Improving ESPRIT via beamforming

Beamforming techniques are presented that improve the performance of the ESPRIT (estimation of signal parameters via rotational invariance techniques) algorithm for solving the narrowband multiple source location problem with uniform linear arrays. Using ESPRIT with these beamforming approaches maintains the computational advantage of the original ESPRIT while further exploiting the special structure of uniform linear arrays. Simulation results show that the use of ESPRIT with beamforming yields significantly improved performance compared with the original ESPRIT     

Performance analysis for DOA estimation algorithms: unification,simplification, and observations

Subspace based direction-of-arrival (DOA) estimation has motivated many performance studies, but limitations such as the assumption of an infinite amount of data and analysis of individual algorithms generally exist in these performance studies. The authors have previously proposed a unified performance analysis based on a finite amount of data and achieved a tractable expression for the mean-squared DOA estimation error for the multiple signal classification (MUSIC). Min-Norm, estimation of signal parameters using rotational invariance techniques (ESPRIT), and state-space realization algorithms. However, this expression uses the singular values and vectors of a data matrix, which are obtained by the highly nonlinear transformation of the singular value decomposition (SVD). Thus the effects of the original data parameters such as numbers of sensors and snapshots, source coherence and separations were not explicitly analyzed. The authors unify and simplify this previous result and derive a unified expression based on the original data parameters. They analytically observe the effects of these parameters on the estimation error     

MIMO雷达DOD和DOA联合估计算法: RTR-ESPRIT

 针对双基地多输入多输出(MIMO)雷达多目标波离角(DOD)和波达角(DOA)的联合估计问题,提出一种接收-发射-接收(RTR)-ESPRIT算法。该算法首先利用一维接收ESPRIT(R-ESPRIT)预估计目标DOA,随后分别利用一维发射ESPRIT(T-ESPRIT)和一维接收ESPRIT得到目标的高精度DOD和DOA估计,在每两次ESPRIT算法之间分别构造正交投影算子对接收信号进行接收波束形成和发射波束形成。与传统ESPRIT算法相比,该算法大大降低了数据协方差矩阵维数和计算复杂度,无需额外的配对算法,且理论证明了该方法还可以用于相干目标和单快拍情况下DOD和DOA的联合估计。仿真结果表明了该算法的正确性及良好的估计性能。     

Sensitivity analysis of DOA estimation algorithms to sensor errors

A unified statistical performance analysis using subspace perturbation expansions is applied to subspace-based algorithms for direction-of-arrival (DOA) estimation in the presence of sensor errors. In particular, the multiple signal classification (MUSIC), min-norm, state-space realization (TAM and DDA) and estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithms are analyzed. This analysis assumes that only a finite amount of data is available. An analytical expression for the mean-squared error of the DOA estimates is developed for theoretical comparison in a simple and self-contained fashion. The tractable formulas provide insight into the algorithms. Simulation results verify the analysis     

基于四线性分解的双基地MIMO雷达的角度和多普勒频率联合估计

研究双基地多输入多输出(Multiple-input Multiple-output, MIMO)雷达中的角度和多普勒频率联合估计问题,提出了一种基于四线性分解(Quadrilinear Decomposition)的离开角(Direction of Departure, DOD)、波达角(Direction of Arrival, DOA)和多普勒频率的联合估计算法。通过对接收端匹配滤波器的输出进行延迟操作,得到符合四线性模型的数据,根据四线性交替最小二乘(Quadrilinear Alternating Least Squares, QALS)进行迭代,得到方向矩阵和多普勒频率矩阵的估计,进而得到角度和频率的估计。该算法无需谱峰搜索,无需知道反射系数,可实现角度和频率的自动配对,且能用于非均匀阵,该算法的角度估计性能优于多维ESPRIT方法和三线性交替最小二乘(Trilinear Alternating Least Squares, TALS)方法。论文分析了所提算法复杂度,并推导了克拉美-罗界(Cramer-Rao bound, CRB)。仿真结果验证了该算法的有效性。     

空间谱估计经典算法性能比较

空间谱估计是阵列信号处理的一个重要研究方向。空间谱估计理论与技术已日趋成熟，近几十年的经典谱估计技术包括：常规波束形成（CBF）、Capon谱估计、多重信号分类（MUSIC）、旋转不变子空间算法（ESPRIT）、最大似然（ML）、子空间拟合（SF），及这些算法的扩展和变形。上述算法在各个分散的文章中均有具体深入的理论分析和研究，亦有类似的2种或3种算法的性能比较，但是针对这些所有算法的性能比较，就笔者所知尚无公开报道，而使工程实现时对算法的选择没有依据。本文对这些经典算法做了简介，列出各个算法的优缺点，并对性能进行仿真比较，能直观地得到各个算法的性能对比，给工程实现算法选择提供理论依据。     

