Orthogonalization Techniques of a Direction Cosine Matrix

Three orthogonalization techniques to correct errors in the computeddirection cosine matrix are introduced. One of these techniques is avectorial technique based on the fact that the three rows of a directioncosine matrix constitute an orthonormal set of vectors in aree-threedimensional space. The other two iterative techniques are based onthe fact that the inverse and transpose of an orthogonal matrix areequal. In computing a time-varying direction cosine matrix computationalional errors are accompanied by the loss of the orthogonaliterty prop-rty of the matrix. When one of these three techniques is useo re-restore the orthogonality of the matrix, the computational errors arealso corrected. These techniques were tested experimentally and theresults, given in this paper, were compared with a method used by the Honeywell Corporation.     

Practical Comparison of Iterative Matrix Orthogonalization Algorithms

In previous work several algorithms for orthogonalizing the direction cosine matrix were introduced and their convergence rate and range were theoretically investigated. Three of the most promising algorithms are examined in this paper. lt is shown that the so-called Dual Algorithm is by far superior to the other two from the point of view of speed, computer memory, accuracy, and convergence rate. lt is therefore recommended that whenever the direction cosine matrix is computed by simple numerical integration of a matrix differential equation, the Dual Algorithm be used to orthogonalize the resultant matrix.     

Iterative Optimal Orthogonalization of the Strapdown Matrix

This paper treats the problem of finding an orthogonal matrix which is the closest, in the Forbenius norm, to a given nonorthogonal matrix. This nonorthogonal matrix is the result of a fast but rather inaccurate computation of the well-known direction cosine matrix (DCM) of a strapdown inertial navigation system. The known closed-form solution to this problem is rederived using the directional derivative method, and the conditions for minimum distance are derived and discussed. A new iterative technique for solving this problem is derived as a result of the application of the gradient projection technique and the directional derivative method. The practical computational problems involved in this technique are discussed. The new technique is demonstrated by three examples. Although particular attention is given to the 3 X 3 direction cosine matrix, the conclusions are nonetheless valid higher order matries.     

求解捷联式方向余弦矩阵的一种新方法

本文提出求解捷联式方向余弦矩阵的一种新方法——三角函数法。建立了三角函数的微分方程;讨论了求解位置矩阵、姿态矩阵正交化等有关问题;对三角函数法的计算误差进行了分析。通过大量的数学模拟,对四元数法、方向余弦法及三角函数法的计算精度作了比较。结果表明,三角函数法运算量较小,精度高,是求解方向余弦矩阵的可行方法。     

Strapdown Guidance Error Analysis

A crucial part of so-called ?strapdown? techniques for inertial guidance systems is the generation of the matrix of direction cosines relating the body axes to the reference axes. This is generally done by direct integration of a set of differential equations having the body angular velocities as inputs. This paper is devoted to an error analysis of two commonly used integration schemes, namely, direction cosines and quaternions. Scale, skew, and drift errors are defined, and the susceptibility of the integration schemes to these types of error is examined. It is concluded that the quaternion scheme offers an advantage because it intrinsically yields zero skew error. The paper is presented in two parts, for convenience.     

Direction-finding with sparse rectangular dual-size spatialinvariance array

A novel sparse array geometry embedding two sizes of spatial invariances is presented for use with a new ESPRIT-based (estimation of signal parameters via rotational invariance techniques) algorithm for aperture extension. The half-wavelength invariance yields unambiguous but high-variance direction cosine estimates to disambiguate low-variance but cyclically ambiguous estimates from the larger invariance. With larger invariance at 60 half-wavelengths, resolution threshold for two closely spaced emitters is reduced by 50 dB and estimation error by 100-fold. Array design formulas are also presented     

Performance of diversely polarized antenna arrays for correlatedsignals

The performance of direction finding systems in a correlated signal environment utilizing diversely polarized antenna arrays is investigated. The Cramer-Rao bound (CRB) is used to evaluate the accuracy of the estimated directions of arrival (DOAs). Compact closed form formulas are presented for the CRB corresponding to the joint estimation of the DOAs, signal covariance matrix, signal polarization parameters, and noise variance. The CRB is evaluated numerically for selected examples, to provide insights into the potential improvement in direction-finding accuracy due to polarization diversity     

