基于TDOAs与GROAs的多信号源被动定位

为提高感知节点位置模糊条件下多目标被动定位结果精度,提出基于TDOAs与GROAs的混合定位代数闭式解算法,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TDOAs与GROAs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TDOAs与GROAs多目标混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,并且GROAs信息的引入给多目标定位精度带来明显性能提升.     

无源时差定位系统最优布站方法研究

为提高基于到达时间差(Time Difference of Arrival,TDOA)的三维无源定位系统的定位精度,提出了一种考虑基站时差测量性能差异的最优布站方法,该方法通过求解目标所在区域定位误差的克拉美罗下界(Cramer Rao Lower Bound,CRLB),以定位误差CRLB的迹的平均值最小为优化准则,采用粒子群算法对指定区域进行最优布站仿真研究。仿真结果表明,该方法求解的最优布站位置与假设TDOA测量误差为恒定高斯分布时求解的位置相比,提高了目标区域的整体定位精度;与用遗传算法求解最优布站位置相比,其收敛速度更快,更适用于需要快速作出反应的侦察定位场景。     

TDoA定位盲区分析与节点部署策略研究

以克拉美罗下界(CRLB)作为定位精度衡量指标进行分析，探讨到达时间差(TDoA)定位场景中定位盲区的产生条件，分析不同因素对定位盲区的影响。此外，以无线传感器网络(WSN)所覆盖区域的平均CRLB为目标函数，构建了传感器节点优化部署问题，并提出基于定位盲区预判断的遗传算法进行求解。仿真验证了单信号源定位时CRLB的性质以及定位盲区的产生条件和出现区域。仿真结果表明，采用所提基于定位盲区预判断的遗传算法获得的节点部署方案时，定位精度比均匀角度部署提高33.92%，比区域顶点部署提升13.74%，比直接遗传算法提升9.65%。     

无源定位观测站站址误差自校正算法

无源定位中观测站的站址误差会对定位精度产生不良影响。本文提出了一种基于观测站站址误差自校正的定位算法,推导了高斯噪声模型下定位误差的克拉美罗下界（CRLB）,通过泰勒级数展开建立了关于站址误差的线性方程并得到了误差的线性最小均方误差（LMMSE）估计,改善了观测站的位置,使用Chan算法得到了定位结果,仿真验证了算法的定位精度在高斯噪声模型下能够达到CRLB。      

基于SSDOA定位算法研究

基于信号接收强度差（SSDOA）的定位技术,提出了建立一个信号强度预测数据库（PSD）的想法,通过把反馈过来的信号强度值获得的信号强度差值与PSD中的值进行比较来确定最终目标位置,并推导基于SSDOA定位的克拉美-罗下界（CRLB）。为了提高定位精度,分析了引起误差的主要原因以及降低误差方法,然后对影响定位精度的几个主要参数进行仿真,得出参数与定位精度的关系,最终给出分析结果和结论。     

多校准站TDOA/FDOA无源定位方法

针对运动目标到达时差（Time Difference-of-Arrival,TDOA）/到达频差（Frequency Difference-of-Arrival,FDOA）定位中的接收站定位误差问题,提出了基于多校准站的TDOA/FDOA定位方法,有效降低接收站定位误差的影响,并推导了该方法的克拉美罗下限（Cramér-Rao Lower Bound,CRLB）。理论分析表明,采用多校准站法能有效降低CRLB,提高目标定位精度。同时,当校准站自身定位存在误差时,也将影响对接收站的校准和目标的定位精度。通过仿真实验定量分析了采用多校准站法对定位精度的改善程度。     

无线传感器网络分布式迭代定位误差控制算法

针对无线传感器网络分布式迭代定位中误差的传播和累积问题,该文首先分析了锚节点几何形状对定位误差的影响,提出了基于几何精度因子的误差控制算法,巧妙设计了加权策略,将锚节点几何形状对定位精度的影响以权值的形式定量体现在迭代定位过程中,在每一轮迭代中有效控制了误差的传递,进而提高了整个网络的分布式定位精度。与传统的最小二乘定位算法和基于轮数的误差控制算法进行了仿真比较,结果表明,基于几何精度因子的误差控制算法定位性能最优,网络定位精度分别提高了25%和15%。     

基于TDOA/FDOA多星联合定位误差与卫星构型分析

针对多星定位系统对地面静态目标的无源定位误差分析问题,运用Fisher信息矩阵、Taylor级数、矩阵理论和统计理论,综合考虑时差、频差、卫星位置误差以及卫星速度误差,推导了到达时间差（time difference of arrival,TDOA）/到达频率差（frequency difference of arrival,FDOA）联合定位误差克拉美·罗界（Cramer-Rao lower bound,CRLB）的简单表达式,以及三星单独TDOA定位误差的CRLB,进而给出了避免TDOA定位盲区的良好卫星构型设计的充分条件.理论分析与仿真结果表明:在单独TDOA定位场景下良好的构型能完全消除定位盲区,定位精度随主星-星下点连线与主星-副星连线的夹角逼近90°而逐渐提高;通过引入FDOA与TDOA联合定位也能有效避免定位盲区,提高定位精度.     

