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...     

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...     

Moving scanning emitter tracking by a single observer using time of interception: Observability analysis and algorithm

The target motion analysis (TMA) for a moving scanning emitter with known fixed scan rate by a single observer using the time of interception (TOI) measurements only is investigated in this paper.By transforming the TOI of multiple scan cycles into the direction difference of arrival (DDOA) model,the observability analysis for the TMA problem is performed.Some necessary conditions for uniquely identifying the scanning emitter trajectory are obtained.This paper also proposes a weighted instrumental variable (WIV) estimator for the scanning emitter TMA,which does not require any initial solution guess and is closed-form and computationally attractive.More importantly,simulations show that the proposed algorithm can provide estimation mean square error close to the Cramer-Rao lower bound (CRLB) at moderate noise levels with significantly lower estimation bias than the conventional pseudo-linear least square (PLS) estimator.     

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。     

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.     

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.     

A closed-form solution for moving source localization using LBI changing rate of phase difference only

Due to the deficiencies in the conventional multiple-receiver localization systems based on direction of arrival(DOA) such as system complexity of interferometer or array and amplitude/phase unbalance between multiple receiving channels and constraint on antenna configuration,a new radiated source localization method using the changing rate of phase difference(CRPD)measured by a long baseline interferometer(LBI) only is studied. To solve the strictly nonlinear problem, a two-stage closed-form solution is proposed. In the first stage, the DOA and its changing rate are estimated from the CRPD of each observer by the pseudolinear least square(PLS) method,and then in the second stage, the source position and velocity are found by another PLS minimization. The bias of the algorithm caused by the correlation between the measurement matrix and the noise in the second stage is analyzed. To reduce this bias, an instrumental variable(IV) method is derived. A weighted IV estimator is given in order to reduce the estimation variance. The proposed method does not need any initial guess and the computation is small. The Cramer–Rao lower bound(CRLB) and mean square error(MSE) are also analyzed. Simulation results show that the proposed method can be close to the CRLB with moderate Gaussian measurement noise.     

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。     

Passive localization of moving emitters using out-of-planemultipath

The purpose of this work is to establish how a moving emitter, such as a jammer, can be localized by a passive receiver through the use of out-of-plane multipath signals reflected by the terrain. This is a novel localization technique that assumes no a priori knowledge of the localization of the multipath sources. The emitter parameters of range, heading, velocity, and altitude are estimated by exploiting the correlation between the direct-path signal and the delayed and Doppler modulated signals. Two basis assumptions about the scattering properties of the terrain lead to different maximum likelihood estimators (MLEs). The Cramer-Rao lower bounds (CRLB) are used to study estimator performance versus emitter velocity for each case. The proposed estimators are successfully demonstrated using field data collected at White Sands Missile Range (WSMR) during the DARPA/Navy Mountaintop program     

仅用相位差变化率的机载单站无源定位方法及其误差分析

针对以往单站无源定位系统中长短基线干涉仪系统复杂、角度测量易受干涉仪通道幅度/相位不一致的影响等问题,提出了一种仅仅利用长基线干涉仪(LBI)的相位差变化率实现单站无源定位的新方法,并对该定位方法误差的克拉美-罗下限(CRLB)进行了推导和分析,计算并分析了不同的干涉仪基线安装方向、不同的观测器运动方式下的定位误差几何分布(GDOP)。结果表明,仅用相位差变化率定位时,为了达到侧翼最好精度,干涉仪最好平行机身安装;为了达到侧前方较好精度,干涉仪需垂直安装;观测器的运动姿态最好发生某种机动变化。     

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。     

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。     

Algebraic two-satellite TOA/FOA position solution on an ellipsoidal Earth

A direct algebraic solution is given for estimates of the ambiguous locations of an RF emitter on the surface of an ellipsoidal Earth given time-of-arrival (TOA) and frequency-of-arrival (FOA) measurements at two satellites.     

