Error analysis of quaternion transformations [inertial navigation]

Three transformation formulas that relate the quaternions to the direction cosine matrix used in strapdown inertial systems are derived. An error model associated with the computed direction cosine matrix is briefly discussed. Error analysis is fully evaluated analytically and tabulated for comparison. Transformation errors associated with these formulas are analyzed. The drift errors evaluated under constant angular velocity are shown to vary slightly among three different transformations. It is shown that the skew errors in three transformation schemes are not all intrinsically zero. The scale errors may differ largely by two orders of magnitude among transformation schemes. This may become a criteria for selection of altitude transformation schemes     

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.     

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.     

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。     

一种基于协方差矩阵加权的阵元误差补偿STAP处理

机载多通道阵列雷达天线在工程实践中不可避免地存在各类阵元误差,所产生的通道失配问题会对空时二维自适应处理的性能造成大的影响。对存在阵元误差时的阵列信号模型进行了分析,提出了一种基于协方差矩阵加权（CMT）的阵元误差补偿空时自适应处理（STAP）方法,在工程应用中该加权矩阵可通过地面天线定标及校飞过程确定,通过对总干扰协方差矩阵估计的加权预处理,可将实际阵元误差对STAP性能的影响控制在测量误差的影响范围,最后通过仿真验证了算法的有效性。     

双轴转台误差对IMU标定精度的影响分析

转台误差影响惯性测量组件标定精度,从某种意义上讲,标定的精度就直接决定惯性器件的使用精度。研究双轴转台水平误差及非正交误差对标定结果的影响。首先,建立标定模型以及转台误差模型,通过余弦矩阵将转台误差引入标定模型中,从理论上分析了转台误差对加速度计及陀螺标定精度的影响,最后进行了仿真分析。分析表明：转台水平误差对加速度计及陀螺的标定系数的影响较小,可以忽略;而转台非正交误差对加速度计和陀螺标定影响较大,特别对加速度计和陀螺安装误差系数影响较大,能够导致同量级的误差。     

一类不确定非线性系统的鲁棒自适应设计

讨论了一类含有广义不确定性的非线性系统的自适应跟踪问题。通过引入一种新颖的鲁棒函数,有效地抑制了系统不确定性对系统的影响,并利用反演设计技术设计了控制器,避免了系统控制矩阵未知时控制器可能出现的奇异问题,证明了系统的状态跟踪误差和参数误差指数收敛于原点的一个邻域。     

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.     

Computational Precision Requirements for Optimal Weights in Adaptive Processing

The required accuracy for computing the estimated optimum weights of an adaptive processor has been analyzed by investigating the effects of errors in computing the inverse matrix. It is shown that the required precision depends upon the matrix. An equation for the general case is derived. Several special cases are considered in detail. It is shown that the case of a single interference source requires the highest precision. The least stressing case is identifi'ed and compared to the worst case. The requirements for a "typical" case are also considered. A comparison of the requirements for the covariance matrix estimation technique and for adaptive weight implementation using gradient descent techniques is given. It is shown that there is a dichotomy in that cases that do not stress one technique tend to stress the other.     

参数曲线形状修改

提出一种新的、基于余弦伸缩函数、针对参数曲线的形状修改与变形方法。首先定义了特殊的伸缩函数 ,在此基础上构造了形状算子矩阵 ,其次将该矩阵与伸缩中心及主方向结合构造出两种变形矩阵 ,最后用变形矩阵去乘待变形曲线在局部坐标系下的位置向量 ,或用它乘以给定向量场再加待变形曲线在原坐标系下的位置向量从而产生变形效果。伸缩函数含有若干可变参数 ,每个参数可产生不同的形状修改效果 ,比如控制被修改部分与未修改部分间的连续阶 ,容易得到理想的变形效果。理论分析实例表明该方法在几何造型 ,计算机图形学等领域有潜在适用性。     

Strapdown inertial measurement units for motion compensation forsynthetic aperture radars