辐射源信号波形已知的超视距目标直接定位方法

现有直接定位（Direct Position Determination,DPD）算法主要研究对象是视距目标.针对传统无线电定位技术对超视距目标定位精度低的问题,提出一种辐射源信号波形已知的超视距直接定位（Over-the-Horizon Direct Position Determination,ODPD）方法.该方法基于电离层电子密度参数,依据最大似然（Maximum Likelihood,ML）准则,从信号数据域直接推导出仅关于目标位置的代价函数.其次,本文推导了关于电离层虚高测量误差的定位误差协方差矩阵.实验表明ODPD方法在低信噪比下相比现有算法,能显著提高超视距目标的定位精度,定位性能更接近克拉美罗界（Cramér-Rao Low Bound,CRLB）.误差分析显示,电离层虚高误差标准差在20km时,引起的定位误差能控制在10km的范围内.     

传感器网络节点定位精度的几何稀释分析

通过分析时间到达(Time of Arrival,TOA)算法的定位原理,利用定位精度的几何稀释(Geometrical Dilution ofPrecision,GDOP),描述定位误差与锚节点群几何布局关系,并给出基于测距的算法中GDOP的计算方法。采用蒙特卡罗仿真方法,仿真次数100,设定锚节点的测距误差相同,取锚节点数为3、5,对基于锚节点群内点、外点的未知节点定位误差的归一化GDOP值和GDOP均值求解,结合质心算法原理,验证了自身节点定位精度与确定该节点位置的锚节点的几何关系密切相关,得到锚节点群内点定位精度高的结论。     

Analyzing localization errors in one-dimensional sensor networks

One-dimensional sensor networks can be found in many fields and demand node location information for various applications. Developing localization algorithms in one-dimensional sensor networks is trivial, due to the fact that existing localization algorithms developed for two- and three-dimensional sensor networks are applicable; nevertheless, analyzing the corresponding localization errors is non-trivial at all, because it is helpful to improving localization accuracy and designing sensor network applications. This paper deals with localization errors in distance-based multi-hop localization procedures of one-dimensional sensor networks through the Cramér-Rao lower bound (CRLB). We analyze the fundamental behaviors of localization errors and show that the localization error for a sensor is locally determined by network elements within a certain range of this sensor. Moreover, we break down the analysis of localization errors in a large-scale sensor network into the analysis in small-scale sensor networks, termed unit networks, in which tight upper and lower bounds on the CRLB can be established. Finally, we investigate two practical issues: the applicability of the analysis based on the CRLB and the optimal anchor placement.     

On the Use of a Calibration Emitter for Source Localization in the Presence of Sensor Position Uncertainty

Sensor position uncertainty is known to degrade significantly the source localization accuracy. This paper investigates the use of a single calibration emitter, whose position is known to the sensor array, to reduce the loss in localization accuracy due to sensor position errors that are random. Using a Gaussian noise model, we first derive the CramÉr–Rao lower bound (CRLB) for a time difference of arrival (TDOA)-based source location estimate with the use of a calibration source. The differential calibration technique that is commonly used in Global Positioning System through the use of a calibration source to mitigate the inaccuracy in satellite ephemeris data is analyzed. The analysis indicates that differential calibration in most cases cannot reach the CRLB accuracy. The paper then proceeds to propose an algebraic closed-form solution for the source location estimate using both TDOA measurements from the unknown and the calibration source. The proposed algorithm is shown analytically, under high signal-to-noise ratio (SNR) and small sensor position noise, or under moderate level of SNR and sensor position noise together with distant unknown and calibration sources, to reach the CRLB accuracy. Simulations are used to corroborate and support the theoretical development.      

Alleviating Sensor Position Error in Source Localization Using Calibration Emitters at Inaccurate Locations

A previous study shows that the use of a calibration emitter whose position is known exactly can significantly reduce the loss in time differences of arrival (TDOA) based source localization accuracy when the available sensor positions have random errors. This paper extends the previous work to a more practical scenario where the exact position of a calibration emitter is not known. By modeling the calibration position error as additive Gaussian noise, the amount of reduction in localization accuracy due to calibration position error is derived through Cramer-Rao lower bound (CRLB) analysis. In addition, the analysis also affirms the previous studies on Bayesian sensor network localization that it remains possible to improve the localization accuracy even if the calibration position is completely unknown. Next, a performance analysis illustrates that the penalty could be very high if one simply pretends the calibration position is accurate and ignores its error. A closed-form solution is then developed by accounting for the calibration position error and it is proved analytically to reach the CRLB accuracy when the sensor and calibration position errors are small relative to the distance between the calibration emitter and the sensor. Finally, the results are generalized to the case where multiple calibration emitters are available. When deploying multiple calibration emitters, although their positions may not be known exactly, we show that it is possible to completely eliminate the sensor position error and recover the best localization accuracy that is limited by the measurement noise in TDOAs only. All the theoretical developments are corroborated by simulations.     

