微小卫星及其编队轨道与姿态一体化确定方法研究
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摘要
自主状态确定是卫星控制的基本前提和基础。对于成本和重量有严格限制的微小卫星，星上敏感器资源及其性能往往有限，如何充分利用有限的敏感器资源、完成自主状态确定任务、改善卫星轨道与姿态确定的精度，进而提高微小卫星功能密度，已成为当前航天领域的热点和难点问题。本学位论文以微小卫星及其编队轨道与姿态等状态确定为研究背景，对单星自主状态确定、卫星编队相对/绝对状态估计等相关问题进行深入研究，具体内容如下：
为充分利用地磁场测量数据中包含的轨道与姿态信息，在基于地磁场测量的卫星轨道与姿态独立确定方法基础上，采用轨道与姿态确定串并联混合的耦合确定模式，提出了基于磁强计的卫星轨道与姿态耦合确定方法。该方法在初始误差较大时采用先定轨后定姿的串联模式确保系统收敛性，待串联策略收敛后采用基于地磁场矢量的姿轨并联确定模式提高系统估计精度，同时基于新息序列设计鲁棒卡尔曼滤波算法，通过自适应调整滤波器的增益矩阵来降低轨道与姿态耦合确定时滤波误差的相互影响。仿真结果表明了该方法在提高系统鲁棒性和估计精度等方面的有效性。
考虑卫星在轨运动以及敏感器测量等方面轨道与姿态相互耦合的特性，在建立卫星轨道与姿态耦合动力学模型和敏感器测量模型的基础上，提出了基于多速率滤波算法的卫星轨道与姿态一体化确定方法，并采用局部可观测性理论以及可观测性矩阵条件数和奇异值分解等对系统的可观测性及可观测度进行分析，从理论方面论述了轨道姿态一体化确定的可行性。为避免由于采用一体化确定模式导致滤波维数增加，进而导致计算量过大的问题，引入长短周期不同时刻点分别采用Schmidt-EKF和统一滤波算法的多速率滤波思想，在保证确定精度的前提下有效地降低了计算量。
针对从星上敏感器测量主星上多个点光源方向矢量的测量模式，提出了基于高斯二阶卡尔曼滤波算法的编队卫星相对位置与姿态一体化确定方法。针对应用中由于待估计特征点与质心不重合等问题，建立考虑特征点质心偏移的相对运动状态方程，设计了基于乘性四元数的UKF算法，提出了考虑非质心影响的相对位置与姿态估计方法，并采用Fisher信息矩阵和误差方差矩阵的迹分析了星间相对距离、点光源数目及其分布情况等对估计精度的影响。为基于视觉的卫星编队相对状态估计系统的设计及应用奠定基础。
针对具有磁强计、陀螺及视觉敏感器等配置的编队成员卫星绝对轨道与姿态确定问题，在基于磁强计/陀螺的姿轨一体化确定算法和基于视觉测量的编队相对状态一体化确定算法的基础上，设计联邦滤波和两步滤波两种分散式滤波算法，提出了考虑相对测量信息的编队卫星绝对轨道与姿态一体化确定方法。在保证高精度绝对状态确定的同时，提高了系统的可靠性和容错能力。针对从星磁强计故障情况，提出了先主星后从星的串联确定策略，并设计了基于球形采样的UKF算法，实现编队双星的绝对状态估计。在双星磁强计都故障时，分析了依靠星间相对测量进行编队卫星绝对轨道确定的可行性。为绝对轨道与姿态测量信息有限时的编队卫星轨道与姿态确定提供了一条可行的解决途径。
Autonomous state determination is the basis of satellite control. Due to the strictlimits of weight and cost, there are always few sensors on small satellite. So how to makefull use of the limited sensor resource to accomplish orbit and attitude determination,improve determination accuracy, and then improve the functional density of smallsatellite has become a hot and difficult problem in the field of aerospace. Under thebackground of orbit and attitude determination for small satellite and formation, thisdissertation focuses on autonomous state determination for single satellite andrelative/absolute state determination for formation satellite. The major contents of thisdissertation consist of the following parts.
