Analysis of single-platform passive emitter location with terraindata

Frequency measurements made at a moving platform can be used to locate an emitter. An error ellipsoid analysis is used to compare the performance under three levels of a priori information on the emitter's altitude: (1) no knowledge, (2) terrain data, and (3) complete knowledge of the emitter's altitude. The analysis is performed for two simple platform paths that provide frequency measurements that are approximately time reversed versions of one another. When no a priori knowledge is available there is little difference between the performance when the platform maneuvers on a concave circular path or on a convex circular path and the performance depends very Little on the platform altitude. However, when some a priori altitude information is available the performance is markedly different on the two paths and is highly dependent on the platform altitude. Thus, this analysis provides the unexpected result that for seemingly similar platform paths, the performance can vary markedly when the emitter altitude is assumed known. Also, an interesting result is that for some cases it is possible to achieve better x-y accuracy when using terrain data than when the emitter's z location is known, because the terrain data provides terrain slope information. These cases are characterized in terms of the terrain slope at the emitter     

差分卫星导航系统定位精度飞行测试方法

针对机载差分卫星导航系统的定位误差特性,提出一种考核机载差分卫星导航系统定位精度的飞行测试方法。在事后数据处理过程中,由于两部卫星接收天线之间安装位置不同而导致的杆臂效应会使最终结果产生较大的计算误差,故提出了一种基于消除杆臂的数据处理方法。通过以上飞行测试方法和数据处理方法可以有效地评估机载差分卫星导航系统的定位精度。     

Moving Emitter Classification

One of the problems that plague emitter location systems is the presence of data from emitters that are in motion. If this motion is not detected, erroneous location estimates and filled data files result. An algorithm to classify an emitter as moving or stationary is presented along with extensive illustrations and results based upon simulated data.     

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。     

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.     

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     

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...     

Determination of ground emitter location

Passive techniques to locate ground emitters from an airborne platform provide threat warning to aircraft in hostile airspace while maintaining the electronic silence of the vehicle. These techniques are based on triangulation methods and extended Kalman filters, using only hearing measurements. An approach that takes into consideration the maximum measurement error of the sensor and approximates an area of uncertainty of the emitter location by polygons is proposed. The performance of this algorithm is demonstrated by simulation results, and an example is shown for the comparison of this algorithm and the extended Kalman filter approach     

PASSIVE LOCATION AND ACCURACY ANALYSIS USING TDOA INFORMATION OF MULTI-STATIONS

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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...     

对卫星目标的仅测角天基单站无源定位可观测性分析

可观测性分析是无源定位与跟踪系统的前提和基础。由于卫星运动系统方程是状态变量的隐函数形式,以及观测方程的非线性,使得对卫星目标仅测角无源定位的可观测性研究难度较大。鉴于此,从伪线性化角度对非线性系统方程进行改造,推导了关于状态变量的显性系统状态方程,对仅测角条件下的单星对星无源定位系统进行了可观测性分析,为进一步研究仅测角单星对星的无源定轨跟踪提供了理论基础。最后给出了仿真实例,验证了理论分析的正确性。     

北斗单点定位的误差补偿方法

北斗是我国自主研制的卫星导航定位系统,当前北斗的单点定位精度优于10m。为提高该系统的定位精度,必须对由其误差源引起的定位误差进行修正。基于对北斗卫星导航系统的组成、定位算法及定位误差的认识,对导航系统定位中星历误差、电离层误差和对流层误差进行了深入分析,提出了减小星历误差的曲面模型、减小电离层误差的双频组合消电离层模型和减小对流层误差的高精度区域融合模型的单点定位误差补偿方法,并应用Matlab软件对修正模型方法进行仿真计算。对比修正前后的定位结果,修正后的定位误差更小,证明了所提出的修正模型是可行的。     

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     

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。     

A Hybrid Navigation Concept Using a Spinning Satellite?Borne Interferometer and Self?Contained Equipment

This paper analyzes a hybrid navigation concept that uses signals from a radio interferometer mounted on a spinning geostationary satellite, preliminary position estimates from self-contained equipment, and stored a priori information on the past performance of this equipment. The craft-borne processor, optimum in the maximum a posteriori (MAP) sense, is designed to estimate position coordinates using only the incoming radio signals, although improved estimates result if the other two items are available. An error analysis starts with the derivation of an estimation error covariance matrix, whose elements depend on additive receiver noise and the physical parameters of the system. A minimum 1? estimation error in position is obtained by trading off these parameters. The effects of other major error sources, such as tropospheric phase fluctuations, multipath, and craft altitude uncertainty, are added to the estimation error to give a total 1? position error on the order of 3.7 to 5.6 km.     

Error Analysis for Relay Type Satellite-Aided Search and Rescue Systems

An analysis is made of the errors in the determination of the position of an emergency transmitter in a satellite-aided search and rescue system. The satellite is assumed to be at a height of 820 km in a near-circular near polar orbit. Short data spans of four minutes or less are used. The error sources considered are measurement noise, transmitter frequency drift, ionospheric effects, and error in the assumed height of the transmitter. The errors are calculated for several different transmitter positions, data rates, and data spans. The only transmitter frequency used was 406 MHz, but the result can be scaled to different frequencies.     

无人艇集群协同定位算法误差分析

无人艇以集群方式被广泛应用于各个领域.无人艇集群完成任务的前提是获知相对的位置关系.为此,针对无人艇集群协同定位算法误差进行了全面分析.首先,给出了基于数据链协同定位原理.在此基础上,深入剖析了协同定位误差种类、特点及影响.最后,针对协同定位算法中对协同定位精度影响较大的3个因素进行了仿真分析.分析结果表明,伪距测量误...     

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.