目标海拔已知的信号到达幅度比无源定位方法

信号到达幅度比方法因测量简便,可实现对窄带信号的无源定位而广泛应用于射频定位系统、无线传感器网络和声源定位中.当目标海拔已知,将其作为定位方程的约束条件可实现对目标更精确的定位,而现有方法没有考虑这个问题.对此本文建立了海拔约束的信号到达幅度比无源定位模型,推导了定位精度的克拉美劳下界,并提出了一种基于Newton迭代的定位算法.理论推导表明该算法在测量误差服从方差较小的零均值高斯分布时能够达到克拉美劳下界,仿真结果与理论推导一致.无线电栅格化监测试验网的验证结果表明,对系统幅度误差进行校正后,该方法能够实现对辐射源的准确定位.     

无线传感器网络中一种改进的分布式加权多维尺度定位算法

本文在无线传感器网络单跳定位误差分析的基础上,分析了多跳节点定位误差的特性,并据此提出针对分布式加权多维尺度定位(Distributed Weighted Multidimensional Scaling,dwMDS)的权值优化算法.在无法获知参考点确切误差的情况下,利用分析出来的克拉美劳下限代替参考点误差并与距离测量误差合并,更准确的反映了多跳定位中的点与点之间的误差,从而有助于设计更优化的权值.仿真结果表明,使用优化权值改进的算法得到的节点定位误差明显减小.     

An Approximately Efficient TDOA Localization Algorithm in Closed-Form for Locating Multiple Disjoint Sources With Erroneous Sensor Positions

This paper considers the problem of time difference-of-arrival (TDOA) source localization when the TDOA measurements from multiple disjoint sources are subject to the same sensor position displacements from the available sensor positions. This is a challenging problem and closed-form solution with good localization accuracy has yet to be found. This paper proposes an estimator that can achieve this purpose. The proposed algorithm jointly estimates the unknown source and sensor positions to take the advantage that the TDOAs from different sources have the same sensor position displacements. The joint estimation is a highly nonlinear problem due to the coupling of source and sensor positions in the measurement equations. We introduce the novel idea of hypothesized source locations in the algorithm development to enable the formulation of psuedolinear equations, thereby leading to the establishment of closed-form solution for source location estimates. Besides the advantage of closed-form, the newly developed algorithm is shown analytically, under the condition that the TDOA measurement noise and the sensor position errors are sufficiently small, to reach the CRLB accuracy. For clarity, the localization of two disjoint sources is used in the algorithm development. The developed algorithm is then examined under the special case of a single source and extended to the more general case of more than two unknown sources. The theoretical developments are supported by simulations.      

基于PDOA着靶点参数估计的阵列布放结构研究

在基于到达相位差(Phase Differences Of Arrival, PDOA)的着靶点参数估计问题中，估计精度受到阵列结构的影响。与一般的单点目标定位问题相比，着靶点参数估计需要同时估计目标的速度和角度参数，情况更加复杂。为了选择合适的阵列结构以对定位结果带来有利影响，该文从灵敏度的角度分析了不同阵列结构下靶点参数估计精度各有差异的原因，为判断不同情况下接收阵列定位性能的优劣提供了理论方法。最后，对3种常见阵列结构进行了计算机仿真对比，仿真结果验证了利用灵敏度指标对阵列布放结构进行评估的可行性。     

Efficient closed-form solution for target localization using TDOA measurements in the presence of sensor position errors

An efficient solution for locating a target was proposed, which by using time difference of arrival (TDOA) measurements in the presence of random sensor position errors to increase the accuracy of estimation. The cause of position estimation errors in two-stage weighted least squares (TSWLS) method is analyzed to develop a simple and effective method for improving the localization performance. Specifically, the reference sensor is selected again and the coordinate system is rotated according to preliminary estimated target position by using TSWLS method, and the final position estimation of the target is obtained by using weighted least squares (WLS). The proposed approach exhibits a closed-form and is as efficient as TSWLS method. Simulation results show that the proposed approach yields low estimation bias and improved robustness with increasing sensor position errors and thus can easily achieve the Cramer-Rao lower bound (CRLB) easily and effectively improve the localization accuracy.     

Maximum likelihood multiple-source localization using acoustic energy measurements with wireless sensor networks

A maximum likelihood (ML) acoustic source location estimation method is presented for the application in a wireless ad hoc sensor network. This method uses acoustic signal energy measurements taken at individual sensors of an ad hoc wireless sensor network to estimate the locations of multiple acoustic sources. Compared to the existing acoustic energy based source localization methods, this proposed ML method delivers more accurate results and offers the enhanced capability of multiple source localization. A multiresolution search algorithm and an expectation-maximization (EM) like iterative algorithm are proposed to expedite the computation of source locations. The Crame/spl acute/r-Rao Bound (CRB) of the ML source location estimate has been derived. The CRB is used to analyze the impacts of sensor placement to the accuracy of location estimates for single target scenario. Extensive simulations have been conducted. It is observed that the proposed ML method consistently outperforms existing acoustic energy based source localization methods. An example applying this method to track military vehicles using real world experiment data also demonstrates the performance advantage of this proposed method over a previously proposed acoustic energy source localization method.