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。     

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...     

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

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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。     

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。     

Closed form algorithm of double-satellite TDOA+AOA localization based on WGS-84 model

In this paper, we consider the double-satellite localization under the earth ellipsoid model of the Wideband Geodetic System(WGS-84) using the Time Difference of Arrival(TDOA)and the Angle-of-Arrival(AOA).Several closed-form solution algorithms via the pseudolinearization of the measurement equations are presented to efficiently estimate the location.These algorithms include the Weighted Least Squares(WLS), the Constrained Total Least Squares(CTLS), and the Taylor-Series Iteration(TSI).Performance comparison of the proposed methods with the Cramér-Rao Lower Bound(CRLB) in the simulation is shown to demonstrate that the proposed algorithms are feasible and have stable performance.     

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.     

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.     

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。     

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.     

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。     

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...     

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     

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.     

Position Location: Triangulation Versus Circulation

Position location algorithms, using data from electronic surveillance systems have, for the most part, been based upon statistical analysis of the points of intersection of the lines of bearing. These triangulation ion algorithms may well minimize the effect of random measurement errors on the location estimate, but few existing algorithms account for systematic (bias) errors. An algorithm based upon intersecting circles which eliminates certain types of systematic error is presented with simulation data utilized to compare the position location estimates obtained from both triangulation and circulation algorithms.     

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。     

Direction finding with a four-element Adcock-Butler matrix antennaarray

The conventional analog Adcock-Butler matrix (ABM) antenna array direction finder suffers from systemic errors, component matching problems, and bandwidth limitations. Three digital bearing estimators are developed as candidates to replace the analog signal processing portion of the ABM. Using the same antenna array, they perform all signal processing in the frequency domain, thereby benefitting from the computational efficiency of the fast Fourier transform (FFT) algorithm. The first estimator requires two analog-to-digital converters (A-D) and three antenna elements. It multiplies the difference between the discrete Fourier transforms (DFTs) of the output signals from two antenna elements with that from a third antenna element. At each frequency component, the phase of this product is a function of the bearing. A weighted least squares (LS) fit through all the phase components then gives a bearing estimate. The second estimator is similar to the first but uses three A-D and all four antenna elements. The output signal from the additional antenna element provides an independent estimate of the weights for the LS fit, giving an improvement in accuracy. The third estimator applies the physical constraint existing between the time-difference-of-arrival (TDOA) of a signal intercepted by two perpendicular sets of antenna elements. This yields a better estimator than simple averaging of the bearing from each set of antenna elements. The simulation studies used sinusoids and broadband signals to corroborate the theoretical treatment and demonstrate the accuracy achievable with these estimators. All three direction finders have superior performance in comparison with the analog ABM     

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。     

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