Strapdown Matrix Orthogonalization: The Dual Iterative Algorithm

There exist several algorithms for the optimal orthogonalization of the Direction Cosine Matrix used in navigation, control and simulation One of these recursive algorithms is shown to be derived from a dual solution to the optimal orthogonalization problem. The duality of the algorithm is demonstrated and its convergence properties are investigated Quadratic convergence is proven and the condition for convergence is determined and illustrated with numerical examples.     

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.     

Orthogonalization of a Direction Cosine Matrix by Iterative Techniques

It is shown that the ?first inversion, transposition, and averaging? technique [1] is, assuming convergence, quadratically convergent, since it can be developed very simply by the use of quasilinearization. Only the three-dimensional case is considered; the art of matrix orthogonalization is practiced in more general settings [2] than considered here.     

On the Convergence of Iterative Orthogonalization Processes

Polar decomposition of matrices is used here to investigate the convergence properties of iterative orthogonalization processes. It is shown that, applying this decomposition, the investigation of a general iterative process of a certain form can be reduced to the investigation of a scalar iterative process which is simple. Three known iterative orthogonalization processes, which are special cases of the general process, are analyzed, their convergence rate (order) is determined, and their range of convergence is established in terms of the spectral radius of the modulus of the matrix which is being orthogonalyzed.     

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.     

捷联式惯导系统动态误差特性研究

根据载体运动状态下捷联惯性导航系统(SINS)的误差方程时变的特点,推导出捷联惯性导航系统动态误差模型,并对其在几种动态环境下的误差特性进行了仿真研究。     

捷联惯导系统圆锥误差分析

捷联惯导系统由于数学平台隔离作用的不完善,当运载体沿机体坐标轴存在同频率的角振动和线振动时,角振动引起的整流效应将在姿态更新计算中产生圆锥误差,角振动和线振动引起的整流效应将在速度计算中产生划桨误差,在位置计算中产生涡卷误差。文中详细分析了圆锥误差产生机理,针对某型飞机装备 SIGMA50 GPS/SINS 组合导航系统对底座安装的精度要求,分析了安装误差、陀螺频带不够宽、姿态更新率过低对姿态精度的影响,并对维护捷联惯导系统提出建议。     

捷联惯导系统发展及其军事应用

从20世纪80年代开始,以激光陀螺和光纤陀螺为代表的捷联惯导系统逐步进入实用阶段,为高新技术武器装备的革新改造打下了坚实技术基础。本文主要介绍捷联惯导系统的组成、原理、特点、发展趋势及其在航空军事领域中的主要应用。     

捷联惯性导航系统高精度动态仿真算法

由于飞行器动态模型航迹生成算法与惯性导航系统算法原理存在差异,无法直接仿真分析惯性传感器不同误差特性对惯性导航系统动态性能的影响.基于飞行器动态模型航迹数据,提出一种捷联惯性导航系统高精度动态仿真实现方法,设计了惯导参数动态计算误差并行补偿方案,实现了对导航系统动态仿真过程中导航参数计算误差的有效分离.在搭建的仿真平台上,有效验证了所提出仿真方法的性能,为实际惯性传感器选型和指标选择提供支撑.     

三维捷联磁传感器误差分析及补偿

磁传感器在导航系统中的应用日益广泛。在车载导航系统工作环境中,外界干扰磁场复杂,严重影响了磁航向测量的精度。因此对磁航向进行适当的罗差补偿是提高磁航向测量精度的有效途径。文中介绍了用磁传感器进行磁航向测量的原理,分析了由于磁场矢量叠加产生的罗差,提出了基于傅立叶级数的罗差模型和补偿方法。工程实践表明,上述方法的使用收到了较好的效果。     

玻璃基复合材料基体裂纹行为和分布规律的研究

碳化硅纤维增强玻璃基复合材料是一种能够在１１００℃高温氧化环境中使用的新型材料。玻璃基复合材料承载后基体产生裂纹，裂纹影响了材料的力学性能。本文改进了实验方法，使用不同加载－卸载循环后试样表面的照片研究了裂纹分布规律，发现裂纹的行为在同一材料，同一加载后，不同区域内有所不同，分为门槛和增长两种类型。在门槛区内，经一定的载荷后，裂纹突然出现，布满全部区域。在增长区内，裂纹随载荷的增加而逐渐增加。本文     

