Emitter localization using clustering-based bearing association

A closed-form emitter location estimator using time difference of arrival (TDOA) measurements is developed based on triangulation of hyperbolic asymptotes. The problem of associating the asymptotes with the emitter is solved by clustering the bearing angles of the linear asymptotes using a kernel density estimate. A closed-form estimate of the emitter location is obtained from triangulation of the clustered bearings using a weighted version of the pseudolinear estimator. By way of simulation examples, the proposed closed-form estimator is shown to outperform the computationally demanding and divergence-prone maximum likelihood (ML) estimator at moderate TDOA noise levels.     

基于短时时差序列的无源定位方法

针对脉冲辐射源定位问题,提出了一种基于短时时差(TDOA)序列的多站无源定位新方法.首先建立了TDoA序列模型,然后推导了该方法定位误差的克拉美罗下限(CRLB),并提出了一种高效的解算方法--两步定位法(TSLM):第1步利用TDOA序列线性估计出TDOA及其变化率信息,第2步基于TDOA及其变化率信息进行定位.典型...     

存在观测站位置误差的转发式时差无源定位

无源定位中,由于观测站安放在运动平台等原因造成的观测站位置误差会影响无源定位精度性能。另外到达时间差(简称时差)(TDOA)的转发式测量需要将不同观测站截获到的辐射源信号都转发到同一位置,如主观测站。针对这两个问题,提出了基于约束总体最小二乘(CTLS)的无源定位算法。首先将转发式时差的非线性定位方程转化为不需要中间变量的直接线性方程,再基于CTLS算法依次转化为约束优化问题和无约束优化问题,最后推导给出定位近似闭式解。仿真实验表明在观测站误差较大时,该算法与其他算法相比定位精度性能较好。     

一种基于概率的双星无源定位算法

针对双星无源定位系统采用时差、频差对地面固定辐射源进行无源定位的问题,提出了一种基于概率的双星无源定位算法。通过公式推导,将复杂的定位方程组化简为简单的二元一次方程组。在介绍定位原理的基础上对该算法进行仿真,通过仿真,分析了定位误差与时差测量精度、频差测量精度的关系。     

Least squares range difference location

An array of n sensors at known locations receives the signal from an emitter whose location is desired. By measuring the time differences of arrival (TDOAs) between pairs of sensors, the range differences (RDs) are available and it becomes possible to compute the emitter location. Traditionally geometric solutions have been based on intersections of hyperbolic lines of position (LOPs). Each measured TDOA provides one hyperbolic LOP. In the absence of measurement noise, the RDs taken around any closed circuit of sensors add to zero. A bivector is introduced from exterior algebra such that when noise is present, the measured bivector of RDs is generally infeasible in that there does not correspond any actual emitter position exhibiting them. A circuital sum trivector is also introduced to represent the infeasibility; a null trivector implies a feasible RD bivector. A 2-step RD Emitter Location algorithm is proposed which exploits this implicit structure. Given the observed noisy RD bivector Δ, (1) calculate the nearest feasible RD bivector Δˆ, and (2) calculate the nearest point to the ( ₃ⁿ) planes of position, one for each of the triads of elements of Δˆ. Both algorithmic steps are least squares (LS) and finite. Numerical comparisons in simulation show a substantial improvement in location error variances     

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。     

Coarse quantization for data compression in coherent location systems

When emitter location systems measure time-difference-of-arrival (TDOA) and differential Doppler (DD) by coherently cross-correlating the signal pairs, data compression techniques are needed to facilitate data transfer of one of the signals to the receiving site of the other signal. Two block-adaptive quantization schemes are analyzed here to determine their impact on the signal-to-noise ratio (SNR) of the quantized signal as well as on the post-correlation SNR. Comparisons are made between two approaches: quantization of the real/imaginary (R/I) components or the magnitude/phase (M/P) components. For the M/P approach, a rule is derived for optimally allocating the bits between the magnitude and phase. The M/P approach provides better post-quantization/precorrelation SNR for most signals; however, when the SNR of the signal not being quantized is small, the post-correlation SNR can be largely unaffected by the quantization. In that case, there is little difference between R/I and M/P, even under the most favorable scenario for M/P.     

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。     

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.     

