Optimal technology of inertial measurements

A technological project for measuring the spacecraft angular velocity vector is justified, the maximum accuracy is attained, and the proposed technology is compared with well-known methods for inertial measurements. The present paper is a continuation of [1].     

基于旋转矢量误差模型的舰载机大失准角传递对准技术（英文）

为实现舰载机大方位失准角条件下的快速传递对准,提出采用旋转矢量误差模型。分别推导了速度匹配和速度加角速度匹配的量测模型。为解决非线性滤波器的稳定性和快速性,提出采用平方根无迹卡尔曼滤波SRUKF来估计失准角。仿真结果表明,旋转矢量误差模型相对于非线性的欧拉角误差模型有更高的估计精度。在海况引起的摇摆运动下,运用速度加角速度匹配方法可以在50 s内完成对准,此时水平精度达到20?以内,航向精度达到1?以内。由此表明所提出的算法可以满足舰载机传递对准快速性和精确性的要求。     

船用捷联惯性导航系统姿态算法精度评估研究

分析了捷联惯性导航系统姿态解算中不可交换性误差产生原因，提出并分析了一种旋转矢量误差估计模型，并从该模型出发推导了几种高精度的捷联姿态算法，提出了由角速度提取角增量的梯形算法。以船舶为应用对象，进行了数字仿真和算法精度分析比较，结果表明：等效旋转矢量法和梯形算法可以提高系统的姿态解算精度。     

速率偏频激光陀螺系统速度数值积分算法误差分析与优化(英文)

用时域泰勒级数展开的方法分析了速率偏频激光陀螺惯导系统常用速度数值积分算法的误差。分析显示速率偏频陀螺本身的高速旋转使惯性导航系统时刻处于大角运动条件下。若其旋转轴与比力方向不平行,则常用速度算法的误差不可忽略。提出了速率偏频激光陀螺惯导系统速度算法的优化改进方法。对常用速度算法和提出的算法进行了仿真比较。仿真显示,用泰勒级数展开分析速度数值积分算法误差是可行的;提出的算法能够将速率偏频激光陀螺惯导系统以及其他惯性导航系统在大机动运动环境下的导航精度提高一阶。     

On the solution of the Darboux problem

We consider the problem of determining the angular position of a rigid body in space from its known angular velocity and initial position (the Darboux problem) in quaternion setting. For an arbitrary angular velocity vector of the body, we present a solution based on Lappo-Danilevskii’s recursion relations [1]. New special cases of solvability of the Darboux problem in closed form are obtained.     

Construction of optimal laws of variation in the angular momentum vector of a dynamically symmetric rigid body

We consider the problem of construction of optimal laws of variation in the angular momentum vector of a dynamically symmetric rigid body so as to ensure the transition of the rigid body from an arbitrary initial angular position to the required final angular position. For the functionals to be minimized, we use combined performance functionals, one of which characterizes the expenditure of time and of the squared modulus of the angular momentum vector in a given proportion, while the other characterizes the expenditure of time and momentum of the modulus of the angular momentum vector necessary to change the rigid body orientation. The control (the vector of the rigid body angular momentum) is assumed to be bounded in the modulus. The problem is solved by using Pontryagin’s maximum principle and the quaternion differential equation [1, 2] relating the vector of the dynamically symmetric rigid body angular momentum to the quaternion of orientation of the coordinate system rotating with respect to the rigid body about its dynamical symmetry axis at an angular velocity proportional to the angular momentum vector projection on the axis. The use of such a model of rotational motion leads to the problem of optimal control with the moving right end of the trajectory and significantly simplifies the analytic study of the problem of construction of optimal laws of variation in the angular momentum vector, because this model explicitly exploits the body angular momentum quaternion (control) instead of the rigid body absolute angular velocity quaternion. We construct general analytic solutions of the differential equations for the boundary-value problems which form systems of nine nonlinear differential equations. It is shown that the process of solving the differential boundary-value problems is reduced to solving two scalar algebraic transcendental equations.     

Efficient approaches of determining the motion of a spherical particle in a swirling fluid flow using weighted residual methods

The motion of a spherical particle released in a swirling fluid flow is studied employing the least-squares method and method of moments. The governing equations are obtained and solved employing the two methods. The accuracy of the results is examined against the results of a fourth-order Runge–Kutta numerical method. The effects of various parameters, namely the initial radius, initial radial velocity, initial angular velocity, and drag-to-inertia ratio, on the non-dimensional velocity profiles and particle position distribution are considered. The results show that the radial velocity increases over time while the angular velocity decreases, and that an increase in the initial radial velocity increases the particle radial distance and angular velocity but decreases the radial velocity profile.     