Coordinate Conversion and Tracking for Very Long Range Radars

The problem of tracking with very long range radars is studied in this paper. First, the measurement conversion from a radar's r-u-v coordinate system to the Cartesian coordinate system is discussed. Although the nonlinearity of this coordinate transformation appears insignificant based on the evaluation of the bias of the converted measurements, it is shown that this nonlinearity can cause significant covariance inconsistency in the conventionally converted measurements (CM1). Since data association depends critically on filter consistency, this issue is very important. Following this, it is shown that a suitably corrected conversion (CM2) eliminates the inconsistency. Then, initialized with the converted measurements (using CM2), four Cartesian filters are evaluated. It is shown that, among these filters, the converted measurement Kalman filter with second order Taylor expansion (CM2KF) is the only one that is consistent for very long range tracking scenarios. Another two approaches, the range-direction-cosine extended Kalman filter (ruvEKF) and the unscented Kalman filter (UKF) are also evaluated and shown to suffer from consistency problems. However, the CM2KF has the disadvantage of reduced accuracy in the range direction. To fix this problem, a consistency-based modification for the standard extended Kalman filter (E1KF) is proposed. This leads to a new filtering approach, designated as measurement covariance adaptive extended Kalman filter (MCAEKF). For very long range tracking scenarios, the MCAEKF is shown to produce consistent filtering results and be able to avoid the loss of accuracy in the range direction. It is also shown that the MCAEKF meets the posterior Carmer-Rao lower bound for the scenarios considered.     

大地测量误差对导弹精度的影响与修正

将导弹发射点的所有测量误差统一为标准发射坐标系与实际坐标系之间的平移和旋转,建立了这两种坐标系之间的变换关系,通过各坐标系内的制导方程,用小偏差法求出了落点偏差与发射点的坐标偏差,高程偏差,方位角偏差及垂线偏差之间的解析关系式,并按该计算模型,对典型远程导弹进行了计算。结果表明,该修正公式计算精度高,能用于导弹射前修正。     

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.     

一种联合估计的有源校正高精度测向算法

针对存在系统误差的阵列模型,提出了一种有源标校下的联合估计测向算法。该算法把误差矩阵估计转化为误差系数估计,并采用到达角精确已知的源信号进行标校,在此基础上使用最小二乘法联合估计幅相不一致误差系数和互耦误差系数,最后使用结合误差矩阵的MUSIC算法测量信号的到达角。仿真表明,该算法仅需要3个标校源,其精度相比于无阵列误差情况下降0.05°,具有较好的工程可实现性。     

Reduced-rank STAP performance analysis

The space-time radar problem is well suited to the application of techniques that take advantage of the low-rank property of the space-time covariance matrix. It is shown that reduced-rank (RR) methods outperform full-rank space-time adaptive processing (STAP) when the space-time covariance matrix is estimated from a data set with limited support. The utility of RR methods is demonstrated by theoretical analysis, simulations and analysis of real data. It is shown that RR processing has two opposite effects on the performance: increased statistical stability which tends to improve performance, and introduction of a bias which lowers the signal-to-noise ratio (SNR). A method for evaluating the theoretical conditioned SNR for fixed RR transforms is also presented. It Is shown that while best performance is obtained using data-dependent transforms, the loss incurred by the application of fixed transforms (such as the discrete cosine transform) may be relatively small. The main advantage of fixed transforms is the availability of efficient computational procedures for their implementation. These findings suggest that RR methods could facilitate the development of practical, real-time STAP technology     

吊挂式模态试验系统动力学建模和分析

根据吊挂式模态试验系统的工作原理,通过合理简化等效,建立了吊挂式模态试验系统的力学基本模型。依据瑞利理论,求解出其在水平和竖直2个方向测试基频的解析计算公式,揭示了测试基频和真实基频的等量关系式,分析了2个方向上基频测试误差的产生机理、影响因素和变化趋势。通过开展标准杆模态试验以及有限元仿真分析,验证了吊挂式模态试验系统力学等效模型合理、正确和有效。结果表明,吊挂式模态试验系统竖直方向的基频测试值偏低,水平方向的基频测试值偏高,需对测试结果进行误差修正,方能得到被测对象较准确的基频值。     

与空时二维自适应滤波兼容的单脉冲测角新方法

针对机载相控阵雷达系统提出了一种空时二维自适应单脉冲测角方法 ,当存在阵元和通道幅相误差时它仍具有较高的测角精度。还给出了一种稳健的自适应和、差波束增益归一化方法 ,并讨论了所提方法的简化兼容实现方案。最后给出了基于高保真雷达杂波模拟数据的仿真实验结果     

Analytical and asymptotic solution of boundary value problems in the mechanics of deformed shells under concentrated loading

The paper proposes an analytical interval conjugation method for solving boundary value problems in the mechanics of deformed shells under concentrated loading. The errors are evaluated in solving the similar problems by means of asymptotic formulas.     

