmetrics estimation method for Range Ratios of Arrival (RROA) and the passive sourcelocalization algorithm based on RROA. Firstly, the eigenvector decomposition (EVD)approach is used to estimate the RROA association metrics. The received noise intensityof each sensor can be estimated by performing EVD on the received signal covariancematrix. Secondly, by rotating the array reference point to be at each of the array sensors,a number of covariance matrices are constructed and the EVD approach can be used tocancel the shadow fading effect. The RROA association metrics can be estimatedreliably. At last, the weighted-least-squares (WLS) algorithm based on the RROAassociation metrics is proposed. The proposed approach is robust to channel shadowfading effect and different received noise intensities.
(2) An efficient iterative algorithm is proposed for passive source localizationbased on TDOA and GROA. It exploits the Broyden-Fletcher-Goldfarb-Shanno (BFGS)Quasi-Newton method to solve nonlinear equations at the source location under theadditive measurement error. The proposed method can overcome the problem that theHessian matrix may be non-positive and the basic Newton method cannot converge tothe global minimum. Compared with two-step WLS method, the proposed approach canachieve the same accuracy and bias with lower computational complexity when SNR ishigh, especially it can achieves better accuracy and smaller bias at lower SNR.Simulation results show that with a good initial guess to begin with, the proposedestimator converges to the true solution and achieves the CRLB accuracy for bothnear-field and far-field sources. It can apply to the actual environment due to itsreal-time property and good robust performance.
(3) It is proposed that a hybrid closed-form solution algorithm based on TDOA andGain Ratios of Arrival (GROA) to improve multiple disjoint sources localizationaccuracy with erroneous sensor positions. The algorithm jointly estimates the unknownsources and sensor positions, and then takes the advantage that the TDOA and GROAfrom different sources have the same sensor position displacements to enhance theposition accuracy. It is also derived that the Cramér-Rao lower bound (CRLB) ofmultiple source localization using both TDOA and GROA. Simulations show that theproposed solution is able to reach the CRLB accuracy very well, and the localizationaccuracy improvements contributed by GROA measurements are significant.
(4) Two methods are proposed to reduce the bias of the well-known algebraicclosed-form solution for source localization by using both TDOA and GROA. Firstly, itstarts by deriving the bias of the source location estimate from the closed-form solution.And then, two methods called BiasSub and BiasRed are developed to reduce the bias.The BiasSub method directly subtracts the expected bias from the closed-form solution.The BiasRed method augments the equation error formulation and imposes a constraintto improve the source location estimate. Analysis shows that both methods reduce thebias considerably for distant source when the noise is Gaussian and small. The BiasRedmethod is able to lower the bias to the same level as the maximum likelihood estimator.
(5) In the presence of sensor position and velocity errors, it is studied that theproblem of simultaneously locating multiple disjoint sources and refining erroneoussensor positions and velocities using TDOA and Frequency Differences of Arrival(FDOA). The proposed method has the existing WLS method based on TDOA andFDOA improved and a new algebraic closed-form solution is given. The new solutiontakes both the source positions and velocities and the sensor positions and velocities asthe targets to be estimated. All of them can achieve the CRLB accuracy very well. Thetheoretical derivation is corroborated by simulations.
（1）当WSNs节点接收噪声强度不同，或无线传输信道存在阴影慢衰落效应时，对目标信号到达距离比（RROA）定位关联度量估计方法，以及被动定位算法进行了研究。将特征值分解技术引入到RROA定位关联度量估计中，通过接收信号协方差矩阵特征值分解估计各节点所接收噪声强度；通过WSNs中参考节点的轮换与特征值分解方法消除阴影衰落效应所引入的定位误差，实现RROA关联度量的可靠估计；最后给出了基于RROA关联度量以及WSNs节点位置信息的最小二乘定位算法，该方法可较好的消除由于节点接收噪声强度不同以及阴影慢衰落效应等因素所带来的定位性能恶化。
（2）对WSNs中基于TDOA与GROA的信号被动定位BFGS拟牛顿算法进行了研究。为满足实际应用中高精度与实时性的要求，将变尺度（BFGS）拟牛顿算法引入到加性测量误差模型下非线性定位方程求解应用中给出了基于TDOA与GROA的BFGS拟牛顿定位算法，该算法克服了基本牛顿法目标函数海瑟矩阵非正定问题，并且在给予较好初始值条件下，对比经典的两步WLS算法具有更优的性能，在适当的信噪比条件下算法收敛于真实值并且无论对远场源还是近场源均可以达到CRLB，对比基本牛顿法与WLS算法，该算法同时具有更低的计算复杂度且易于系统实现。
（3）对WSNs节点位置模糊条件下基于TDOA与到达增益比GROA的多目标联合被动定位算法进行了研究。提出了该条件下多目标联合被动定位的代数闭式解算法，该算法联合估计未知信号源位置与带误差感知节点位置，利用TDOA与GROA所包含的相同感知节点位置误差信息提升定位精度，并推导得到基于TDOA与GROA多目标联合定位的克拉美罗下界（CRLB），仿真结果表明所提算法能较好的达到CRLB，并验证了GROA信息的引入给多目标定位精度所带来的性能提升量。
（4）对基于TDOA与GROA信号源被动定位代数闭式解的偏差消除算法进行了研究。首先对经典代数闭式解算法的偏差进行了推导，然后给出BiasRed与BiasSub两种偏差消减算法，BiasSub法从原始代数闭式解中直接减去期望偏差，BiasRed法通过分析误差表达方程并引入二次约束来提升定位估计精度；分析表明两种方法均可针对远距离信号源，在较小高斯误差情况下有效消减定位偏差，BiasRed法可将偏差降低到最大似然估计（MLE）算法的水平。
