Optimization of observer trajectories for bearings-only targetlocalization

The problem of bearings-only target localization is to estimate the location of a fixed target from a sequence of noisy bearing measurements. Although, in theory, this process is observable even without an observer maneuver, estimation performance (i.e., accuracy, stability and convergence rate) can be greatly enhanced by properly exploiting observer motion to increase observability. This work addresses the optimization of observer trajectories for bearings-only fixed-target localization. The approach presented herein is based on maximizing the determinant of the Fisher information matrix (FIM), subject to state constraints imposed on the observer trajectory (e.g., by the target defense system). Direct optimal control numerical schemes, including the recently introduced differential inclusion (DI) method, are used to solve the resulting optimal control problem. Computer simulations, utilizing the familiar Stansfield and maximum likelihood (ML) estimators, demonstrate the enhancement to target position estimability using the optimal observer trajectories     

Maximum likelihood angle extractor for two closely spaced targets

In a scenario of closely spaced targets special attention has to be paid to radar signal processing. We present an advanced processing technique, which uses the maximum likelihood (ML) criterion to extract from a monopulse radar separate angle measurements for unresolved targets. This processing results in a significant improvement, in terms of measurement error standard deviations, over angle estimators using the monopulse ratio. Algorithms are developed for Swerling I as well as Swerling III models of radar cross section (RCS) fluctuations. The accuracy of the results is compared with the Cramer Rao lower bound (CRLB) and also to the monopulse ratio technique. A novel technique to detect the presence of two unresolved targets is also discussed. The performance of the ML estimator was evaluated in a benchmark scenario of closely spaced targets - closer than half power beamwidth of a monopulse radar. The interacting multiple model probabilistic data association (IMMPDA) track estimator was used in conjunction with the ML angle extractor     

基于MCIS技术的相位差变化率单站无源定位

针对最大似然估计（ML）方法求解测相位差变化率单站无源定位问题计算量大、定位慢的问题,本文提出一种利用蒙特卡洛重要性抽样技术（MCIS）高精度、低复杂度的估计方法。根据Pincus定理推导出ML问题的近似全局解,利用重要性抽样（IS）技术构建符合高斯分布概率密度（PDF）的重要性函数,作为样本选取的依据,通过逆变换采样获得样本集,统计样本均值直接得到辐射源位置估计结果。MCIS方法简单易实现且运算量低,能够克服传统ML估计多维网格搜索耗时较长的缺陷,而且对目标位置初始估计误差有较低的敏感性。实验结果表明,MCIS算法在相同测量噪声水平下,定位精度优于EKF、NLS算法,有效减小了初始化估计误差对算法定位精度的影响,也进一步讨论分析了算法参数和不同观测条件对定位性能的影响。     

Accuracy of using point targets for SAR calibration

The peak and integral methods for radiometric calibration of a synthetic aperture radar (SAR) using reference point targets are analyzed. Both calibration methods are shown to be unbiased, but the peak method requires knowledge of the equivalent rectangle system resolution which is sensitive to system focus. Exact expressions for the RMS errors of both methods are derived. It is shown that the RMS error resulting from the peak method is always smaller than or equal to that from the integral method for a well-focused system. However, for robust radiometric calibration of SAR, or when nonlinear phase errors are present, the integral method is recommended, because it does not require detailed knowledge of the impulse response and the resulting RMS error is not dependent on system focus     

Angle estimation for two unresolved targets with monopulse radar

Most present-day radar systems use monopulse techniques to extract angular measurements of sunbeam accuracy. The familiar "monopulse ratio" is a very effective means to derive the angle of a single target within a radar beam. For the simultaneous estimation of the angles of two closely-spaced targets, a modification on the monopulse ratio was derived in (Blair and Pearce, 2001), while (Sinha et al., 2002) presented a maximum likelihood (ML) technique via numerical search. In this paper it is shown that the ML solution can in fact be found explicitly, and the numerical search of ((Sinha et al., 2002) is unnecessary. However, the ML solution requires the signal to noise ratio (SNR) for each target to be known, and hence we generalize it so it requires only the relative SNR. Several versions of expectation maximization (EM) joint angle estimators are also derived, these differing in the degree to which prior information on SNR and on beam pattern are assumed. The performances of the different direction-of-arrival (DOA) estimators for unresolved targets are studied via Monte Carlo, and it is found that most have similar performance: this is remarkable since the use of prior information (SNR, relative SNR, beam pattern) varies widely between them. There is, however, considerable performance variability as a function of the two targets' off-boresight angles. A simple combined technique that fuses the results from different approaches is thus proposed, and it performs well uniformly.     