It is shown that synthetic-aperture radar (SAR) motion can be compensated by using an antenna-mounted strapdown inertial measurement unit (IMU) as the motion sensing system, but sensor and system errors affect SAR image quality. A strapdown IMU consists of three accelerator channels and three gyro channels. Strapdown IMU errors include gyro-scale and accelerometer-scale factor and bias errors, velocity error, platform tilt, and errors induced by limited inertial sensor bandwidth. The effects of these errors on the SAR image quality are presented in terms of the SAR impulse response. IMU errors that cause low-frequency phase errors (less than one cycle per array time) are categorized in terms of quadratic and cubic phase errors. IMU errors that cause high-frequency phase errors (greater than one cycle per array time) are categorized in terms of the integrated sidelobe ratio and peak sidelobe ratio. A motion compensation system conceptualization is described wherein a strapdown IMU is attached to an antenna and transfer-aligns to the aircraft's master navigator     

一种适用于曲面结构的机器人制孔误差在线补偿技术

针对工业机器人应用于飞机零部件自动钻孔时各项误差累积造成制孔精度差的问题，提出一种利用单应关系计算机器人驱动坐标三维偏差，以在线补偿机器人制孔精度的方法。首先利用外部测量设备建立机器人制孔系统中各坐标系关系；在标定阶段，通过以一定倾斜角度固联于机器人末端的相机拍摄一幅安装于制孔工作平面上与刀轴正对的平面标定板图像，并据此完成基于单应变换的手-眼关系标定；在实际制孔过程中，机器人在测距传感器及相机的辅助下，从基准孔理论坐标对应的姿态，不断调整至基准孔正上方理想位置，通过手-眼关系计算基准孔实际位置对应的机器人驱动坐标，然后根据一组基准孔的机器人三维驱动误差，计算三维驱动误差变换矩阵，据此获得这组基准孔邻域范围内各待钻孔的机器人驱动坐标补偿量，从而实现待钻孔定位误差补偿。以飞机结构实验件为对象进行了模拟制孔验证，实验结果表明，补偿前待钻孔三维综合定位误差和法向误差测量值范围分别为2.28~2.85 mm和2.09°~3.93°，平均为2.55 mm和3.30°，补偿后制孔最大误差分别不超过0.30 mm和0.21°，满足自动制孔位置精度要求。     

Error Analysis of the Optimal Antenna Array Processors

The optimal weights of an antenna array processor, which maximizes the output signal-to-noise ratio (SNR) in the absence of errors, are computed using the noise-alone matrix inverse (NAMI) and the steering vector in the look direction or the signal-plus-noise matrix inverse (SPNMI) and the steering vector. In practice the estimated steering vector as well as the estimated optimal weights are corrupted by random errors. This paper has analyzed the effects of these errors on the performance of the NAMI processor and the SPNMI processor by deriving analytic expressions for the output signal power, output noise power, output SNR, and the array gain as a function of the error variance. The treatment is for a general array configuration and no assumption about a particular array geometry is made.     

一种宽带阵列幅相与互耦误差联合校正算法

宽带数字阵列雷达接收通道中存在随频率变化的幅相误差和互耦误差,会严重影响雷达性能。针对这一问题,提出了一种宽带数字阵列幅相与互耦误差联合校正算法。首先选取通带内多个离散频点,对于每个频点,将幅相误差和互耦误差作为一个整体,采用基于子空间原理的窄带校正算法估计其阵列失真参数,并计算校正矩阵;然后将其组合起来,构成频域离散校正矩阵;最后基于最小二乘准则,设计了宽带有限长脉冲响应(FIR)校正滤波器矩阵。利用该矩阵,可实现通带范围内任意带宽入射信号的校正。计算机仿真实验验证了该算法的有效性。对实测数据的处理结果表明该算法在宽带数字阵列雷达系统中具有实用价值。     

