A direct position determination method with combined TDOA and FDOA based on particle filter

The localization of a stationary transmitter using moving receivers is considered. The original Direct Position Determination (DPD) methods, with combined Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA), do not perform well under low Signal-to-Noise Ratio (SNR), and worse still, the computation cost is difficult to accept when the computational capabilities are limited. To get better positioning performance, we present a new DPD algorithm that proves to be more computationally efficient and more precise for weak signals than the conventional approach. The algorithm partitions the signal received with the same receiver into multiple non-overlapping short-time signal segments, and then uses the TDOA, the FDOA and the coherency among the short-time signals to locate the target. The fast maximum likelihood estimation, one iterative method based on particle filter, is designed to solve the problem of high computation load. A secondary but important result is a derivation of closed-form expressions of the Cramer-Rao Lower Bound (CRLB). The simulation results show that the algorithm proposed in this paper outperforms the traditional DPD algorithms with more accurate results and higher computational efficiency, and especially at low SNR, it is more close to the CRLB.     

利用重要性采样的时差-频差联合估计算法

针对无源定位中参考信号真实值未知的时差(TDOA)-频差(FDOA)联合估计问题,构建了一种新的时差-频差最大似然(ML)估计模型,并采用重要性采样(IS)方法求解似然函数极大值,得到时差-频差联合估计。算法通过生成时差-频差样本,并统计样本加权均值得到估计值,克服了传统互模糊函数(CAF)算法只能得到时域和频域采样间隔整数倍估计值的问题,且不存在期望最大化(EM)等迭代算法的初值依赖和收敛问题。推导了时差-频差联合估计的克拉美罗下界(CRLB),并通过仿真实验表明,算法的计算复杂度适中,估计精度优于CAF算法和EM算法,在不同信噪比条件下估计误差接近CRLB。     

一种4站情况下基于TDOA/FDOA的无源定位方法

在基于时频差的三维运动目标无源定位系统中,针对在4个接收站的情况下搜索法实时性低的问题,提出了一种基于改进的加权最小二乘法（MWLS）与萤火虫算法（FA）相结合的无源定位方法（MWLS-FA）。该方法的第1步通过构造一组新的方程来对加权最小二乘（WLS）方法进行改进,使得改进后的WLS方法在4站情况下也能得到目标位置和速度的初始值,第2步利用这个初始值为FA方法提供一个动态的搜索区域,同时在约束条件的添加和参数选择两个方面针对性地对FA方法做出了调整和改进。仿真结果表明,该方法在4站情况下对目标的定位精度可以达到克拉美罗下限（CRLB）,而且在实时性和抗噪性方面优于传统的搜索法,同时该方法在5站情况下的抗噪性能优于两步加权最小二乘法（TSWLS）和约束加权最小二乘（CWLS）法。     

传感器参数误差下的运动目标TDOA/FDOA无源定位算法

在运动目标无源定位系统中，许多算法的前提是精确已知传感器的位置以及速度，但实际情况下可利用的传感器的参数均会存在一些噪声扰动。针对这一问题，提出一种改进的两步加权最小二乘（TSWLS）时差（TDOA）与频差（FDOA）定位算法。该算法是一种闭式算法并且分为2步。第1步与经典的两步加权最小二乘算法相同，第2步进一步研究了额外变量与目标参数之间的关系并且建立了新的矩阵方程。随后，利用加权最小二乘技术给出了最终解。理论分析证明了在测量噪声较小时该算法能够达到克拉美罗界（CRLB）。所提算法具有计算复杂度低，实时性高的优点；另外，经过适当的维度调整，该算法同样适用于对多非相交源进行定位求解。计算机仿真进一步证明了理论分析的正确性。     

