Determining Spacecraft Motion from Four Star Sensor Measurements

The BOKZ-M60 star sensor (a module that measures the coordinates of stars) has been designed for determining the parameters of the orientation of the intrinsic coordinate system relative to the inertial system from observations of stellar sky sections. The methods and results of processing of measurements by a set of four BOKZ-M60 sensors on the Resurs-P satellite no. 2 have been described. The time interval at which the satellite was in orbital orientation exceeds three orbital revolutions (19003 s). The joint processing of measurements by the four sensors conducted at the same time instants allowed the sensors to be associated with the universal coordinate system. With a root-mean-square error of less than 0.4′′ for each angle of rotation around its axes, this system is consistent with the model of the satellite’s rotational motion. The position of the universal system with respect to the instrumental coordinate system of the satellite was determined from the angular velocity measurements. Here, the root-mean-square errors for the values determined by the angles of rotation of the universal system around its axes were 0.044°, 0.051°, and 0.18°. The low-frequency (with frequencies less than 0.05 Hz) variations in the positions of intrinsic sensor coordinate systems relative to the universal system do not exceed 10′′. These are periodic variations with a fundamental frequency equal to the orbital frequency. The root-mean-square values of high-frequency components of these variations do not exceed 18′′.     

An Analysis of the Low-Frequency Component in Measurements of Angular Velocity and Microacceleration onboard the Foton-12 Satellite

We compare the results of two methods used to determine the angular velocity of the Foton-12 satellite and the low-frequency component of microaccelerations onboard it. The first method is based on reconstruction of the satellite's rotational motion using the data of onboard measurements of the strength of the Earth's magnetic field. The motion (time dependence of the orientation parameters and angular velocity) was found from the condition of best approximation of the measurement data by the functions calculated along the solutions to equations of attitude motion of the satellite. The solutions found were used to calculate the quasistatic component of microaccelerations at certain points of the satellite, in particular, at the point of location of an accelerometer of the QSAM system. Filtration of the low-frequency component of the angular velocity and microacceleration from the data of measurements by a sensor of angular velocity and by the accelerometer of this system served as a second method. The filtration was made using the discrete Fourier series. A spectral analysis of the functions representing the results of determining the angular velocity and microacceleration by both methods is performed. Comparing the frequencies and amplitudes of the harmonic component of these functions allowed us to estimate the accuracy of measurements made by the QSAM system in the low-frequency range.     

Three-axis attitude determination using incomplete vector observations

Attitude determination refers to determining the orientation of a vehicle relative to its reference coordinate system. This paper presents a new algorithm for three-axis attitude determination using measurement vectors composed of incomplete vector components. The attitude determination performance of the proposed algorithm is compared with those of the TRIAD and QUEST algorithms in a simulation.     

Periodic motions of a satellite-gyrostat relative to its center of mass under the action of gravitational torque

We investigated periodic motions of the axis of symmetry of a model satellite of the Earth, which are similar to the motions of the longitudinal axes of the Mir orbital station in 1999–2001 and the Foton-M3 satellite in 2007. The motions of these spacecraft represented weakly disturbed regular Euler precession with the angular momentum vector of motion relative to the center of mass close to the orbital plane. The direction of this vector during the motion was not practically changed. The model satellite represents an axisymmetric gyrostat with gyrostatic moment directed along the axis of symmetry. The satellite moves in a circular orbit and undergoes the action of the gravitational torque. The motion of the axis of symmetry of this satellite relative to the absolute space is described by fourth-order differential equations with periodic coefficients. The periodic solutions to this system with special symmetry properties are constructed using analytical and numerical methods.     

一种空间推扫型光学成像系统几何映射方法

卫星光学遥感器在轨成像会受到颤振的影响,因此图像品质受姿态稳定度的影响很大,而高分辨率图像受到平台误差的影响更加明显。通过研究空间相机的几何模型,提出了一种从地球坐标系到空间光学遥感器坐标系之间的转换关系;分析了在轨卫星的姿态误差和运动源,并在几何模型中加入了内外方位元素特征;然后进行了空间TDICCD相机的成像仿真实验。为了在像面上模拟颤振,分别进行不同模态的颤振仿真,并且对视线范围内多模态综合作用进行仿真。仿真实验是基于三个轴系方向的,并且计算了TDICCD仿真图像的几何畸变量,模型中几何畸变量的测量尺度达到亚像素级,结果有利于指导卫星平台和遥感器的参数设计。     