Integrals of motion for the classical two-body problem with drag

Integrals of motion for the two-body problem with drag are obtained by operating on the second-order vector differential equation describing the motion. The force field consists of an inverse-square gravitational attraction and a drag force proportional to the velocity vector and inversely proportional to the square of the distance to the attracting center. The developed integrals are the analogs of the Keplerian scalar energy, the vector angular momentum, and the Laplace vector.     

Solution of the problem of flow of a non-axisymmetric swirling submerged jets

This paper considers the problem of a non-axisymmetric swirling jet of an incompressible viscous fluid flowing in a space flooded with the same fluid. The far field of the jet is studied under the assumption that the angular momentum vector corresponding to the swirling of the jet is not collinear to the momentum vector of the jet. It is shown that the main terms of the asymptotic expansion of the full solution for the velocity field are determined by the exact integrals of conservation of momentum, mass, and angular momentum. An analytical solution of the problem describing the axisymmetric swirling jet is obtained.     

动态环境下光纤陀螺误差辨识与补偿技术

为了提高光纤陀螺在高动态环境下的测量精度,需要精确地辨识角加速度信息以便有效地补偿。针对直接对陀螺的角速度信息微分处理后得到角加速度的方法误差较大的问题,提出了将微分后的角加速度信息分为线性和非线性两个部分,其中线性部分采用Savitzky-golay最小二乘拟合,而非线性部分则采用RBF神经网络技术进行拟合。上述处理方法能更真实地反映实际物理过程,具有较强的自适应性和较好的拟合效果。通过试验验证,证明了该方法的有效性和准确性,提高了角加速度辨识精度,比直接微分的方法测量精度提高二个数量级,有效地补偿了陀螺仪在高动态环境下的测量精度。     

Measurement of velocity vectors with orthogonal and non-orthogonal triple-sensor probes

A new method of interpreting the signals from triple-sensor thermal anemometer probes has been developed based on fast solution for all the roots of the non-linear Jorgensen (1971) equations describing the directional response of each cylindrical sensor. The sensors can be oriented at arbitrary angles to each other, but always within a range of probe geometries that keep prong interference and thermal wake interference below acceptable levels. The properties of a class of non-orthogonal symmetric tetrahedral probe geometries are studied in relation to the range of flow vector angles that can be measured, the sensitivity of the probe with respect to changes in flow angle, and the sensitivity of the computed velocity components due to angular errors associated with the construction of the probe. The solutions of Jorgensen's equations are inherently multiple-valued, but if the velocity vector is restricted to be within a cone of angles, they are unique. It is shown that measurements with non-orthogonal triple sensor signals are sensitive to angular deviations of a few degrees of the sensor angles from the nominally orthogonal probe geometry, indicating the need of a non-orthogonal algorithm. The mean, rms, Reynolds stress, and power spectrum of the velocity in fully developed turbulent pipe flow were measured using a specially designed triple sensor probe and the proposed algorithm.Presently with the Dept. of Mechanical Engineering at The University of Iowa     

捷联惯导系统圆锥补偿算法优化设计

高速、高速度的圆锥偿补算法是提高捷联惯性导航系统（ＳＩＮＳ）性能的重要环节。本文对Ｃｈａｎ Ｇｏｏｋ Ｐａｒｋ等提出的新圆锥补偿方法进行了进一步的研究。文中给出了经典圆锥运动的角速度模型,推导出了经典圆锥运动的角增量公式、角增量叉乘公式、圆锥补偿系数方程和误差公式,并将该方法拓展至利用前一圆锥补偿周期角增量和的圆锥补偿算法。     

单陀螺多加速度计捷联惯性导航解算方法

六加速度计无陀螺惯导系统误差随时间发散比较严重。为了有效提高导航系统精度,提出了一种单陀螺仪多加速度计(五加速度计)的捷联惯性导航解算方法。该导航解算方法通过合理配置5个加速度计和1个陀螺仪,可不经积分而直接解算角速度,完全消除了加速度计输出方程中角加速度项的影响,能使在姿态和位置解算时分别减少1次积分,从而有效抑制误差随时间发散。给出了单陀螺多加速度计捷联惯导姿态和位置解算原理的理论推导过程,并对该导航解算方法进行了仿真。在仿真时间为80 s时,与无陀螺惯导相比,该方法的姿态解算和位置解算精度均提高了60%以上。     

Simulation of angular velocity sensor measurements using telemetry data on the motion of an object

An algorithm for the formation of smooth trajectories corresponding to telemetry data on the coordinates and orientation angles of a flying object with a strapdown inertial navigation system is proposed. Another algorithm of forming the angular velocity sensor measurements corresponding to this trajectory is developed. These algorithms allow one to analyze the accuracy of various numerical methods of determining the orientation of such system using the information on motions close to the real motions with known telemetry data.     

