Source localization and calibration using TDOA and FDOA measurements in the presence of sensor location uncertainty

Source localization accuracy is very sensitive to sensor location error.This paper performs analysis and develops a solution for locating a moving source using time difference of arrival(TDOA)and frequency difference of arrival(FDOA)measurements with the use of a calibration emitter.Using a Gaussian random signal model,we first derive the Cram′er-Rao lower bound(CRLB)for source location estimate in this scenario.Then we analyze the differential calibration technique which is commonly used in Global Positioning System.It is indicated that the differential calibration cannot attain the CRLB accuracy in most cases.A closed-form solution is then proposed which takes a calibration emitter into account to reduce sensor location error.It is shown analytically that under some mild approximations,our approach is able to reach the CRLB accuracy.Numerical simulations are included to corroborate the theoretical developments.     

Localization of multiple disjoint sources with prior knowledge on source locations in the presence of sensor location errors

Sensor location errors are known to be able to degrade the source localization accuracy significantly. This paper considers the problem of localizing multiple disjoint sources where prior knowledge on the source locations is available to mitigate the effect of sensor location uncertainty. The error in the priorly known source location is assumed to follow a zero-mean Gaussian distribution. When a source location is completely unknown, the covariance matrix of its prior location would go to infinity. The localization of multiple disjoint sources is achieved through exploring the time difference of arrival (TDOA) and the frequency difference of arrival (FDOA) measurements. In this work, we derive the Cramér–Rao lower bound (CRLB) of the source location estimates. The CRLB is shown analytically to be able to unify several CRLBs introduced in literature. We next compare the localization performance when multiple source locations are determined jointly and individually. In the presence of sensor location errors, the superiority of joint localization of multiple sources in terms of greatly improved localization accuracy is established. Two methods for localizing multiple disjoint sources are proposed, one for the case where only some sources have prior location information and the other for the scenario where all sources have prior location information. Both algorithms can reach the CRLB accuracy when sensor location errors are small. Simulations corroborate the theoretical developments.     

Iterative constrained weighted least squares estimator for TDOA and FDOA positioning of multiple disjoint sources in the presence of sensor position and velocity uncertainties

Sensor position and velocity uncertainties are known to be able to degrade the source localization accuracy significantly. This paper focuses on the problem of locating multiple disjoint sources using time differences of arrival (TDOAs) and frequency differences of arrival (FDOAs) in the presence of sensor position and velocity errors. First, the explicit Cramér–Rao bound (CRB) expression for joint estimation of source and sensor positions and velocities is derived under the Gaussian noise assumption. Subsequently, we compare the localization accuracy when multiple-source positions and velocities are determined jointly and individually based on the obtained CRB results. The performance gain resulted from multiple-target cooperative positioning is also quantified using the orthogonal projection matrix. Next, the paper proposes a new estimator that formulates the localization problem as a quadratic programming with some indefinite quadratic equality constraints. Due to the non-convex nature of the optimization problem, an iterative constrained weighted least squares (ICWLS) method is developed based on matrix QR decomposition, which can be achieved through some simple and efficient numerical algorithms. The newly proposed iterative method uses a set of linear equality constraints instead of the quadratic constraints to produce a closed-form solution in each iteration. Theoretical analysis demonstrates that the proposed method, if converges, can provide the optimal solution of the formulated non-convex minimization problem. Moreover, its estimation mean-square-error (MSE) is able to reach the corresponding CRB under moderate noise level. Simulations are included to corroborate and support the theoretical development in this paper.     

基于TDOA定位机制的无线传感器网络节点设计

介绍了一种具有到达时间差(TDOA)定位机制的基于数字信号处理器(DSP)的无线传感器网络节点。它包括TMS320F2812DSP,512 kB的SRAM,2.4 GHz波段的无线收发模块、音频信号收发模块及电源管理模块等。节点通过测量RF同步信号与音频信号的TDOA来测量节点间的间隔距离,并采用互相关时延估计算法来实现节点定位。实验数据表明:该节点最远测距距离超过25m,角度误差小于3.7%。     

TOA source localization and DOA estimation algorithms using prior distribution for calibrated source

This paper presents an a priori probability density function (pdf)-based time-of-arrival (TOA) source localization algorithms. Range measurements are used to estimate the location parameter for TOA source localization. Previous information on the position of the calibrated source is employed to improve the existing likelihood-based localization method. The cost function where the prior distribution was combined with the likelihood function is minimized by the adaptive expectation maximization (EM) and space-alternating generalized expectation–maximization (SAGE) algorithms. The variance of the prior distribution does not need to be known a priori because it can be estimated using Bayes inference in the proposed adaptive EM algorithm. Note that the variance of the prior distribution should be known in the existing three-step WLS method [1]. The resulting positioning accuracy of the proposed methods was much better than the existing algorithms in regimes of large noise variances. Furthermore, the proposed algorithms can also effectively perform the localization in line-of-sight (LOS)/non-line-of-sight (NLOS) mixture situations.     