To make full use of earth magnetic field measurement data, an orbit and attitudecoupled determination method is proposed based on traditional separate processing mode,which combines sequential and parallel modes for orbit and attitude determination. Wheninitial estimation error is large, orbit and attitude are sequentially determined in thesequential mode to ensure the convergence. Then they are synchronously determined inthe parallel mode both using earth magnetic field vector measurement when theestimation error becomes small enough, which improves the estimation accuracy.Meanwhile, an innovation-based robust Kalman filter is designed to reduce the influencebetween the orbit and attitude determination systems through adjusting the Kalman gain,which improves the determination accuracy and enhances the robustness of the system.
Considering the coupling between orbit and attitude from satellite motion andsensor measurement, coupled dynamic model and measurement model are established,and a multi-rate-based integrated orbit and attitude determination algorithm is proposed.System observability is analysed based on local observability theory, and degree ofobservability is analysed through condition number and singular value decomposition ofobservability matrix, which can verify the feasibility in theory for integrated orbit andattitude determination. In order to avoid the large computation induced by the increase ofsystem dimension, a multi-rate filter is introduced. At the short-period sampling time, aSchmidt-EKF is adopted to estimate attitude and propagate orbit. While at the long-period sampling time, a unified Kalman filter is used to estimate orbit and attitudesimultaneously. Simulation results indicate that this method can reduce computation loadeffectively with guarantee of estimation accuracy.
Regarding to deputy sensor measuring direction vectors of different beacons onchief, a Gauss second-order Kalman filter is proposed to determine the relative positionand attitude for formation satellite. For relative state estimation of the point apart from the center of mass on deputy, a coupled relative translational and rotational dynamics isestablished, and an UKF algorithm is proposed to estimate relative position and attitude.Besides, the influence of relative distance, number of beacons and their distribution onestimation accuracy is analysed through the traces of the Fisher information matrix anderror covariance matrix. These can lay the foundation for vision-based relative statemeasurement system design and application for formation satellite.
For the absolute state determination of formation satellite with magnetometer, gyroand relative measurement, federated filter and two-step filter are designed respectively toestimate the absolute orbit and attitude of formation satellite based on integrated orbitand attitude determination method for single satellite and relative state estimation methodfor formation satellite, both of which improve the reliability and fault tolerance undercondition of guarantee of estimation accuracy. State estimation with sensor failure is alsoinvestigated. When deputy magnetometer fails, a chief and deputy state sequentialdetermination scheme is proposed based on a spherical sampled UKF, thus thecomputation load is reduced. In view of the magnetometer failure of both satellites, thefeasibility of absolute orbit determination only based on relative measurement is analysed.These researches can provide a viable approach for absolute orbit and attitudedetermination of formation satellite with limited measurement.
为充分利用地磁场测量数据中包含的轨道与姿态信息，在基于地磁场测量的卫星轨道与姿态独立确定方法基础上，采用轨道与姿态确定串并联混合的耦合确定模式，提出了基于磁强计的卫星轨道与姿态耦合确定方法。该方法在初始误差较大时采用先定轨后定姿的串联模式确保系统收敛性，待串联策略收敛后采用基于地磁场矢量的姿轨并联确定模式提高系统估计精度，同时基于新息序列设计鲁棒卡尔曼滤波算法，通过自适应调整滤波器的增益矩阵来降低轨道与姿态耦合确定时滤波误差的相互影响。仿真结果表明了该方法在提高系统鲁棒性和估计精度等方面的有效性。
考虑卫星在轨运动以及敏感器测量等方面轨道与姿态相互耦合的特性，在建立卫星轨道与姿态耦合动力学模型和敏感器测量模型的基础上，提出了基于多速率滤波算法的卫星轨道与姿态一体化确定方法，并采用局部可观测性理论以及可观测性矩阵条件数和奇异值分解等对系统的可观测性及可观测度进行分析，从理论方面论述了轨道姿态一体化确定的可行性。为避免由于采用一体化确定模式导致滤波维数增加，进而导致计算量过大的问题，引入长短周期不同时刻点分别采用Schmidt-EKF和统一滤波算法的多速率滤波思想，在保证确定精度的前提下有效地降低了计算量。
针对从星上敏感器测量主星上多个点光源方向矢量的测量模式，提出了基于高斯二阶卡尔曼滤波算法的编队卫星相对位置与姿态一体化确定方法。针对应用中由于待估计特征点与质心不重合等问题，建立考虑特征点质心偏移的相对运动状态方程，设计了基于乘性四元数的UKF算法，提出了考虑非质心影响的相对位置与姿态估计方法，并采用Fisher信息矩阵和误差方差矩阵的迹分析了星间相对距离、点光源数目及其分布情况等对估计精度的影响。为基于视觉的卫星编队相对状态估计系统的设计及应用奠定基础。
针对具有磁强计、陀螺及视觉敏感器等配置的编队成员卫星绝对轨道与姿态确定问题，在基于磁强计/陀螺的姿轨一体化确定算法和基于视觉测量的编队相对状态一体化确定算法的基础上，设计联邦滤波和两步滤波两种分散式滤波算法，提出了考虑相对测量信息的编队卫星绝对轨道与姿态一体化确定方法。在保证高精度绝对状态确定的同时，提高了系统的可靠性和容错能力。针对从星磁强计故障情况，提出了先主星后从星的串联确定策略，并设计了基于球形采样的UKF算法，实现编队双星的绝对状态估计。在双星磁强计都故障时，分析了依靠星间相对测量进行编队卫星绝对轨道确定的可行性。为绝对轨道与姿态测量信息有限时的编队卫星轨道与姿态确定提供了一条可行的解决途径。