Wide-Aperture Digital VOR

The very high frequency (VHF) omnirange has undergone a number of evolutionary changes in the past 30 years. Early measurements of large errors led to the development of the Doppler VHF omnidirectional irectioal range (VOR) and its use. Further developments have been the precision multilobe VOR and the precision Doppler VOR. Interest in area navigation has led to the desire for a VOR greatly superior to any so far developed. Specifically, the objectives of the improved VOR would be a system that would significantly reduce magnitude of siting errors, provide greater accuracy and use digital techniques to simplify processing. ssing. The wide-aperture digital VOR described herein has been developed to meet these objectives. Its design is based on the crossed-pair interferometer principle where eight such pairs are energized successively by a set of pulses and phase shifts. The time multiplexed signal, detected by the aircraft receiver, is processed and simple digital computations are performedto determine the angular coordinates. The performance improvements have been achieved by the combination of using a 275-ft antenna aperture, and the use of digital techniques to generate the ground-radiated navigational signals and to process them in the airborne processor. Field tests of the feasibility model indicate it is a high performance ance system, capable of achieving an order of magnitude improvement in both site error reduction and in accuracy compared to present VOR systems. The measured accuracies were 0.11-degree standard deviation.     

基于Walsh基和二值离散余弦基单像素成像的对比分析

为提升单像素成像的测量效率,对Walsh基和二值离散余弦基单像素成像进行了对比研究。针对Walsh变换和抖动二值化后的离散余弦变换,提出了一种借鉴机器学习的排序方法,即通过分别统计80000幅图像的Walsh测量基和离散余弦测量基各自相应测量权重绝对值,按权重由大到小排序得到了两种具有先验知识的测量基优化排序。按两种测量基优化排序,研究了在相同压缩采样下的单像素成像。利用随机选取的500幅图像,定量分析了成像的峰值信噪比和结构相似度。研究发现,两类测量基在压缩采样为5%时,500幅图像平均峰值信噪比可达20dB,平均结构相似度达0.5以上;在采样率1%~10%的区间,二值化的离散余弦基重建结果占优;在采样率10%~20%的区间,两种测量基效果相当;在采样率大于20%时,Walsh基占优。该结论为单像素成像技术实现快速、高信噪比成像提供了一种方法,对推进单像素成像测量基的选取具有较好的参考价值。     

New Autocorrelation and Prediction Techniques for the Demodulation of Binary Signals

The classic problem of detecting a narrowband signal received in a wideband noise is treated via new techniques, namely, autocorrelation computation and linear adaptive filtering. It is shown by analysis and simulation that the proposed techniques yield probility of bit errors cimparable to those provided by coding techniques. Expressions are derived for the detectability parameter of the new test statistics, and it is shown that these statistics are very close to the Gaussian approximation. The improvements obtained in the signal-to-noise ratio and the Gaussian nature of the new statistic implies an improvement in the capacity of the channel by the nonlinear and storage processes involved in the new techniques, something not achievable by linear filtering and/or memoryless detection techniques.     

Eigenanalysis-based space-time adaptive radar: 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. The performance of an eigenanalysis-based detector with respect to convergence rate and robustness to calibration errors is analyzed. Analytical expressions are developed for receiver operating curves when the clutter signal environment is assumed to be Gaussian. The curves are derived from the asymptotic expansion of the distribution of the principal components of the covariance matrix. Simulation results are provided to corroborate the theoretical analysis. Examples from the Mountain-Top dataset are used to illustrate the higher convergence rate and increased robustness of the eigenanalysis method.     

一种基于约束因子的超载迟滞模型

在常幅载荷中加入一个超载会明显影响后续一段时间裂纹扩展的速率.要准确预测结构在变幅载荷谱下的疲劳裂纹扩展寿命,必须研究超载对裂纹扩展的影响.现有的变幅疲劳裂纹扩展模型大致可分为屈服区模型、经验的裂纹闭合模型和条带屈服模型.条带屈服模型预测较准确但需要数值迭代求解,计算量大,且程序复杂,不利于工程应用;屈服区模型比较简单...     

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