飞行器角速度测量的三轴加速度计法

飞行器角速度的测量在航空航天领域是极为重要的问题,然而现在主流的利用陀螺仪测量角速度的方法有造价较高这一问题。本文提出了一种通过测量刚体上非共线三点的加速度得到刚体角速度的方法,可以利用极为廉价的高精度加速度计较为准确地测量高速稳态飞行器的角速度。本文应用刚体运动学中的基点法,得到由刚体上非共线三点的加速度和其距离表示的刚体角速度,并对其进行了误差分析。最终采用数值模拟的方法,分析了此方法在具有较高角速度的飞行器和具有较低角速度的稳态卫星上得到的角速度的适用性。模拟结果表明,此种方法适用于稳态高角速度的飞行器。     

PIV速度场坏矢量的本征正交分解处理技术

介绍了一种针对粒子图像测速(PIV)基于本征正交分解(POD)的速度场后处理技术.该技术改变了现在后处理技术将速度场坏矢量识别和修正分开实现的局面,通过迭代方法有效地实现了速度场坏点统一的识别和修复算法.算法利用POD分解的低阶模态信息重构出可以用于坏矢量识别的参考速度场,利用该参考速度场对全流场进行坏点识别并完成修正.通过对一套光滑的PIV速度场数据引入高斯分布的随机误差,测试验证了该POD方法的优越性.在坏矢量识别方面新方法较归一化中值检验有更高的正确性,能识别大面积出现的坏矢量区域.在坏矢量修补的插值算法中,新方法的计算效率又高于传统Gappy POD方法,且计算精度优于常见的矢量场内插数学方法.特别是在数据缺失的大连通区域,该方法对物理流场有很好的预测效果.     

An instrumented drive axle to measure tire tractive performance

An instrumented drive axle is introduced for a prototype tractor using in field research on tractor and implement performance. This mechanism was developed to determine whether such an instrumented drive axle is practical. The drive axle was equipped with a set of transducers to measure wheel angular velocity, rear axle torque and dynamic weight, as well as tire side forces. Measuring the drawbar pull acting on the tractor provides data for calculating net traction, motion resistance and chassis resistance for each driven wheel.     

基于交互式多模型滤波的船体变形惯性测量方法

基于惯性测量单元的匹配滤波算法是测量船体变形的发展趋势,然而在实际航行中,船体变形模型参数是未知或存在不确定性,模型参数的这一特性对滤波估计结果影响较大。针对此问题,利用"速度+角速度"匹配算法分析了模型参数未知对滤波估计效果的影响,引入交互式多模型卡尔曼滤波方法,利用不同模型参数的似然函数进行概率分配。最后通过仿真对提出的方法进行了验证,结果表明,与传统卡尔曼滤波相比,估计精度提高了5%~10%,收敛时间提高了1倍,动态变形角的收敛时间在10 s以内,静态变形角的收敛时间在5s以内,提高了系统的环境适应性。     

Evolution of the satellite fast rotation due to the gravitational torque in a dragging medium

We study the fast rotational motion of a dynamically nonsymmetric satellite about the center of mass under the action of the gravitational torque and the drag torque. Orbital motions with arbitrary eccentricity are assumed to be given. The drag torque is assumed to be a linear function of the angular velocity. The system obtained after the averaging over the Euler-Poinsot motion is studied. We discover the following phenomena: the modulus of the angular momentum and the kinetic energy decrease, and there exist quasistationary regimes of motion (along the polhodes). The orientation of the angular momentum vector in the orbital frame of reference is determined. The general case is studied numerically, and an analytic study is performed in a neighborhood of the axial rotation and in the case of small dissipation.     

Kinematics of haylage bale in 3D space as a body of one fix point and two rotations

This paper presents mechanical-mathematical matrix simulation of haylage bale kinematics in 3D space as a body of one fix point and two rotations. There are defined: the matrices of transition from the coordinate system connected stationary with the body to the starting (global) coordinate system; the position vector, absolute linear speed and absolute linear acceleration of bale arbitrary point; the vector of absolute angular velocity and absolute angular acceleration projected in the starting and in the local coordinate systems of the body. Numerical example is provided.