行星着陆动力下降段相对视觉导航方法

针对行星着陆动力下降段视觉导航自然路标匮乏的问题,提出了一种相对视觉导航方法。该方法利用相机和雷达的测量信息构建相对导航坐标系并求解随机视觉特征点在该坐标系下的位置矢量,利用求解得到的特征点为导航参考,设计相对导航系统,估计着陆器在相对导航坐标系下的位置、速度及姿态信息。同时,构建可观性矩阵,解耦分析位置和姿态的可观性。通过可观性分析可知利用相对导航坐标系下的一个随机特征点即可实现着陆器全状态可观。最后通过仿真分析着陆器状态误差,验证了可观测度理论分析及导航性能。该相对导航方法无需行星地形数据库,且可以实现着陆器全状态的高精度估计,满足行星精确软着陆的需求。     

Modes of uncontrolled rotational motion of the <Emphasis Type="Italic">Progress M-29M</Emphasis> spacecraft

We have reconstructed the uncontrolled rotational motion of the Progress M-29M transport cargo spacecraft in the single-axis solar orientation mode (the so-called sunward spin) and in the mode of the gravitational orientation of a rotating satellite. The modes were implemented on April 3–7, 2016 as a part of preparation for experiments with the DAKON convection sensor onboard the Progress spacecraft. The reconstruction was performed by integral statistical techniques using the measurements of the spacecraft’s angular velocity and electric current from its solar arrays. The measurement data obtained in a certain time interval have been jointly processed using the least-squares method by integrating the equations of the spacecraft’s motion relative to the center of mass. As a result of processing, the initial conditions of motion and parameters of the mathematical model have been estimated. The motion in the sunward spin mode is the rotation of the spacecraft with an angular velocity of 2.2 deg/s about the normal to the plane of solar arrays; the normal is oriented toward the Sun or forms a small angle with this direction. The duration of the mode is several orbit passes. The reconstruction has been performed over time intervals of up to 1 h. As a result, the actual rotational motion of the spacecraft relative to the Earth–Sun direction was obtained. In the gravitational orientation mode, the spacecraft was rotated about its longitudinal axis with an angular velocity of 0.1–0.2 deg/s; the longitudinal axis executed small oscillated relative to the local vertical. The reconstruction of motion relative to the orbital coordinate system was performed in time intervals of up to 7 h using only the angularvelocity measurements. The measurements of the electric current from solar arrays were used for verification.     

星上遥测的精度分析

分析了三轴稳定平台卫星产生遥测测量误差的原因,并对典型星载传感器(热敏电阻、压力变换器、电压)、模拟量通道、A/D变换器等单个误差项目逐一进行了误差分析。根据误差正态分布的特性,得出单个项目的最大测量误差及均方误差,然后合成单个项目的误差,给出整星各种类型被测参数的总误差。最后,根据目前卫星平台的设计现状,提出了进一步提高测量精度的建议。     

CCD太阳敏感器误差分析与补偿

介绍了星载CCD太阳敏感器的工作原理,用空间几何模型阐述了线阵CCD太阳敏感器测量两轴姿态信息的方法,进行了误差分析,建立了系统的误差补偿模型。通过标定试验,确定了模型参数,进行了物理补偿,同时针对系统的残差,提出了数学补偿的方法。测试结果表明敏感器实现了较高的测量精度,验证了误差补偿方法的有效性。     

Estimating the accuracy of the technique of reconstructing the rotational motion of a satellite based on the measurements of its angular velocity and the magnetic field of the Earth

The paper has studied the accuracy of the technique that allows the rotational motion of the Earth artificial satellites (AES) to be reconstructed based on the data of onboard measurements of angular velocity vectors and the strength of the Earth magnetic field (EMF). The technique is based on kinematic equations of the rotational motion of a rigid body. Both types of measurement data collected over some time interval have been processed jointly. The angular velocity measurements have been approximated using convenient formulas, which are substituted into the kinematic differential equations for the quaternion that specifies the transition from the body-fixed coordinate system of a satellite to the inertial coordinate system. Thus obtained equations represent a kinematic model of the rotational motion of a satellite. The solution of these equations, which approximate real motion, has been found by the least-square method from the condition of best fitting between the data of measurements of the EMF strength vector and its calculated values. The accuracy of the technique has been estimated by processing the data obtained from the board of the service module of the International Space Station (ISS). The reconstruction of station motion using the aforementioned technique has been compared with the telemetry data on the actual motion of the station. The technique has allowed us to reconstruct the station motion in the orbital orientation mode with a maximum error less than 0.6° and the turns with a maximal error of less than 1.2°.     