Gyro Misalignment and Encoder Quantization Effects During Multi-Axis Evaluation of Strapdown Gyros

This paper presents a quantitative discussion of two error sources which affect the accuracy of data comparison between instrument outputs and reference angle computations during multi-axis evaluation of strapdown gyros. The error due to misalignment of gyro input axes is formulated in terms of closed-form solutions for typical relationships between the three table gimbal rotation histories. If the angular positions of the table gimbal axes are measured by shaft encoders, then any measurement has an uncertainty in the range from plus to minus one-half of the quantization level. It is shown that the effect of encoder quantization error on the computer transformed angles in the bodyfixed coordinate system can be divided into two parts: the initial uncertainty of the zero positions of the gimbals before table motion is begun, and all subsequent error contributions during table test. Typical data for gyro misalignment and encoder quantization error effects are presented.     

牛顿迭代收敛的加速

基于Newton迭代法单根的二阶收敛性和重根的线性收敛性,提出了加速牛顿迭代收敛的思想。利用反函数的性质,取Taylor展开式的前三项进行迭代;并利用差商代替导数的方法,构造出更高收敛阶的迭代公式。大量的数值实验结果表明,本文算法理论上的推导是完全可行的,且有效地提高了迭代公式的收敛速度。     

基于迭代学习的PID控制器研究

将目前对u(t)的记忆与修正改成对期望控制ud(t)的记忆与修正,提出两种新的拟合控制系统的PID控制器参数的方法。这两种方法实现的PID控制器较常规的PID控制器结构简单,作用于系统可获得较佳的动态特性和较强的鲁棒性。研究目的是为迭代学习控制理论在设计性能优良的控制器方面扩大应用领域。     

动力学反演的迭代过程及应用

把结构动力学反演归结为一类广义特征值反问题 ,提出了一种迭代算法 ,并讨论了解的存在条件。大量数值实验结果表明 ,本文迭代过程收敛性好。结合某型直升机旋翼桨叶的动力学设计 ,文中给出了工程应用的数值例子 ,结果令人满意。     

Detection Loss of the Sample Matrix Inversion Technique

The sample matrix inversion (SMI) technique is used for Doppler and/or array processing. Previous analysis of the technique has been in terms of signal-to-interference plus noise ratio (SINR). For Gaussian statistics, this performance measure gives the same loss values as does a probability of detection analysis for linear-time invariant systems. It is often somewhat less valid for nonlinear or time variant systems. As SMI is a nonlinear technique, a probability of detection analysis has been performed. It is shown that the detection loss is larger than that computed by the SINR measure. It is also shown that though the loss predicted by the SINR measure only depends upon the number of measurements used to estimate the covariance matrix, the detection loss depends upon the false alarm probability and the number of adaptable elements in addition to the number of measurements.     

一种变射面飞行导弹的弹上迭代制导方法

针对变射面飞行的弹道导弹,制导方法需要满足射面变换起控点的位置、速度和姿态要求。提出了一种变射面飞行导弹的弹上迭代制导方法,以各射面弹道终点的弹道倾角为约束,弹上迭代计算虚拟目标和需要速度,求取导引姿态角进而进行导引控制。仿真算例表明,该制导方法能够实现变射面飞行的制导控制要求,且方法误差较小。     

Comment on "Gyro Misalignment and Encoder Quantization Effects During Multi-Axis Evaluation of Strapdown Gyros"

A recent paper1 discusses certain aspects of strapdown attitude error sources. It is pointed out here that the long term effects of these and several additional sources have previously been determined, within the framework of a complete attitude reference [4] and navigation [5] system.     

基于迭代学习控制的飞机全电刹车系统的研究

通过对飞机全电刹车系统模型的分析,结合迭代学习控制的特点设计出一种新的全电刹车系统的控制律。通过在matlab/simulink中仿真,取得了理想的效果,表明控制律的设计基本合理、可行。