基于声波传播时间估计的气流速度测量方法

 为实现对亚声速和超声速气流速度的统一测量,提出了一种基于声传感器的新型测量方法。首先,根据声波在亚声速和超声速气流中的传播特性,利用特定的测量装置建立了声波传播时间与气流速度之间的数学模型,从而将气流速度的测量问题转化为声波传播时间的测量问题。然后,在此基础上,利用计时法和最大似然估计(MLE)方法来估计声波传播时间;其中,计时法在实时性上优势明显,而MLE方法则在可靠性上优于前者。最后,分别从阵元位置扰动性、计时误差和克拉美-罗界(CRB)3个方面对所提算法的性能进行了分析与仿真验证。结果表明,该算法能够实现对亚声速和超声速气流速度的精确测量。     

2-D spatial smoothing for multipath coherent signal separation

The use of two-dimensional spatial smoothing (SS) to increase channel capacity of wireless communications system is discussed, The necessary and sufficient conditions on array configuration for applying SS to multiple signal classification (MUSIC), and adaptive beamforming algorithms are defined and proved, This array must have an orientational invariance structure with an ambiguity free center array, and the number of subarrays must be larger than or equal to the size of the largest group of coherent signals. We also studied the cause of ambiguities in a multipath environment. We found the necessary and sufficient conditions for a three-sensor array manifold to be ambiguity free and identified several higher order ambiguity situations, If an array is also central symmetric, the forward/backward SS (FBSS) can be used to improve the resolution. Finally, we extended our results to the estimation of signal parameters via rotational invariance techniques (ESPRIT). All the predicted results are verified by simulations     

基于改进TLS-ESPRIT算法的相干定位信号波达方向空间平滑

针对室内角度定位,在定位信号相干条件下无法实现准确估计波达方向(DOA)的问题,提出了一种基于TLS-ESPRIT算法的双向空间平滑方法。该算法先对定位相干信号进行双向空间平滑处理,然后用TLS-ESPRIT算法进行DOA的精确估计,使其最大限度地利用信号子空间的信息,从而解决了算法计算过程中输出信号的协方差矩阵秩亏损情况。该算法能够准确实现定位信号相干条件下DOA估计,与传统的空间平滑结合其他改进ESPRIT算法相比,具有更好的平稳性及抗干扰能力。最后通过仿真实验验证了算法的有效性和稳定性。     

Angle measurement in the presence of mainbeam interference

The problem of reducing interference impinging on an antenna array when the sources lie in the main beam is addressed. Adaptive antenna arrays are incorporated to form adapted sum and difference beams in which the interference signals are suppressed. Monopulse error curves are then obtained, providing the necessary distortion correction curves across the entire mainbeam tracking angle region. New Cramer-Rao (C-R) bounds on the angle estimation error are derived with generalized assumptions on the signal amplitude and phase. The bounds previously derived by others are valid under different conditions. With these generalized assumptions on the signal characteristics, a Monte Carlo simulation is performed, based on the estimation procedure presented, to determine the angle estimation error. These errors are compared with the C-R bounds. Good performance is shown for sufficient S/N₀ and angular separation between the target and the interference sources     

Angle of arrival estimation of coherent signals using an arraydoublet in motion

Shown here is how the estimation of signal parameters via relational invariance techniques (ESPRIT) algorithm may be used with a single pair of antennas in motion to estimate angles of arrival (AOA) for coherent signals. The approach exploits the Doppler frequency shifts caused by the doubler in motion. With this estimator, the number of signals that can be handled is not limited by the size of the array, as in the usual ESPRIT application, but by an adjustable parameter. A theoretical performance analysis of the estimator and typical examples showing the use of this estimator are given     

窄带信号小样本谱估计算法

针对窄带平稳随机信号的小样本谱估计问题,结合均匀线性阵列的空间谱估计算法,提出了一种高性能小样本谱估计算法。该算法首先利用采样数据构造一个Toeplitz矩阵;然后对该矩阵进行特征值分解得到信号子空间和噪声子空间;再结合MUSIC、ESPRIT等子空间算法,即可实现对小样本采样数据的谱估计。数值仿真验证了该算法的有效性。     

一种基于协方差矩阵重构的相干信源DOA估计算法

针对空间相干信源的波达方向估计问题,提出了一种基于协方差矩阵重构的TSVD-ESPRIT算法。它利用包含所有信源信息的特征向量构造Toeplitz协方差矩阵,避免了阵列有效孔径的损失,分辨率高且稳定性好;并且利用ESPRIT算法代替MUSIC算法进行DOA估计,避免了谱峰搜索,大大降低了计算量。数据仿真和分析证明了该算法的正确性和有效性。     

基于时空结构的双基MIMO雷达多维参数联合估计

为了充分利用目标的时域特性来改善双基多输入多输出(MIMO)雷达波达方向(DOA)和离波方向(DOD)的估计性能,探讨了双基MIMO雷达在时-空模型下的多维参数联合估计问题。针对慢动目标,基于多维旋转不变技术信号参数估计(ESPRIT)算法,同时利用时域相邻两级延迟包含的时间相位差、发射阵列相邻阵元包含的空间相位差以及接收阵列相邻阵元包含的空间相位差作为旋转因子,形成旋转不变子空间,再根据矩阵、矩阵的特征值及特征值对应的特征向量三者之间的关系解决了参数配对问题,实现了三维参数联合估计。该方法在信噪比低、积累脉冲数少时,目标的DOA与DOD估计性能比不利用时域特性时有明显改善。仿真结果验证了本方法的有效性。     