基于定位误差修正的运动目标TDOA/FDOA无源定位方法

针对时差(TDOA)、频差(FDOA)无源定位的两步加权最小二乘(TSWLS)方法定位均方根误差(RMSE)和定位偏差适应测量噪声能力差的问题,在分析了影响两步法定位性能的因素基础上提出一种基于一阶泰勒级数展开的定位误差修正方法。该方法的第1步和两步法相同;其第2步避免了两步法第2步中引入估计偏差的平方运算,利用一阶泰勒级数展开得到第1步定位误差的线性最小均方估计,修正第1步定位结果得到目标位置和速度的最终估计,从理论上证明了该方法可以达到定位的克拉美罗下限(CRLB)。计算机仿真对比了新方法和TSWLS方法、基于泰勒级数(TS)展开的迭代极大似然(ML)方法以及约束总体最小二乘(CTLS)方法的定位性能,新算法复杂度和两步法相当,且均方误差和定位偏差低于两步法、泰勒级数法和CTLS方法。     

WGS-84模型下时差频差半定规划定位算法

利用多颗卫星的时差频差对辐射源进行位置和速度的测量,其本质意义上是一个含有噪声项的高度非线性方程组求解问题,针对地面目标而言,可以采用基于WGS-84地球模型作为目标位置和速度约束,更进一步的增加了定位系统的复杂性。提出了一种基于半定规划(SDP)的定位解算法,将非线性方程求解问题通过适当的松弛,转化为半定优化(SDO)的问题,借助于业界较为成熟的CVX等优化软件进行定位求解,并研究了该模型条件下的克拉美罗下界(CRLB)。仿真结果表明,该算法能够较好地逼近克拉美罗下界。     

一种基于观测站数目最小化的TDOA/FDOA无源定位算法

在三维（3D）运动目标无源定位系统中,无模糊定位最少需要4个观测站。而传统的两步加权最小二乘（TSWLS）及其改进的闭式算法至少需要5个观测站进行求解,当减少一个观测站时,这些闭式算法往往无法提供可靠解。针对这一问题,提出一种最小化观测站数目的到达时间差（TDOA）与到达频率差（FDOA）定位算法。该算法是一种闭式解法并且能够在三维场景下仅使用4个观测站进行定位。该算法分为两步：第1步分离传统的TSWLS算法中未知参数空间,建立了一组新的等式,并且利用加权最小二乘（WLS）算法得到目标位置与速度的初始值;第2步利用泰勒级数展开算法将中间变量线性化,对目标位置和速度初始值进一步校正。理论分析证明了在适当的噪声水平下该算法能够达到克拉美罗界（CRLB）。此外,计算机仿真表明仅使用4个观测站时,该算法对于近场以及远场目标参数的估计精度在测量噪声较小时可以实现CRLB;并且还表明使用5个观测站估计时,该算法比TSWLS及其改进算法能更好地适应大的测量噪声。     

基于频率补偿的时延估计方法

无源时差定位中,当目标处于运动状态时,多普勒频率的存在将导致时延差估计精度变差。自相关法和互相关法相结合的多普勒频差估计方法可以获得可靠性较高、估计精度较好的频差估计结果。对该结果进行频差补偿后,采用基于相位谱的时延估计方法获得两信号间的时延差。经过仿真验证,这种基于频差补偿的时延估计方法可以有效降低多普勒频差对时延差估计精度的影响。     

Emitter Location Accuracy Using TDOA and Differential Doppler

Two methods for locating a radio or sonar transmitter are briefly described: time difference of arrival (TDOA). d differential Doppler. Two formulas are derived which relate the accuracy of the time and frequency measurements the ?one-sigma widths? of the lines of constant TDOA onstant differential Doppler on the surface of the FDOA.     

传感器位置误差条件下仅用到达频率差的无源定位性能分析

传感器自身的位置误差对辐射源的无源定位精度可能有较大影响,详细分析并推导了在存在传感器位置误差条件下,仅使用到达频率差(FDOA)参数对辐射源定位时,定位精度的克拉美罗下限(CRLB)和均方误差(MSE).在传感器位置误差条件下,提出仅用FDOA来同时估计辐射源和传感器位置的泰勒级数方法,并证明该定位方法理论上的MSE...     