Autonomous state determination is the basis of satellite control. Due to the strictlimits of weight and cost, there are always few sensors on small satellite. So how to makefull use of the limited sensor resource to accomplish orbit and attitude determination,improve determination accuracy, and then improve the functional density of smallsatellite has become a hot and difficult problem in the field of aerospace. Under thebackground of orbit and attitude determination for small satellite and formation, thisdissertation focuses on autonomous state determination for single satellite andrelative/absolute state determination for formation satellite. The major contents of thisdissertation consist of the following parts.
To make full use of earth magnetic field measurement data, an orbit and attitudecoupled determination method is proposed based on traditional separate processing mode,which combines sequential and parallel modes for orbit and attitude determination. Wheninitial estimation error is large, orbit and attitude are sequentially determined in thesequential mode to ensure the convergence. Then they are synchronously determined inthe parallel mode both using earth magnetic field vector measurement when theestimation error becomes small enough, which improves the estimation accuracy.Meanwhile, an innovation-based robust Kalman filter is designed to reduce the influencebetween the orbit and attitude determination systems through adjusting the Kalman gain,which improves the determination accuracy and enhances the robustness of the system.
Considering the coupling between orbit and attitude from satellite motion andsensor measurement, coupled dynamic model and measurement model are established,and a multi-rate-based integrated orbit and attitude determination algorithm is proposed.System observability is analysed based on local observability theory, and degree ofobservability is analysed through condition number and singular value decomposition ofobservability matrix, which can verify the feasibility in theory for integrated orbit andattitude determination. In order to avoid the large computation induced by the increase ofsystem dimension, a multi-rate filter is introduced. At the short-period sampling time, aSchmidt-EKF is adopted to estimate attitude and propagate orbit. While at the long-period sampling time, a unified Kalman filter is used to estimate orbit and attitudesimultaneously. Simulation results indicate that this method can reduce computation loadeffectively with guarantee of estimation accuracy.
Regarding to deputy sensor measuring direction vectors of different beacons onchief, a Gauss second-order Kalman filter is proposed to determine the relative positionand attitude for formation satellite. For relative state estimation of the point apart from the center of mass on deputy, a coupled relative translational and rotational dynamics isestablished, and an UKF algorithm is proposed to estimate relative position and attitude.Besides, the influence of relative distance, number of beacons and their distribution onestimation accuracy is analysed through the traces of the Fisher information matrix anderror covariance matrix. These can lay the foundation for vision-based relative statemeasurement system design and application for formation satellite.
For the absolute state determination of formation satellite with magnetometer, gyroand relative measurement, federated filter and two-step filter are designed respectively toestimate the absolute orbit and attitude of formation satellite based on integrated orbitand attitude determination method for single satellite and relative state estimation methodfor formation satellite, both of which improve the reliability and fault tolerance undercondition of guarantee of estimation accuracy. State estimation with sensor failure is alsoinvestigated. When deputy magnetometer fails, a chief and deputy state sequentialdetermination scheme is proposed based on a spherical sampled UKF, thus thecomputation load is reduced. In view of the magnetometer failure of both satellites, thefeasibility of absolute orbit determination only based on relative measurement is analysed.These researches can provide a viable approach for absolute orbit and attitudedetermination of formation satellite with limited measurement.
引文
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