Estimation techniques for GMSK using linear detectors in satellite communications

This paper describes data-aided signal level and noise variance estimators for Gaussian minimum shift keying (GMSK) when the observations are limited to the output of a filter matched to the first pulse-amplitude modulation (PAM) pulse in the equivalent PAM representation. The estimators are based on the maximum likelihood (ML) principle and assume burst-mode transmission with known timing and a block of L₀ known bits. While it is well known that ML estimators are asymptotically unbiased and efficient, the analysis quantifies the rate at which the estimators approach these asymptotic properties. It is shown that the carrier phase, amplitude, and noise variance estimators are unbiased and can achieve their corresponding Cramer-Rao bounds with modest combinations of signal-to-noise ratio and observation length. The estimates are used to estimate the signal-to-noise ratio. It is shown that the mean squared error performance of the ratio increases with signal-to-noise ratio while the mean squared error performance of the ratio in decibels decreases with signal-to-noise ratio. Simulation results are provided to confirm the accuracy of the analytic results.     

Evaluation of estimation algorithms part I: incomprehensive measures of performance

Practical metrics for performance evaluation of estimation algorithms are discussed. A variety of metrics useful for evaluating various aspects of the performance of an estimation algorithm is introduced and justified. They can be classified in two different ways: 1) absolute error measures (without a reference), relative error measures (with a reference), or frequency counts (of some events), and 2) optimistic (i.e., how good the performance is), pessimistic (i.e., how bad the performance is), or balanced (neither optimistic nor pessimistic). Pros and cons of these metrics and the widely-used RMS error are explained. The paper advocates replacing the RMS error in many cases by a measure called average Euclidean error     

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.     

An efficient method of passive emitter location

The problem of locating a stationary emitter from passive bearing and frequency measurements taken by a moving and autonomously operating sensor along its trajectory is considered. The estimation procedure based on bearings only is quite different from that based on frequency measurements. From the Cramer-Rao (CR) analysis of the single-measurement case, the characteristic features of each method become transparent and an intuitive understanding of both methods is provided. One of the major results is that the orientation of the error ellipses of the bearings method (BM) and frequency method (FM) differ significantly. From this a considerable integration gain in accuracy results, when processing the combined set of bearing and frequency measurements. The results of the theoretical CR analysis are verified in a numerical simulation based on the maximum-likelihood (ML) estimation. The simulations demonstrate that a combined method is definitely superior to BM and FM with respect to the bias and the size of the error ellipses     

A divide and conquer approach to least-squares estimation

The problem of estimating parameters &thetas; which determine the mean μ(&thetas;) of a Gaussian-distributed observation X is considered. It is noted that the maximum-likelihood (ML) estimate, in this case the least-squares estimate, has desirable statistical properties but can be difficult to compute when μ(&thetas;) is a nonlinear function of &thetas;. An estimate formed by combining ML estimates based on subsections of the data vector X is proposed as a computationally inexpensive alternative. The main result is that this alternative estimate, termed here the divide-and-conquer (DAC) estimate, has ML performance in the small-error region when X is appropriately subdivided. As an example application, an inexpensive range-difference-based position estimator is derived and shown by means of Monte-Carlo simulation to have small-error-region mean-square error equal to the Cramer-Rao lower bound     

具有通信约束的分布式SOR多智能体轨迹估计算法

针对传统多智能体轨迹估计算法信息交换量大，计算量随群规模指数增长，可扩展性差等诸多不足，提出了一种基于超松弛迭代（SOR）的分布式多智能体轨迹估计算法，通过将最大似然（ML）准则下的轨迹估计转化为两级线性优化问题，并综合利用分布式超松弛迭代（Distributed SOR）和标记初始化方法，加快求解速度并简化信息交换流程，最终实现了多智能体位姿轨迹优化和协作定位。实验表明，所提的分布式方法能达到集中式算法的精度水平，在49个智能体规模条件下，位置估计误差小于0.15 m，姿态估计误差小于0.03°，且数据交换量仅到现有主流分布式方法DDF-SAM的0.06%，能很好用于大规模集群的场景。     

基于定位误差修正的运动目标TDOA/FDOA无源定位方法

针对时差(TDOA)、频差(FDOA)无源定位的两步加权最小二乘(TSWLS)方法定位均方根误差(RMSE)和定位偏差适应测量噪声能力差的问题,在分析了影响两步法定位性能的因素基础上提出一种基于一阶泰勒级数展开的定位误差修正方法。该方法的第1步和两步法相同;其第2步避免了两步法第2步中引入估计偏差的平方运算,利用一阶泰勒级数展开得到第1步定位误差的线性最小均方估计,修正第1步定位结果得到目标位置和速度的最终估计,从理论上证明了该方法可以达到定位的克拉美罗下限(CRLB)。计算机仿真对比了新方法和TSWLS方法、基于泰勒级数(TS)展开的迭代极大似然(ML)方法以及约束总体最小二乘(CTLS)方法的定位性能,新算法复杂度和两步法相当,且均方误差和定位偏差低于两步法、泰勒级数法和CTLS方法。     

Error Reduction in HF Loop DF Systems

Techniques for reducing bearing errors in vertical loop HF direction finders for ionospherically propagated signals were evaluated in a dual-channel system. A main channel provides a bearing display from the output of a rotating loop; an auxiliary channel unblanks the bearing ng display when propagation conditions are favorable for minimum bearing error. Circuitry to provide optimum unblanking for a wide variety of signal and fade conditions is described. The results of an operational evaluation are presented and show that a large majority of the unblanked bearings can be restricted to ±15° of the great-circle bearing with average bearing errors of 10° or less. Operational comparison with a contemporary system shows that the dual-channel system performance is superior with a 2 to 1 reduction ion in bearing spreads, standard deviations, and RMS error.     