（5）对WSNs节点存在位置误差与速度误差情况下，基于TDOA与到达频率差FDOA的多目标联合被动定位算法进行了研究。给出了该条件下多目标联合被动定位以及节点位置与速度误差同步修正的代数闭式解算法，该算法将待估计的定位目标位置与速度信息，以及节点位置与速度信息同时作为被估计变量，对前人所提出的两步加权最小二乘（WLS）算法进行了优化，多个被定位目标与感知节点阵列的位置及速度可同时较好地达到CRLB。
In recent years, passive source localization based on wireless sensor networks(PSL-WSNs) has been paid comprehensive attention from domestic and alien scholars.It is widely used both in civil and military realms, and also it has been the hotspot to bestudied and developed in the world. But there are still many problems to be solved,which are related to the “Association Metrics Estimation (AME)” phase based onprocessing the received signals at the sensors and the “Metrics Fusion Localization(MFL)” phase by using association metrics and WSNs sensor positions. Thisdissertation is mainly concerned with the research on several key technologies to solvethese problems. The author’s major contributions are outlined as follows:
(1) When WSNs sensors have different received noise intensities or the wirelesstransmission channel has the shadow fading effect, it is studied that the associationmetrics estimation method for Range Ratios of Arrival (RROA) and the passive sourcelocalization algorithm based on RROA. Firstly, the eigenvector decomposition (EVD)approach is used to estimate the RROA association metrics. The received noise intensityof each sensor can be estimated by performing EVD on the received signal covariancematrix. Secondly, by rotating the array reference point to be at each of the array sensors,a number of covariance matrices are constructed and the EVD approach can be used tocancel the shadow fading effect. The RROA association metrics can be estimatedreliably. At last, the weighted-least-squares (WLS) algorithm based on the RROAassociation metrics is proposed. The proposed approach is robust to channel shadowfading effect and different received noise intensities.
(2) An efficient iterative algorithm is proposed for passive source localizationbased on TDOA and GROA. It exploits the Broyden-Fletcher-Goldfarb-Shanno (BFGS)Quasi-Newton method to solve nonlinear equations at the source location under theadditive measurement error. The proposed method can overcome the problem that theHessian matrix may be non-positive and the basic Newton method cannot converge tothe global minimum. Compared with two-step WLS method, the proposed approach canachieve the same accuracy and bias with lower computational complexity when SNR ishigh, especially it can achieves better accuracy and smaller bias at lower SNR.Simulation results show that with a good initial guess to begin with, the proposedestimator converges to the true solution and achieves the CRLB accuracy for bothnear-field and far-field sources. It can apply to the actual environment due to itsreal-time property and good robust performance.
(3) It is proposed that a hybrid closed-form solution algorithm based on TDOA andGain Ratios of Arrival (GROA) to improve multiple disjoint sources localizationaccuracy with erroneous sensor positions. The algorithm jointly estimates the unknownsources and sensor positions, and then takes the advantage that the TDOA and GROAfrom different sources have the same sensor position displacements to enhance theposition accuracy. It is also derived that the Cramér-Rao lower bound (CRLB) ofmultiple source localization using both TDOA and GROA. Simulations show that theproposed solution is able to reach the CRLB accuracy very well, and the localizationaccuracy improvements contributed by GROA measurements are significant.
(4) Two methods are proposed to reduce the bias of the well-known algebraicclosed-form solution for source localization by using both TDOA and GROA. Firstly, itstarts by deriving the bias of the source location estimate from the closed-form solution.And then, two methods called BiasSub and BiasRed are developed to reduce the bias.The BiasSub method directly subtracts the expected bias from the closed-form solution.The BiasRed method augments the equation error formulation and imposes a constraintto improve the source location estimate. Analysis shows that both methods reduce thebias considerably for distant source when the noise is Gaussian and small. The BiasRedmethod is able to lower the bias to the same level as the maximum likelihood estimator.
(5) In the presence of sensor position and velocity errors, it is studied that theproblem of simultaneously locating multiple disjoint sources and refining erroneoussensor positions and velocities using TDOA and Frequency Differences of Arrival(FDOA). The proposed method has the existing WLS method based on TDOA andFDOA improved and a new algebraic closed-form solution is given. The new solutiontakes both the source positions and velocities and the sensor positions and velocities asthe targets to be estimated. All of them can achieve the CRLB accuracy very well. Thetheoretical derivation is corroborated by simulations.
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