一种考虑地球扁率的卫星自主导航方法研究

研究用2个红外地球敏感器和1个星敏感器实现卫星自主导航的方法,地心矢量的测量精度是影响导航精度的重要原因之一,而地心矢量的测量又受到地球扁率的影响.研究地球扁率对地心矢量测量的影响,并提出一种零姿态扁率误差补偿方法,通过仿真验证了这种导航方法及扁率误差补偿算法的有效性.     

Determination of the Attitude Motion of a Satellite Based on a Kinematical Model of Motion and Using Data of Measurements of Its Angular Velocity and the Earth’s Magnetic Field Strength

An integral statistical procedure of determination of the attitude motion of a satellite using the data of onboard measurements of angular velocity vectors and the strength of the Earth’s magnetic field (EMF) is suggested. The procedure uses only the equations of kinematics of a solid body and is applicable to determining both controlled and uncontrollable motions of a satellite at any external mechanical moments acting upon it. When applying this procedure, the data of measurements of both types, accumulated during a certain interval of time, are processed jointly. The data of measuring the angular velocity are smoothed by discrete Fourier series, and these series are substituted into kinematical Poisson equations for elements of the matrix of transition from a satellite-fixed coordinate system to the orbital coordinate system. The equations thus obtained represent a kinematical model of the satellite motion. The solution to these equations (which approximate the actual motion of a satellite) is found from the condition of the best (in the sense of the least squares method) fit of the data of measuring the EMF strength vector to its calculated values. The results of testing the suggested procedure using the data of measurements of the angular velocity vectors onboard the Foton-12 satellite and measurements of EMF strengths are presented.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 295–305.Original Russian Text Copyright © 2005 by Abrashkin, Volkov, Voronov, Egorov, Kazakova, Pankratov, Sazonov, Semkin.     

Development of a high-precision selenodetic coordinate system for the physical surface of the Moon based on LED beacons on its surface

The paper presents a mathematical algorithm for processing an array of angular measurements of light beacons on images of the lunar surface onboard a polar artificial lunar satellite (PALS) during the Luna–Glob mission and coordinate–time referencing of the PALS for the development of reference selenocentric coordinate systems. The algorithm makes it possible to obtain angular positions of point light beacons located on the surface of the Moon in selenocentric celestial coordinates. The operation of measurement systems that determine the position and orientation of the PALS during its active existence have been numerically simulated. Recommendations have been made for the optimal use of different types of measurements, including ground radio trajectory measurements, navigational star sensors based on the onboard star catalog, gyroscopic orientation systems, and space videos of the lunar surface.     

基于测距观测的静地卫星定轨精度分析

在卫星动力法定轨的协方差分析基础上,提出了一种针对地球静止轨道(GEO)卫星的简化定轨精度分析方法。根据GEO卫星的线性化状态转移方程,通过设定地面跟踪网坐标和卫星星下点经度计算叠加矩阵,由观测弧长和采样间隔直接计算定轨精度评定公式中的主要部分。公式扩展后,能比较各种系统误差源对定轨精度的影响,并将影响较大的作为附加参数纳入估计过程并重新评价定轨精度。用该法对10 m定轨精度的测距跟踪网优化设计和测距偏差对定轨精度的影响特性进行分析的结果表明,测量系统中的系统性误差可能以近20的放大倍率传播到卫星沿迹方向和法向,且不能通过自校准测距常值偏差提高定轨精度。     

星敏感器光轴测量的锥面误差模型及其应用

星敏感器是卫星高精度姿态测量系统中的重要器件,根据其测量可以建立不同形式的星敏感器测量模型,准确分析测量模型中测量误差的特性是保证卫星姿态确定精度的重要条件。本文针对广泛采用的星敏感器光轴矢量测量方程,从几何角度出发,结合实际情况,提出了一种新颖的星敏感器光轴测量的锥面误差模型。在两个锥面参数分别服从一定的概率分布的条件下,对测量误差特性进行了深入分析,确定出新的测量误差协方差矩阵。上述研究能够在不增加算法计算量的前提下,从新的角度,更为直观地建立了星敏感器光轴矢量测量模型。最后在仿真实验中,将新的锥面误差测量模型应用于基于扩展卡尔曼滤波（EKF）的姿态确定方法中,结果表明了利用该测量模型进行姿态确定的有效性。     