Moving target localization in distributed MIMO radar with transmitter and receiver location uncertainties

In this paper, the problem of moving target localization from Bistatic Range(BR) and Bistatic Range Rate(BRR) measurements in a Multiple-Input Multiple-Output(MIMO) radar system having widely separated antennas is investigated. We consider a practically motivated scenario,where the accurate knowledge of transmitter and receiver locations is not known and only the nominal values are available for processing. With the transmitter and receiver location uncertainties,which are usually neglected in MIMO radar systems by prior studies, taken into account in the measurement model, we develop a novel algebraic solution to reduce the estimation error for moving target localization. The proposed algorithm is based on the pseudolinear set of equations and two-step weighted least squares estimation. The Cramer-Rao Lower Bound(CRLB) is derived in the presence of transmitter and receiver location uncertainties. Theoretical accuracy analysis demonstrates that the proposed solution attains the CRLB, and numerical examples show that the proposed solution achieves significant performance improvement over the existing algorithms.     

Performance of a Square Law Pseudonoise Ranging Time-of-Arrival Estimator

The performance of a square law time-of-arrival (TOA) estimator that has been proposed for use in ASTRO-DABS, part of a possible satellite-based fourth generation air traffic control system is considered. The transmitted message consists of a pulse amplitude modulated (PAM) ranging sequence that, due to transmitter characteristics, is corrupted by an unknown frequency offset. The optimum TOA estimator, for the case of no frequency uncertainty, is first presented, together with a lower bound on the variance of the estimate generated. This is followed by the consideration of a suboptimum TOA estimator for which a high signal-to-noise ratio (SNR) performance analysis is carried out; here, the effects of frequency uncertainty are included. Next, the zero-crossing properties of the derivative of the (suboptimum) estimation statistic are presented and the results used to derive an upper bound to the TOA estimate variance that is valid for all SNR values. This latter result is significant because it displays the system threshold effect and complements performance lower bounds that may be derived via other methods. In addition, the method presented here may be applied to other optimum and suboptimum systems where a discrete set of parameters is to be estimated.     

机载单站无源定位系统中相位差变化率提取方法(英文)

相位差变化率含有目标辐射源的距离信息,是机载单站无源定位系统中的重要参数。本文以正弦单载波脉冲信号为例,分析了基于相位差变化率的单站无源定位原理,以及测量误差的组成。基于对Cramer-Rao下限的分析,提出了一种基于多次观测的相位差变化率的高精度测量方法——时间片处理法。在相位差变化率的测量中,当信噪比较低时,频域鉴相方法优于时域鉴相方法,多时间片处理能够显著地降低测量方差,仿真验证了此算法的正确性和有效性。典型的无源定位场景的仿真验证了算法对动态测量的适应性。此测量算法简单、计算量小,易于实现。     

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.     

A novel pulse TOA analysis technique for radar identification

A new processing technique is presented for identifying individual pulse trains in a buffer load of pulse time-of-arrival (TOA) data from radar warning receiver sets currently in use for electronic warfare (EW). The method is based on the numerical characteristics of the matrix of the differences of the TOA data points. In particular, for a uniform pulse repetition interval (PRI) emitter, this matrix is a symmetrical harmonic Toeplitz matrix the inverse of which has banded tridiagonal form. This form leads to an estimator for the PRI in terms of the trace of the inverted matrix     

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

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Low observable target motion analysis using amplitude information

In conventional passive and active sonar system, target amplitude information (AI) at the output of the signal processor is used only to declare detections and provide measurements. We show that the AI can be used in passive sonar system, with or without frequency measurements, in the estimation process itself to enhance the performance in the presence of clutter where the target-originated measurements cannot be identified with certainty, i.e., for “low observable” or “dim” (low signal-to-noise ratio (SNR)) targets. A probabilistic data association (PDA) based maximum likelihood (ML) estimator for target motion analysis (TMA) that uses amplitude information is derived. A track formation algorithm and the Cramer-Rao lower bound (CRLB) in the presence of false measurements, which is met by the estimator even under low SNR conditions, are also given. The CRLB is met by the proposed estimator even at 6 dB in a cell (which corresponds to 0 dB for 1 Hz bandwidth in the case of a 0.25 Hz frequency cell) whereas the estimator without AI works only down to 9 dB. Results demonstrate improved accuracy and superior global convergence when compared with the estimator without AI. The same methodology can be used for bistatic radar