Geolocation of a known altitude object from TDOA and FDOA measurements

Most satellite systems for locating an object on Earth use only time difference of arrival (TDOA) measurements. When there are relative motions between an emitter and receivers, frequency difference of arrival (FDOA) measurements can be used as well. Often, the altitude of an object is known (it is zero, for example) or can be measured with an altimeter. Two sets of geolocation solutions are proposed which exploit the altitude constraint to improve the localization accuracy. One is for TDOAs alone and the other for the combination of TDOA and FDOA measurements. The additional complexity by imposing the constraint is a one-dimensional Newton's search and the rooting of a polynomial. The covariance matrices of the new estimators are derived under a small measurement noise assumption and shown to attain the constrained Cramer-Rao lower bound (CRLB). When there is a bias error in the assumed altitude, using the altitude constraint will introduce a bias to the solution. Since applying the constraint decreases the variance, there is a tradeoff between variance and bias in the mean square error (MSE). The maximum allowable altitude error such that the constraint solution will remain superior to the unconstraint is given. Simulation results are included to corroborate the theoretical development.     

基于CDMA蜂窝网的飞行器三维定位算法

针对中低空飞行器提出了一种将码分多址(CDMA)蜂窝网导频信号被动定位与惯性导航系统进行组合的导航定位方法。该定位方法是根据CDMA蜂窝网导频信号的到达时差（TDOA）进行两次加权最小二乘解算,并利用飞行器惯性组合的原始信息进行解模糊,从而实现中低空飞行器的三维实时定位。蒙特卡罗仿真证明：在高斯白噪声条件下,该算法运算速度快,精度高,其均方误差逼近克拉美罗下界（CRLB）,为组合导航实时性要求提供了理论参考。     

去中心化时差频差直接定位方法

针对原始利用时差频差的直接定位(DPD)方法存在数据传输量和计算量大的瓶颈,提出了两种去中心化直接定位方法。第1种方法采用去中心化配对方案,只将各观测站截获信号在站间进行一次传输,将数据传输和计算分散到各观测站间并行计算互模糊函数(CAF),构造仅满足满秩条件的互模糊矩阵(CAM)。第2种方法根据推导的任意互模糊函数间关系公式,采用归约方式去中心化的在各观测站并行计算余下互模糊函数,补全互模糊矩阵。两种方法都降低了直接定位数据传输量,提高了计算效率。性能分析和仿真实验表明本文两种方法精度性能优于两步定位方法,在低信噪比时两种方法都可达到比较理想的精度性能,在高信噪比时第2种方法与原始直接定位方法的精度性能相当。     

A Linear-correction Least-squares Approach for Geolocation Using FDOA Measurements Only

  A linear-correction least-squares(LCLS) estimation procedure is proposed for geolocation using frequency difference of arrival (FDOA) measurements only. We first analyze the measurements of FDOA, and further derive the Cram閞-Rao lower bound (CRLB) of geolocation using FDOA measurements. For the localization model is a nonlinear least squares(LS) estimator with a nonlinear constrained, a linearizing method is used to convert the model to a linear least squares estimator with a nonlinear constrained. The Gauss-Newton iteration method is developed to conquer the source localization problem. From the analysis of solving Lagrange multiplier, the algorithm is a generalization of linear-correction least squares estimation procedure under the condition of geolocation using FDOA measurements only. The algorithm is compared with common least squares estimation. Comparisons of their estimation accuracy and the CRLB are made, and the proposed method attains the CRLB. Simulation results are included to corroborate the theoretical development.     

Approximate Maximum Likelihood Algorithm for Moving Source Localization Using TDOA and FDOA Measurements

 A closed-form approximate maximum likelihood (AML) algorithm for estimating the position and velocity of a moving source is proposed by utilizing the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements of a signal received at a number of receivers. The maximum likelihood (ML) technique is a powerful tool to solve this problem. But a direct approach that uses the ML estimator to solve the localization problem is exhaustive search in the solution space, and it is very computationally expensive, and prohibits real-time processing. On the basis of ML function, a closed-form approximate solution to the ML equations can be obtained, which can allow real-time implementation as well as global convergence. Simulation results show that the proposed estimator achieves better performance than the two-step weighted least squares (WLS) approach, which makes it possible to attain the Cram閞-Rao lower bound (CRLB) at a sufficiently high noise level before the threshold effect occurs.     

