基于GPS的航天器姿态、相对姿态确定研究
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摘要
本文系统地研究了GPS姿态确定问题。GPS姿态确定问题分两大部分，一部分是模糊度求解，另一部分是姿态确定算法。
深入分析了模糊度求解的基本原理，建立了模糊度求解的完整理论。在此基础上，提出了一种基于遗传算法的模糊度搜索算法。通过白化处理模糊度，减少模糊度搜索中指标函数的局部极值点，采用适当的编码和遗传操作使得在种群个体较少的情况下避免搜索陷入早熟。通过仿真结果与原有的基于简单遗传算法搜索策略相比提高了搜索速度，能够快速得到正确模糊度组合。提出了一种综合的模糊度求解算法。利用三差最小二乘求解模糊度浮点解，然后采用整数高斯变换降低模糊度分量间的相关性，再根据QR分解和基线几何约束减少需搜索的模糊度组合，采用Cholesky分解在搜索过程中及早淘汰不正确的模糊度组合，最后利用ratio检验与基线几何约束条件相结合检验模糊度组合，尽快固定正确的模糊度。通过静、动态实验验证了该算法。
深入分析了GPS姿态确定的原理，定性分析了GPS姿态确定的各种误差，在此基础上提出了一种基于矩阵元素的卡尔曼滤波算法。以矩阵元素为状态变量，简化了算法结构，提高了算法速度。并进一步提出了并行卡尔曼滤波算法。将递推过程分为相对独立的三个部分，可以同时分别计算，大大加快了算法速度。针对模型的不准确带来的滤波性能下降甚至发散，提出了分别基于运动学模型和动力学模型的预测滤波算法。该算法首先估计模型误差，然后利用模型误差修正系统模型，由修正后的系统模型给出状态估计。在有较大时变干扰力矩情况下基于动力学模型的预测滤波算法能够很好地跟踪姿态变化，而在对系统模型一无所知，系统动态不高的条件下利用基于运动学的预测滤波算法可以得到较好的姿态估计。提出了基于QUEST算法的相对姿态确定算法和基于矩阵元素的最小二乘相对姿态确定算法。两种算法都不需要编队卫星间的姿态动力学联系。通过建立联系编队卫星姿态关系的虚拟观测量求解相对姿态。定性分析了相对位置确定中的误差。讨论了三种相对位置确定方案。建立了GPS三维姿态确定和编队卫星相对姿态确定实验系统，编制了姿态确定、相对姿态确定软件。设计了实验，验证姿态确定及相对姿态、位置确定。
In this thesis, the method of the attitude determination by GPS is developed. The method consists of two parts: ambiguity resolution and attitude determination.
The theory of ambiguity resolution is elaborated, and model of ambiguity resolution is established. An algorithm of ambiguity resolution based on genetics algorithm is proposed. By whitening the covariance matrix of flat ambiguity, correlation between ambiguity components, the number of local extrema of cost function is reduced. The search program getting into precocity is avoided by suitable encoding and genetic operation. Combining with the genetic algorithms, the right ambiguity is rapidly obtained. A integrated algorithm of ambiguity resolution is proposed. By using triple carrier phase, integer Gauss transformations, QR factorization, Cholesky factorization, and geometry constraint, the correlation between ambiguity components is reduced, and more error ambiguity can be discarded, also process of ambiguity searching getting rapidly. The ratio test combining constraint of baseline is used to fix ambiguity rapidly. The algorithm is tested by static and dynamic experiment.
Theory of attitude determination by GPS is addressed in detial. Error of attitude determination by GPS is analyzed. Then a Kalman filter is developed in which taking the components of attitude matrix as state variable, Kalman filter is simplified and the veolecty of algorithm is raised. Furthermore a distributed Kalman filter is developed. In this algorithm, Kalman filter is divided into three independent parts, which is processed at the same timed. For Kalman filter will tend to instability if dynamical model is incorrect, two algorithms is developed named predictive filter, Which are based on kinematics model and dynamics model respectively. The procedure of the algorithm consists of three steps, first, model error was estimated, second, model error is used to correct system model, finaly attitude is estimated with corrected model. Simulation result indicated that predictive filter of the dynamics model may be followed the attitude movement, if disturbance moment is time variable and large relative to gradient moment of gravity, and predictive filter based kinematics is
suitable if there is no information about dynamics.
Two algorithms are developed to estimate relative attitude between spacecraft in formation flying, one is algorithm baesd QUEST (QUaternion ESTimator) and the other is least square estimation based on element of attitude matrix. The two algorithms do not use information of relative attitude dynamics between spacecrafts. Relative attitude is estimated by pseudo observation. Error of relative positioning is analyzed qualitatively.
A test platform for three dimensions attitude and relative attitude determination is established. The algorithms and the test platform is tested. The attitude determination algorithm of predictive filter, QUEST algorithm, least square estimation based on element of attitude matrix are tested by the platform.