Frequency Diversity in Low-Angle Radar Tracking

Elevation angle errors due to sea-reflected multipath are evaluated theoretically for a radar operating in an off-boresight monopulse tracking mode. The computer simulation accounts only for specular reflection. Angle estimates at three frequencies are assumed to be available. It is shown that one can improve upon a simple average of the three indicated angles by unequally weighting them according to rank (lowest, middle, or highest). Some sample computations show that there is an optimum difference between the three frequencies.     

伺服加工平台的综合误差建模与补偿

伺服加工平台的几何误差是影响工件加工形貌精度的重要因素。在多体系统理论的基础上,首先,运用低序体阵列描述伺服平台多体系统的拓扑结构,建立各相邻体间的齐次变换矩阵,构建其综合误差模型;其次,利用雷尼绍测量系统对平台的定位误差、直线度误差、俯仰误差、偏摆误差以及两轴之间的垂直度误差进行辨识,将辨识得到的误差值代入构建的模型得出平台几何综合误差;最后,选择凸锥面、平面、球面3种面型工件补偿试验,对误差模型进行原理性验证。研究表明,经补偿后加工所得3种面型工件表面精度均提高了25%左右,证实了提出的补偿方法可用于伺服加工平台几何误差控制。     

机载雷达的空中定位研究

雷达告警器通过接收威胁源的雷达信号,经计算机处理、分析其信号特征,进而判别其类型、方位等信息,实时为空勤人员提供视、听觉告警信号,因而成为现代战机必备的电子对抗设备。以往相关文献中仅讨论了地面雷达对地面目标的定位问题,本文就机载全向雷达告警器的双机空中定位问题,经过严密的数学推导,利用方向余弦给出了威胁源的空间坐标计算公式,该公式简洁明了,程序运行时间短,为对威胁源进行实时监测提供了理论保障,同时本文对定位误码率差从两个角度做了理论分析,并相应给出了误差区和最大误差限。     

旋转坐标系下分区计算的LU隐式方法

将隐式时间迭代方法应用于并行计算是CFD研究中的热点问题,研究发现LU-SGS格式在旋转坐标系下对分区边界比较敏感,对旋翼悬停状态进行分区并行计算时碰到了计算发散的问题。针对此问题,对基于LU分解的3种隐式时间迭代格式（LU-SGS、DP-LUR和HLU-SGS）进行了对比研究,设计了静止流场下的旋转网格算例对计算方法进行测试。结果表明,LU-SGS格式在网格边界采用简化处理方法,当边界的逆变速度增大时会引起数值误差放大,误差的不断积累导致计算发散。DP-LUR和HLU-SGS格式通过在边界单元采用雅克比迭代算法,能有效消除分区边界影响,使计算格式在大CFL数条件下保持稳定,其中HLU-SGS继承了LU-SGS迭代效率高的特点。在此基础上,采用并行化的LU隐式方法对Caradonna-Tung旋翼进行了并行计算,针对两套稀密程度不同的背景网格,在产生复杂分区边界的计算网格条件下,均获得了气动力和旋翼尾迹都充分收敛的流场。通过计算,分析了背景网格密度对预测气动力性能和捕捉尾迹流场的影响,计算结果与试验值吻合良好,验证了当前隐式计算方法适用于旋转坐标系并行计算,适合于推广至其他大规模并行分区的流场计算。     

Reduced-rank STAP for high PRF radar

Due to the range ambiguity of high pulse-repetition frequency (HPRF) radars, echoes from far-range fold over near-range returns. This effect may cause low Doppler targets to compete with near-range strong clutter. Another consequence of the range ambiguity is that the sample support for estimating the array covariance matrix is reduced, leading to degraded performance. It is shown that space-time adaptive processing (STAP) techniques are required to reject the clutter in HPRF radar. Four STAP methods are studied in the context of the HPRF radar problem: low rank approximation sample matrix inversion (SMI), diagonally loaded SMI, eigencanceler, and element-space post-Doppler. These three methods are evaluated in typical HPRF radar scenarios and for various training conditions, including when the target is present in the training data