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。     

基于星间激光测距的三星时差定位系统标校方法

利用精确的星间激光测距信息,提出了基于星间测距的三星时差定位系统标校方法。该方法消除了副星相对位置系统误差对定位精度的影响,同时提出了副星相对位置系统误差的解析解法,建立了模型误差和对副星相对位置系统误差进行估算的误差的定量关系,并证实了基于星间激光测距的标校方法可以在较大范围内提高定位精度。     

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。     

Aperture error mitigation via local-state estimation for frequency-based emitter location

This paper considers the problem of locating a stationary coherent emitter via a single moving platform making frequency measurements in the presence of aperture state uncertainty. It is shown that the estimated emitter location is most sensitive to the receiving aperture velocity uncertainty. The required aperture velocity accuracy is determined through a noninfinitesimal perturbation analysis. A solution to location accuracy enhancement with a minimal hardware addition is attempted. It is shown that this can be achieved by mounting a high-resolution tri-axis microelectromechanical systems (MEMS) accelerometer at the aperture to measure its velocity, which can deviate significantly from that estimated by the on-board navigation system. The Doppler shifts of the GPS signal carrier frequency, whenever it can be acquired through the aperture, are also considered as a way to aid the aperture velocity measurement. A decentralized, federated processing method for the aperture velocity estimate referenced at the aperture, integrating all measurement data, is presented. An upper bound for the error of aperture velocity estimate is derived. The potential for significant accuracy enhancement for emitter location is demonstrated.     

基于两步最小二乘定位的偏差改进算法

针对传统最小二乘(LS)定位算法在噪声较大时会出现有偏估计的问题。首先详细推导了传统两步最小二乘算法在时差角度联合定位场景下的理论偏差,给出了出现偏差的原因;其次对误差均值加入二次约束条件,提出一种基于时差角度联合定位的改进算法,并详细推导新算法的理论偏差以及均方误差。相比于其他加限制条件的方法,新算法能有效降低估计偏差,另外由于其不需要进行特征值分解且能得到闭式解,计算复杂度较小。仿真结果表明,新算法在保持原有均方误差(MSE)的前提下能显著降低估计偏差,其定位偏差与最大似然估计器相当。     

Solution and performance analysis of geolocation by TDOA

One method of geolocation is based on measuring the time difference of arrivals (TDOAs) of a signal received by three or four geostationary satellites. The received signals are cross-correlated to determine the TDOAs and a set of nonlinear equations are solved to produce the location estimate. An exact solution for the transmitter position is derived for the three or four receiver cases. Extension of the solution method to more receivers is straightforward. An analysis of the performance of the system is given, together with expressions for predicting the localization mean-square errors (MSEs) and bias, and the Cramer-Rao bound. Both precision in TDOA measurements and the relative geometry between receivers and transmitter affect the localization accuracy. The geometric factors act as multipliers to the TDOA variance in the bias and MSE formulae. A study of the dependency of the geometric factors on transmitter position and satellite spacings are provided, as well as simulation results     

基于圆形轨道的卫星位置递推方法

卫星无源定位系统对目标进行定位时,用于定位的卫星位置与时差或相位差等信息可能不同步,无法进行定位,需要把定位信息统一到同一时刻。针对这一问题,提出了基于圆形轨道的卫星位置递推方法,把卫星位置信息同其它信息统一到同一时刻,然后进行定位。该方法比常用的直线轨道递推方法误差更小,准确度更高,对提高定位精度具有较大应用价值。     

一种多点定位的目标位置精确解算方法

多点定位是民航飞机导航系统的新技术,精确的目标位置解算方法是多点定位的关键.通过设定参考站和变换,将非线性到达时间(TOA)方程组转化为线性到在时间差(TDOA)方程组,提出了一种两步求解目标位置的闭式算法.首先忽略TDOA测量误差,获得了目标位置的粗解,在粗解的基础上做泰勒级数展开,克服了未知量不独立对精度的影响,再...     

利用不机动单站DOA、TOA的测量实现被动定位与跟踪

 可以利用多个被动探测器或单个机动的探测器实现对运动辐射源的被动定位与跟踪。本文介绍的是一种利用非机动的单个探测器所获得的DOATOA测量值,对运动辐射源实现被动定位与跟踪的新方法。在二维平面内对运动辐射源使用这种方法,通过计算机仿真显示可以获得收敛而精确的跟踪数据。     

双平台交叉定位去除虚假点方法研究

针对测向交叉定位方法在多辐射目标源的情况下存在的虚假定位,提出了一种去除虚假点的新方法——结合时差去除法。该方法通过计算双平台间测量数据的相近度来进行最优匹配,去除虚假定位。该方法无需先验信息,只需两个测量平台,降低了平台间数据传输和时间同步的复杂性。仿真结果表明,该方法运算速度快,对水平编队目标群定位精度高。     

A new method for finding electromagnetic emitter location

The position of a source of radiation is often obtained from bearing data, taken over an interval of time, and combining it with navigation data. A new method using total least squares (TLS) has been suggested for the accurate estimation of an emitter location when bearing observation errors are random. Further, an iterative two-stage approach involving TLS and Kalman filtering is developed for accurate estimation of the emitter location when bearing observation errors are an algebraic sum of random and systematic errors. The elegance and efficacy of the proposed methods are illustrated through digital computer simulated examples