深入分析了模糊度求解的基本原理，建立了模糊度求解的完整理论。在此基础上，提出了一种基于遗传算法的模糊度搜索算法。通过白化处理模糊度，减少模糊度搜索中指标函数的局部极值点，采用适当的编码和遗传操作使得在种群个体较少的情况下避免搜索陷入早熟。通过仿真结果与原有的基于简单遗传算法搜索策略相比提高了搜索速度，能够快速得到正确模糊度组合。提出了一种综合的模糊度求解算法。利用三差最小二乘求解模糊度浮点解，然后采用整数高斯变换降低模糊度分量间的相关性，再根据QR分解和基线几何约束减少需搜索的模糊度组合，采用Cholesky分解在搜索过程中及早淘汰不正确的模糊度组合，最后利用ratio检验与基线几何约束条件相结合检验模糊度组合，尽快固定正确的模糊度。通过静、动态实验验证了该算法。
深入分析了GPS姿态确定的原理，定性分析了GPS姿态确定的各种误差，在此基础上提出了一种基于矩阵元素的卡尔曼滤波算法。以矩阵元素为状态变量，简化了算法结构，提高了算法速度。并进一步提出了并行卡尔曼滤波算法。将递推过程分为相对独立的三个部分，可以同时分别计算，大大加快了算法速度。针对模型的不准确带来的滤波性能下降甚至发散，提出了分别基于运动学模型和动力学模型的预测滤波算法。该算法首先估计模型误差，然后利用模型误差修正系统模型，由修正后的系统模型给出状态估计。在有较大时变干扰力矩情况下基于动力学模型的预测滤波算法能够很好地跟踪姿态变化，而在对系统模型一无所知，系统动态不高的条件下利用基于运动学的预测滤波算法可以得到较好的姿态估计。提出了基于QUEST算法的相对姿态确定算法和基于矩阵元素的最小二乘相对姿态确定算法。两种算法都不需要编队卫星间的姿态动力学联系。通过建立联系编队卫星姿态关系的虚拟观测量求解相对姿态。定性分析了相对位置确定中的误差。讨论了三种相对位置确定方案。建立了GPS三维姿态确定和编队卫星相对姿态确定实验系统，编制了姿态确定、相对姿态确定软件。设计了实验，验证姿态确定及相对姿态、位置确定。
In this thesis, the method of the attitude determination by GPS is developed. The method consists of two parts: ambiguity resolution and attitude determination.
The theory of ambiguity resolution is elaborated, and model of ambiguity resolution is established. An algorithm of ambiguity resolution based on genetics algorithm is proposed. By whitening the covariance matrix of flat ambiguity, correlation between ambiguity components, the number of local extrema of cost function is reduced. The search program getting into precocity is avoided by suitable encoding and genetic operation. Combining with the genetic algorithms, the right ambiguity is rapidly obtained. A integrated algorithm of ambiguity resolution is proposed. By using triple carrier phase, integer Gauss transformations, QR factorization, Cholesky factorization, and geometry constraint, the correlation between ambiguity components is reduced, and more error ambiguity can be discarded, also process of ambiguity searching getting rapidly. The ratio test combining constraint of baseline is used to fix ambiguity rapidly. The algorithm is tested by static and dynamic experiment.
Theory of attitude determination by GPS is addressed in detial. Error of attitude determination by GPS is analyzed. Then a Kalman filter is developed in which taking the components of attitude matrix as state variable, Kalman filter is simplified and the veolecty of algorithm is raised. Furthermore a distributed Kalman filter is developed. In this algorithm, Kalman filter is divided into three independent parts, which is processed at the same timed. For Kalman filter will tend to instability if dynamical model is incorrect, two algorithms is developed named predictive filter, Which are based on kinematics model and dynamics model respectively. The procedure of the algorithm consists of three steps, first, model error was estimated, second, model error is used to correct system model, finaly attitude is estimated with corrected model. Simulation result indicated that predictive filter of the dynamics model may be followed the attitude movement, if disturbance moment is time variable and large relative to gradient moment of gravity, and predictive filter based kinematics is
suitable if there is no information about dynamics.
Two algorithms are developed to estimate relative attitude between spacecraft in formation flying, one is algorithm baesd QUEST (QUaternion ESTimator) and the other is least square estimation based on element of attitude matrix. The two algorithms do not use information of relative attitude dynamics between spacecrafts. Relative attitude is estimated by pseudo observation. Error of relative positioning is analyzed qualitatively.
A test platform for three dimensions attitude and relative attitude determination is established. The algorithms and the test platform is tested. The attitude determination algorithm of predictive filter, QUEST algorithm, least square estimation based on element of attitude matrix are tested by the platform.
引文
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