中心刚体-柔性梁系统的旋转运动控制

中心刚体-柔性梁系统是一个典型的刚柔耦合动力学系统,对其动力学与控制的研究一直是国内外的研究热点问题之一。采用一次近似简化模型对中心刚体-柔性梁系统的旋转运动控制进行研究,其中控制律采用变结构控制方法进行设计。切换面的设计采用最优化方法而得出,控制律的设计采用指数趋近律方法。因为所设计的控制律是模态坐标的函数,而模态坐标不可能通过物理测量直接获得,因此给出一个从物理测量中提取模态坐标的滤波器方法。数值仿真结果显示,模态滤波器能够较好地提取出控制律所需的模态坐标;变结构控制能够使得系统达到所期望的运动状态,并可使柔性梁的残余振动得到抑制。     

陀螺经纬仪在大型航天产品精测中的应用

陀螺经纬仪通常是做某一方向与当地大地北向的方位角关系测量用。文章针对“天宫一号”目标飞行器精测中遇到的问题,即高空不同平台间两台设备需要姿态关系测量的需求,通过对陀螺经纬仪测量原理的研究,借助大地坐标系作为中间传递坐标系,解决了经纬仪测量因互瞄被遮挡无法建立基准镜坐标系间关系的问题。测量误差分析结果验证了这种新方法的可行性,该方法可用于大型航天产品设备安装精度的测量。     

考虑传感器故障检测能力的PHM系统传感器优化配置方法

传感器优化配置是航空航天设备PHM系统功能得以有效实现的基础和保证。针对目前传感器配置研究中未考虑传感器实际属性的问题,建立了考虑传感器故障检测能力的PHM系统传感器优化配置模型。首先分析了系统故障-传感器相关性矩阵的含义,将传感器的故障检测能力和相关性矩阵相结合,以概率形式描述了传感器对故障的检测性能。在此基础上根据系统的测试性指标要求建立传感器优化配置模型,并采用混沌二进制粒子群优化算法求解。仿真实例结果表明,本文建立的优化模型更加符合实际情况,配置结果更加准确和可靠。     

Fault detection,identification and reconstruction for gyroscope in satellite based on independent component analysis

Although satellites are designed with high reliability, faults do occur when satellites are in orbit. To avoid the important services being affected, redundancy is used in satellites. There are many sensors in satellites. In order to reduce the cost, space, weight and power consumption, redundant sensors should be added to satellite as few as possible. Analytical redundancy is an efficient way to optimize the application of redundant. The gyroscope is the attitude determination sensor of the satellite. The minimum redundant structure of the gyroscope system is as follows: three gyroscopes installed in three-axis orthogonally and one gyroscope installed with slantwise for redundancy(3o+1S).To achieve fault detection, identification and reconstruction, hypothesis of statistical independence between the three-axis angular rates and hypothesis of statistical independence between the angular rates and fault are proposed. The scenario that only one sensor is faulting and there are only additive fault and full fault is supposed. Under these assumptions, firstly a threshold method is used for fault detection. After a fault is detected, independent component analysis (ICA) based algorithm for fault identification is employed. To overcome the ambiguities of ICA, correlation coefficients and prior information of the mixed matrix are used. Finally, the reconstruction matrix is obtained. By using this matrix fault signal is extracted so that the yaw, roll and pitch axes (three-axis) angular rates of the satellite can be recovered. Numerical simulations show this method can fulfill fault detection, identification and reconstruction of the gyroscope system.     

用于微振动测量的高精度加速度传感器标定方法

微振动试验中所用的加速度传感器简称高精度加速度传感器,其相比于常规加速度传感器测量量级很低,可以达到10-5g量级甚至更低,用常规的加速度动态标定技术无法实现该量级水平的标定,也无从验证其测量精度的准确性。针对高精度加速度传感器测试精度的标定难题,文章提出在气浮台上设置比对梁的方法,通过激光测振仪和高精度加速度传感器对同一测点进行测量,并将两者的测量结果进行比对分析,以标定高精度加速度传感器的低量级测试精度。同时设计试验对手头现有的微振动加速度传感器进行标定以验证该方法的有效性,试验结果表明:利用激光测振仪标定现有高精度加速度传感器得到的比对结果符合预期;高精度加速度传感器测得的时域波形及频域波形与激光测振仪测得的基本一致,比对偏差在10%左右,满足标定方法要求。