Resolution of signal sources via spectral moment estimation

In different practical situations it is desired to estimate the number of signal sources and their positions in space or in frequency domain. The first problem is known as the detection or the order estimation and the second one as the resolution. For the resolution problem techniques such as nonlinear least squares (NLSM), high-order Yule-Walker method (HOYW), multiple signal classification (MUSIC), Pisarenko harmonic retrieval method, min-norm method, estimation of signal parameters by rotational invariance technique (ESPRIT), were proposed (Marple, 1987 and Stoica and Moses, 1997). All these high-resolution methods are based on the analysis of the signal covariance matrix. But the covariance matrix is not the only choice to represent the signal spectrum. In different applications (weather radars, synthetic aperture radar (SAR) signal processing, ultrasound imaging in medicine, atmospheric turbulence measurements) the signal spectrum can be modeled through its algebraic moments. Recently a number of efficient nonparametric methods have been proposed to estimate the algebraic spectral moments (Monakov, 1999). The presented paper is an attempt to solve the direction of arrival (DOA) problem via estimation of the algebraic spectral moments. A method proposed in the article is comparable in its accuracy with the MUSIC method. At the same time its computational burden is much lower. The method permits to estimate the signal power of sources easily to complete the full spectral line analysis. Additionally the method shows good robustness in situations when signal sources have noticeable spatial extend     

An operational system implementation of the ESPIRIT DF algorithm

The practical implementation of the ESPRIT algorithm into direction-finding system architecture is considered. In particular, the problems of phase ambiguity resolution for extended array separations and multidimensional azimuth/elevation estimation are addressed. Generalized solutions for these problems are proposed, and a bearing quality indicator that provides a measure of credibility associated with each angle-of-arrival estimate is developed. Plots of computer simulated performance are presented in order to assess the probability of detection, of failure to alarm, and of false alarm as a function of azimuthal separation and period of signal observation     

Analysis of Min-Norm and MUSIC with arbitrary array geometry

A nonasymptotic performance comparison is presented between the Min-Norm and MUSIC algorithms for estimating the directions of arrival of narrowband plane waves impinging on an array of sensors. The analysis is based on a finite amount of sensor data. The analysis makes the assumption of high signal-to-noise ratio (SNR), and it applies to arrays of arbitrary geometry. It is shown that Min-Norm can be expressed as a certain data-dependent weighted MUSIC algorithm, and that this relationship allows a unified performance comparison. It is also shown that the variances of the estimated directions-of-arrival from the MUSIC algorithm are always smaller than those of the Min-Norm algorithm at high SNR when both algorithms employ a numerical search procedure to obtain the estimates     

修正Rodrigues参数在飞行器定姿中的应用(英文)

There are two attitude estimation algorithms based on the different representations of attitude errors when modified Rodrigues parameters are applied to attitude estimation. The first is multiplicative error attitude estimator （MEAE）, whose attitude error is expressed by the modified Rodrigues parameters representing the rotation from the estimated to the true attitude. The second is subtractive error attitude estimator （SEAE）, whose attitude error is expressed by the arithmetic difference between the true and the estimated attitudes. It is proved that the two algorithms are equivalent in the case of small attitude errors. It is possible to describe rotation without encountering singularity by switching between the modified Rodrigues parameters and their shadow parameters. The attitude parameter switching does not bring disturbance to MEAE, but it does to SEAE. This article introduces a modification to eliminate the disturbance on SEAE, and simulation results demonstrate the efficacy of the presented algorithm.     

Circular array STAP

Traditionally, space-time adaptive processing (STAP) for airborne early warning (AEW) radar has been applied to uniform linear arrays (ULAs). However, when considering the overall radar system, electronically scanned circular arrays have advantages: a better combination of even and continual angular and temporal coverage, and mechanical simplicity because it does not need to rotate. This paper answers the question “How well does STAP perform when applied to a circular array?” This paper shows that for the AEW mission, circular arrays are indeed STAP compatible. However, when conventional STAP algorithms are used there may be a small loss in performance when compared with a ULA. With some care in the choice and implementation of the STAP algorithm, the majority of the degradation is at close ranges, where the target returns are relatively strong. At long ranges performance is barely affected. A STAP algorithm which compensates for the circular array environment and provides better performance than existing algorithms is presented     

Autonomous Control Reconfiguration of Aerospace Vehicle Based on Control Effectiveness Estimation

未来空天飞行器跨空天两域飞行,要求有较高的自主性以适应由故障和环境变化带来的不确定因素。针对空天飞行器的不确定性,提出了自主控制重构方案。研究了线性模型的时变控制效益的估计方法,提出并证明了效益矩阵可估计的充分条件,给出了相应的算法并证明了其收敛性和对噪声的鲁棒性;提出了基于线性规划和模糊逻辑的控制分配算法,通过冗余效应器实现了不确定条件下的自主控制重构。系统集成和仿真结果分析验证了方案和算法的有效性。