Effective bias reduction methods for passive source localization using TDOA and GROA

For passive source localization based on both TDOA and GROA, this paper proposes two bias reduction methods for the well-known Weighted-Least-Squares (WLS) estimator. We first derive the passive source localization bias from the two-step algebraic closed-form solution. This bias is found to be considerably larger than the Maximum Likelihood Estimator (MLE) and limits the WLS estimator’s practical applications. In this paper, We develop two methods to reduce the bias. The first one called Bias-Subtraction-Method (BSM) directly subtracts the expected bias from the solution of the WLS estimator, and the second one called Bias-Reduction-Method (BRM) imposes a constraint to the equation error formulation to improve the source location estimate. The noise covariance matrix must be known exactly in calculating the expected bias in BSM, and we only need to know the structure of it in BRM. For far-field sources localization when the noise is Gaussian and not too large, both of the two proposed methods can reduce the localization bias effectively and achieve the Cramér-Rao Lower Bound (CRLB) performance very well, and the BRM almost has the same performance as the MLE estimator. Simulations corroborate the performance of the two proposed methods.     

一种基于优化TDOA的无线传感网络定位算法

运用TDOA方法对节点定位时,需要对节点测距。由于时间精度及硬件的限制,其定位精度有时不能达到要求。针对这一问题,提出一种对TDOA定位方法的改进算法,减小了由于测距产生的定位误差。并通过仿真证明了改进算法的优越性。     

利用外辐射源的TDOA和FDOA目标定位算法

针对单站外辐射源条件下的目标定位问题,提出了一种基于最大似然的时差-频差联合定位算法。首先根据时差和频差的观测方程,构建目标位置和速度的最大似然估计模型。然后采用牛顿迭代算法对最大似然估计模型求解,得到目标位置和速度估计。最后,推导了算法的克拉美罗界和理论误差,并证明了二者相等。仿真结果表明,算法定位精度高于两步加权最小二乘算法和约束总体最小二乘算法,在测量误差较高时仍能达到克拉美罗界。通过对系统几何精度因子图的分析,确定目标及外辐射源数量和位置也是影响定位精度的重要因素。     

无线传感器网络中基于TDOA/FDOA的增强半正定松弛定位算法研究

本文在无线传感器网络定位问题中,考虑了基于到达时间差（Time-Difference-of-Arrival,TDOA）和到达频率差（Frequency-Difference-of-Arrival,FDOA）的移动未知目标定位问题,TDOA/FDOA联合定位可以有效利用传感器的位置和速度信息,提高了定位精度。本文在现有的半正定松弛（Semidefinite Relaxation, SDR）方法的基础上,提出了一种增强半正定松弛方法。通过挖掘现有半正定规划问题中优化变量之间的内在联系并将这些联系转化为凸约束,有效提高了现有半正定松弛方法的紧度,从而使估计的未知目标的位置和速度精度达到了克拉美-罗下界 (Cramer Rao lower bound,CRLB)。仿真结果表明,该方法的性能在大噪声时优于现有方法。     

Achievable accuracy in Gaussian plume parameter estimation using a network of binary sensors

The Gaussian plume model is the core of most regulatory atmospheric dispersion models. The parameters of the model include the source characteristics (e.g. location, strength) and environmental parameters (wind speed, direction, atmospheric stability conditions). The paper presents a theoretical analysis of the best achievable accuracy in estimation of Gaussian plume parameters in the context of a continuous point-source release and using a binary sensor network for acquisition of measurements. The problem is relevant for automatic localisation of atmospheric pollutants with applications in public health and defence. The theoretical bounds of achievable accuracy provide a guideline for sensor network deployment and its performance under various environmental conditions. The bounds are compared with empirical errors obtained using a Markov chain Monte Carlo (MCMC) parameter estimation technique.     

Coherent summation of multiple short-time signals for direct positioning of a wideband source based on delay and Doppler

We consider identifying the source position directly from the received source signals. This direct position determination (DPD) approach has been shown to be superior in terms of better estimation accuracy and improved robustness to low signal-to-noise ratios (SNRs) to the conventional two-step localization technique, where signal measurements are extracted first and the source position is then estimated from them. The localization of a wideband source such as a communication transmitter or a radar whose signal should be considered deterministic is investigated in this paper. Both passive and active localization scenarios, which correspond to the source signal waveform being unknown and being known respectively, are studied. In both cases, the source signal received at each receiver is partitioned into multiple non-overlapping short-time signal segments for the DPD task. This paper proposes the use of coherent summation that takes into account the coherency among the short-time signals received at the same receiver. The study begins with deriving the Cramér–Rao lower bounds (CRLBs) of the source position under coherent summation-based and non-coherent summation-based DPDs. Interestingly, we show analytically that with coherent summation, the localization accuracy of the DPD improves as the time interval between two short-time signals increases. This paper also develops approximate maximum likelihood (ML) estimators for DPDs with coherent and non-coherent summations. The CRLB results and the performance of the proposed source position estimators are illustrated via simulations.     

