Joint TDOA,FDOA and differential Doppler rate estimation: Method and its performance analysis

Considering the estimation accuracy reduction of Frequency Difference of Arrival(FDOA) caused by relative Doppler companding, a joint Time Difference of Arrival(TDOA),FDOA and differential Doppler rate estimation method is proposed and its Cramer-Rao low bound is derived in this paper.Firstly, second-order ambiguity function is utilized to reduce the dimensionality and estimate initial TDOA and differential Doppler rate.Secondly, the TDOA estimation is updated and FDOA is obtained using cross ambiguity function, in which relative Doppler companding is compensated by the existing differential Doppler rate.Thirdly, differential Doppler rate estimation is updated using cross estimator.Theoretical analysis on estimation variance and Cramer-Rao low bound shows that the final estimation of TDOA, FDOA and differential Doppler rate performs well at both low and high signal–noise ratio, although the initial estimation accuracy of TDOA and differential Doppler rate is relatively poor under low signal–noise ratio conditions.Simulation results finally verify the theoretical analysis and show that the proposed method can overcome relative Doppler companding problem and performs well for all TDOA, FDOA and differential Doppler rate estimation.     

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.     

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...     

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。     

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

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二阶和四阶互模糊函数在工程中的时频性能比较

利用两种方法,即模糊函数和四阶累积量模糊函数对目标的两个主要参量TDOA(time-delay of arrival)和FDOA(frequency - delay of arrival)进行理论上精确的推导和实际应用中在工程上的估计,并且指出了两种方法在理论与实际应用中所得到的两种几乎截然不同的结果,并对其加以详细的分析,阐明了这种矛盾的根源之所在,并由给出的仿真结果对上述结论加以说明.     

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。     

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。     

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。     

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.     

Satellite Broadcasting of WWV Signals

An experiment concerning the broadcasting of time and frequency information from geostationary satellites is discussed. Included are discussions on satellite motion, time delay, Doppler shift, and delay calculations. Ground station requirements, time recovery techniques, and timing resolution and accuracy are also included. Delay computation aids for the user were designed to provide free space delays between the master clock and the user. Measurements made in North and South America demonstrated a timing resolution of about 10 ?s and an accuracy of 25 ?s.     

Sensitivity analysis of dual-satellite geolocation

An analytic solution is presented for the linearized estimation problem arising from the dual-satellite geolocation of the source of a narrowband signal using time- and frequency-difference-of-arrival (TDOA and FDOA, respectively) observations and an altitude constraint. This solution is used to analyze the covariance matrix of the resultant source location estimate, along with the sensitivity of its mean to errors in the presumed source altitude and velocity, and the measured or predicted positions and velocities of the satellites. Following the practice of differential Global Positioning System, the technique of differential calibration is used to reduce or eliminate various sources of solution bias which would otherwise require tight, and consequently expensive, individual calibration     

Clutter Performance of Coherent Pulse Trains for Targets with Range Acceleration

The clutter performance of coherent pulse trains is examined when the duration of the pulse train is increased to values for which range acceleration effects must be taken into account. The problem of target detection against a clutter background with differential Doppler is studied in terms of the range acceleration effects on the conventional Doppler response. Specifically considered are the consequences on the sidelobe level and width of the main Doppler lobe. The analysis shows that the sidelobe level remains essentially unchanged when the range acceleration mismatch becomes significant. However, the main Doppler response broadens in proportion to the magnitude of the acceleration mismatch. Thus, an increase of the signal duration for better Doppler resolution is useful only until acceleration effects spread the Doppler spectrum of the clutter and eliminate the differential Doppler between targets and clutter.     

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     

Tracking Accuracies with Position and Rate Measurements

Tracking accuracies for the radial component of motion are computed for a track-while-scan radar system which obtains position and rate data during the dwell time on a target These results will be of interest to persons developing trackers for pulse Doppler surveillance radars. The normalized accuracies, computed for a two state Kalman tracking filter with white noise maneuver capability, are shown to depend upon two parameters, r = 4?0/?aT2 and s = ?dT/?0. The symbols ?0 and ?d are the position and rate measurement accuracies, respectively, ?a is the standard deviation of the white noise maneuver process and T is the antenna scan time. The scalar tracking filter equations are derived and numerical results are presented. Lower steady state tracking errors plus the earlier attainment of steady state accuracies are the direct consequence of incorporating the rate measurements into the tracking filter.     

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。     

基于角度变化率的机载多普勒直接测距方法

基于角度变化率与多普勒频差之间的关系,提出了一种机载单基线多普勒测距方法,该方法将前置角的正弦变化率引入多普勒频移方程,借助于微分变形所产生的角速度参量就能获得被测目标的距离。模拟分析验证了所导出公式的正确性,同时还分析证明了基于角度变化率的直接测距方法和基于多普勒频移变化率的直接测距方法等效,并基于频率分辨率,给出了...     

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.     

一种新的基于TDOA与GROA的无源定位算法

针对基于到达时间差(TDOA)与到达增益比(GROA)的辐射源无源定位问题,提出了一种新的定位算法。首先通过引入一个中间变量,根据TDOA和GROA测量模型,构造一个约束加权最小二乘(CWLS)估计。由于这个CWLS问题是非凸的优化问题,现有的方法不能很好地求解。为此,提出了一种有效的方法可以求解到其全局最优解。最后,所提算法被推广到观测站存在自定位误差时的定位求解。计算机仿真结果验证了所提算法能够获得优于传统两步加权最小二乘法(2WLS)的定位性能,能够在更大的噪声条件下达到克拉美罗下界(CRLB)。