诱偏信号对时差定位精度的影响分析

从装备面临的实际战场情况出发,在分析时差定位原理和雷达诱偏合成信号特性的基础上,分析了时差定位系统在存在诱偏信号情况下的侦收信号情况,对相关处理后的时差输出进行了建模和仿真研究,并分析了诱偏信号对时差定位系统精度的影响原因。针对三站时差定位系统和三点源诱偏系统,对典型态势下由诱偏信号引入的定位误差进行了仿真计算,得到了诱偏信号引入的误差分布情况和规律。     

传感器位置误差条件下的约束总体最小二乘时差定位算法

 现代定位系统中,传感器往往被安放在运动平台上,其位置无法精确得知,存在估计误差,将严重影响对目标的定位精度。针对这一问题,提出基于约束总体最小二乘(CTLS)的到达时差(TDOA)定位算法。首先通过引入中间变量,将非线性TDOA定位方程转化为伪线性方程,再利用CTLS技术,全面考虑伪线性方程所有系数中的噪声。在此基础上推导了定位方程的目标函数,再根据牛顿迭代方法,进行数值迭代,快速得到精确解。采用一阶小噪声扰动分析方法,对该算法的理论性能进行了分析,证明了算法的无偏性和逼近克拉美-罗下限(CRLB)。仿真实验表明,该算法克服了现有总体最小二乘(TLS)算法不能达到CRLB、两步加权最小二乘(two-step WLS)算法在较高噪声时性能发散的缺陷,在较高噪声时定位精度仍然能达到CRLB。     

基于最大似然估计的TDOA/FDOA无源定位偏差补偿算法

在到达时差/到达频差(TDOA/FDOA)无源定位系统中,定位问题的非线性使得定位的结果存在偏差,特别是在噪声较大或者接收站布站不合理的情况下,定位的偏差尤其显著。针对这一问题,提出了一种基于最大似然估计的偏差补偿算法。该方法分为3步:首先,利用最大似然估计器对目标的位置和速度进行求解;其次,通过利用目标定位的估计值和含噪的测量值,对目标的位置和速度偏差值进行理论分析和推导;最后,将最大似然估计解减去理论偏差值,得到经过偏差补偿的新的目标定位解。理论分析和实验仿真证明,在一定噪声的情况下,所推导的目标位置和速度的理论偏差值与实际偏差值相符,并且经过偏差补偿后的定位算法,在保持目标定位的均方根误差(RMSE)与原最大似然算法一致的情况下,目标的位置和速度偏差值远远小于原最大似然算法的偏差值,目标定位精度得到了有效的提高。     

Arrival Time Estimation by Adaptive Thresholding

Arrival time estimation by adaptive thresholding is described. The probability density of arrival time is derived for differentiable Markov processes. The special case of additive, stationary noise is given particular attention. A direct derivation of the probability density of arrival time for pulses with sharply rising edges is given for arbitrary noise. The results are applied to the Gaussian and Rice distributions. Comparison with the Cramer-Rao bound of estimation theory indicates the asymptotic optimality of adaptive thresholding in the latter two cases.     

Accurate single-observer passive coherent location estimation based on TDOA and DOA

This paper investigates the problem of target position estimation with a single-observer passive coherent location(PCL) system. An approach that combines angle with time difference of arrival(ATDOA) is used to estimate the location of a target. Compared with the TDOA-only method which needs two steps, the proposed method estimates the target position more directly. The constrained total least squares(CTLS) technique is applied in this approach. It achieves the Cramer–Rao lower bound(CRLB) when the parameter measurements are subject to small Gaussian-distributed errors. Performance analysis and the CRLB of this approach are also studied. Theory verifies that the ATDOA method gets a lower CRLB than the TDOA-only method with the same TDOA measuring error. It can also be seen that the position of the target affects estimating precision.At the same time, the locations of transmitters affect the precision and its gradient direction.Compared with the TDOA, the ATDOA method can obtain more precise target position estimation.Furthermore, the proposed method accomplishes target position estimation with a single transmitter,while the TDOA-only method needs at least four transmitters to get the target position. Furthermore,the transmitters' position errors also affect precision of estimation regularly.