基于飞行理论萤火虫算法的TDOA与GROA定位机制

节点定位是无线传感器网络中最为关键的一项技术。针对无源定位的问题,提出一种到达时间差(TDOA)和到达信号增益比(GROA)联合定位算法,并且采用飞行机制的萤火虫算法(GSO)来求得最终结果。结合TDOA和GROA定位模型,引入辅助变量将方程伪线性化,然后采用修正两步加权最小二乘算法(TSWLS)来进行求解。并且在不影响收敛速度和精度的前提下,采用带有飞行机制的GSO算法来寻求目标定位的最优解,克服粒子群算法易陷入局部最优的缺点。仿真结果表明,该算法相比较TDOA算法而言,定位精度提高了23 dB,并且具有相对较高和较稳定的定位精度。     

基于非同步采集方式小型声源定位系统设计

利用非同步采集设备,通过广义互相关(GCC)时延估计算法,估算出通道间的相对时延;对非同步采集方式产生的时延误差进行软件补偿;利用基于到达时间差(TDOA)声源定位算法的双步定位特性,估算出声源的位置.分别设计了四元均匀线阵系统和四元平面十字阵列系统对以上方法进行验证,系统能够较准确地实现对声源方位的估计.     

无线传感器网络中的信标优化选择算法

针对无线传感器网络中节点定位精度的问题,提出了一种基于距离和Cramer-Rao下界的信标优化选择算法。该算法通过分析信标与节点间的距离和位置拓扑关系对定位精度的影响,选择CRLB值最小的信标子集进行位置估计,减少节点定位误差。仿真结果表明,该方法较大地提高了定位精度,降低了计算量,为合理选择信标子集提供了依据。     

基于移动锚节点的无线传感器网络三边质心定位

探讨了无线传感器网络(WSN)定位技术的意义,研究基于移动锚节点的测距定位技术;设计了移动锚节点运动轨迹,在利用无线电与超声波到达时间差(TDOA)测得锚节点到待定位节点距离的情况下,给出了一种新的定位算法——三边质心定位算法,该算法通过求解待定位节点的定位近点所构成几何图形的质心来完成定位;仿真结果表明,该定位技术能够明显减小定位误差与锚节点数量。     

修正的UKF滤波时差定位算法

为了降低到达时问差(TDOA)测距在非视距(NLOS)传播环境中的误差,提出了在强跟踪无迹卡尔曼滤波(UKF)基础上改进的算法.在状态发生突变时,给预测协方差矩阵加入次优渐消因子;对NLOS误差进行正负判断,利用整体偏移法修改滤波增益,但估计协方差矩阵不做改进,以免出现不收敛.实验结果表明:该算法不仅能有效地抑制突变带来的影响,也能高效地消除NLOS误差,提高了NLOS传播的到达时间差定位精度.     

传感网中UWB和IMU融合定位的性能评估

位置信息是物体的基本属性之一.随着无线传感器网络(wireless sensor network, WSN)的蓬勃发展,传感器网络中节点位置信息的获取变得尤为重要.超宽带(ultra-wideband, UWB)和惯性测量单元(inertial measurement units, IMU)以其高定位精度,在WSN中得到了广泛应用.UWB精度高,但容易受多径效应和节点间的相对几何位置关系影响.IMU惯性测量单元能够提供连续的惯性信息,但累积误差问题难以解决.基于IMU和UWB结合的融合定位方法,能够在提高定位精度的同时补偿UWB的多径效应影响和IMU的误差累积问题.因此,提出一种新的基于UWB和IMU的融合定位方法,实现传感网中目标节点的高精度位置追踪,并通过计算克拉美罗下限(Cramer-Rao lower bound, CRLB)表征融合定位方法的空间定位性能验证其在解决多径和几何拓扑问题上的有效性,通过计算后验克拉美罗下限(posterior Cramer-Rao lower bound, PCRLB)表征融合定位方法的时间定位性能验证其在累积误差纠正上的有效性,为基于UWB和IMU融合定位算法的设计和仿真提供理论支持.实验结果表明：融合定位方法具有更好的时空定位性能,更能接近实际应用的理论精度下限.     

改进粒子群优化算法在TDOA定位中的应用

针对TDOA定位估计中的非线性最优化问题,提出了一种基于改进粒子群优化的TDOA定位算法。该算法在自适应粒子群优化算法的基础上,引入禁忌搜索策略,有效地解决了粒子群优化算法容易陷入局部最优的问题,使算法快速收敛到全局最优解。仿真结果表明:该算法性能稳定,定位精度高。     

蜂窝网无线定位技术在铁路场景下的应用

针对蜂窝网络定位技术定位精度不高和在铁路实际中难以应用的缺点,提出一种新的列车定位方法.方法的核心是将速度传感器和蜂窝网的定位参数处理为若干列车可能的位置区域,并计算区域中列车位置出现的概率,以所有位置中出现概率最大为优化目标,建立列车定位的误差优化模型.在此基础上进一步引入遗传粒子群优化算法对模型进行求解,并用Matlab仿真.仿真结果表明:在复杂的铁路环境中,该定位方法对不同来源的误差有很好的吸收作用,是一种有效的定位方法.