机舱内部超宽带确定性信道建模

将室内无线信道仿真中常用的几何光学和射线追踪技术,引入到对客机机舱内部的超宽带(Ultra-WideBand,UWB)信道研究当中。信道仿真的主要算法基于一种称为射线密度归一化(RayDensityNormalization,RDN)的方法。该方法使用射线密度的概念来计算每条射线对接收点处总信号强度的贡献。为了验证方法的有效性,实验构建了一个Boeing737-200客机机舱模型进行仿真。仿真将接收机设置在每个座位的顶部、扶手和底部,以研究不同水平高度信道的差别。仿真中对路径损耗和均方根(RMS)时延扩展两类大尺度信道参数进行了统计和分析,部分仿真结果与国外实测结果进行了对比。对比结果证明了仿真结果的保真度以及现有仿真工具的有效性。     

基于H∞算法的飞机机翼结冰气动参数辨识

针对国内大型飞机结冰防护需求,开展针对大型结冰研究样机的H_∞算法参数辨识结冰探测研究。首先通过参数调节选取一组合适的H_∞算法参数,利用考虑测量噪声的结冰研究样机飞行仿真数据验证H_∞算法的辨识能力,由结果对比发现辨识算法能够跟踪飞机气动导数随结冰累积过程的变化趋势,辨识精度较高,其最大归一化平方根（RMS）误差仅为真值的11%;分析了H_∞算法对81种不同结冰累积过程的辨识能力,通过结果分析发现结冰累积时间较长且结冰速度较慢的情况辨识效果较差,结冰累积时间在100~300 s之间辨识精度较高;最后利用蒙特卡罗仿真分析了不同测量噪声大小对H_∞算法辨识精度和跟踪延时的影响,给出了3个纵向气动导数在随机误差影响下的辨识误差和跟踪延时的统计结果,发现在给定噪声标准差变化范围内,升力和俯仰力矩关于迎角的导数能够得到较为准确的辨识结果,二者的归一化平方根误差均值仅为各自真值的1.8%和4%,其预报延时均值最大仅为3 s和9.5 s。     

Tilt-Table Alignment for Inertial-Platform Maintenance without a Surveyed Site

A method for aligning the rotary tilt table for an inertial-platform maintenance facility without surveying the site is analyzed and evaluated. The method utilizes multiple measurements of the tilt-table azimuth alignment error with different inertial platforms to determine a best estimate of the alignment error. Error analysis indicates that useful facility performance can be obtained with only a small number of measurements. The tilt-tablealignment accuracy can be improved as more measurements of the alignment error are made during normal facility operation.     

Refractive Errors in Angle-of-Elevation Measurements

It is shown that the errors associated with radio elevation measurements may be investigated systematically using a variational technique. The error occurring when spaced antennas are used is compared with that for a single directional antenna. Integral expressions are obtained for the refractive errors.     

Multiple radar targets estimation by exploiting induced amplitude modulation

This work deals with the problem of estimating complex amplitudes, Doppler frequencies, and directions of arrival (DOA) of multiple targets present in the same range-azimuth resolution cell of a surveillance radar. The maximum likelihood (ML) and the asymptotic (large sample size) ML (AML) estimators are derived. To reduce the computational complexity of the maximization of the nonlinear two-dimensional criterion function of the AML estimator, we propose a computationally efficient algorithm based on the RELAXation method. It allows decoupling the problem of jointly estimating the parameters of the signal components into a sequence of simpler problems, where the parameters of each component are separately and iteratively estimated. The proposed method overcomes the resolution limitation of the classical monopulse technique and resolves multiple targets exhibiting an arbitrarily small difference in azimuth as long as their Doppler frequencies differ at least by the inverse of the number of integrated pulses, provided that enough signal-to-noise ratio (SNR) per pulse is available. The performance of the proposed AML-RELAX estimator is numerically investigated through Monte Carlo simulation and Cramer-Rao lower bound (CRLB) calculation.     

轴流风扇/压气机管道周向声模态的测量

利用管道内部周向均匀分布的麦克风阵列对某单级风扇在高背景噪声和较大硬壁反射条件下的管道周向声模态进行了实验测量.利用与参考信号互相关(CC)模态分解技术和传统的方均根(RMS)模态分解技术得到了主要的周向声模态振幅.通过与Tyler和Sofrin的理论分析对比,发现在高背景噪声和较大硬壁反射条件下,两种模态分解技术都能获得较为理想的模态分解结果;并且发现CC模态分解技术获得的模态振幅较低,初步分析这是由于和RMS模态分解技术相比,CC模态分解技术可以降低随机噪声对模态振幅分解结果的影响.此外,周向麦克风个数大于所要分解周向声模态阶数的4倍时,使用CC模态分解技术获得的模态振幅误差可以控制在1dB之内.