卫星轨道控制与轨道确定算法研究
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摘要
随着航天任务需求的多样化和复杂化，卫星的轨道控制和轨道确定提出了新的要求。经典的轨道控制和轨道确定方法有时无法满足这些要求。本文是基于这些新的要求对轨道控制和轨道确定算法进行了研究。
传统的轨道控制一般基于两种方法，一种是代数优化方法，这种方法与卫星的轨道几何特性相结合进行分析，将轨道的几何特性和优化指标用代数方程的形式表示出来进行求解，这种方法主要用于冲量式控制。但在多指标的要求下，这种方法难以求得最优解；另一种方法是应用Pontryagin最大值原理解决有限推力最优控制问题，但对复杂的或者含有不确定因素的系统往往难以奏效。本文用智能控制的方法来解决轨道控制中某些用经典控制难以求解的问题：用进化算法解决轨道转移的时间-能量优化问题，用模糊控制方法解决相对运动方程有限推力控制问题。
本文首先对一般的进化算法进行了研究，对SPEA方法(一种多目标进化算法)进行了改进：引入多体交叉和Cauchy变异来代替两体交叉和正态变异，并对SPEA进行了收敛性分析。然后分别用一般的进化算法和改进的SPEA方法解决轨道转移的时间-能量优化问题，对于相对运动方程有限推力控制问题，本文用模糊控制的方法加以解决。
轨道确定的传统估计算法是最小二乘算法和Kalman滤波。当观测数据含有非线性因素时，它们的估计性能比较差，而这些非线性因素在实际当中往往是不可避免的。本文提出的半参数回归方法较好的解决了上述问题，并给出了相应的算法：这是一种线性估计和非线性估计相互迭代的方法，线性估计是最小二乘法，而非线性估计是基于小波对残差去噪的方法。本文提出的这种算法比经典的最小二乘算法或Kalman滤波方法具有更高的定轨精度，仿真数据和实际观测数据的计算结果证实了算法的有效性。
With the diversification and complication of space mission requirements, it is necessary for orbital control and orbital determination to meet these requirements. However classical methods could not meet these requirements in some cases. This paper improved these methods based on the requirements 0
There are two methods for conventional orbital control: one is algebra method which deals with the problems by optimization based on orbit geometry characteristics The first method is applied when we adopt impulsive control, but in the multiobjective cases the method has its limitation. The other method is Pontryagin maximum value principle dealing with low thrust control problem. However when the system is very complex, especially when the system contains uncertain factors, the method is not effective. In this paper we introduce some intelligent control methods to solve them.
Firstly the paper introduces evolutionary algorithms(EA), presents the improved SPEA, which adopts multiple-chromosome crossover and Cauchy mutation instead of bi-chromosome crossover and norm mutation, also gives convergence analysis of SPEA. Then the paper applies EA and SPEA to an orbital transformation problem.- time-energy optimization o The paper also solve low thrust control problem of relative motion using fuzzy logic.
The classical algorithms for orbital determination are least square estimation (LSE) and Kalman filtering. But when the observing data contains nonlinear factors, which is always encountered in practice, the performance of the algorithms is very poor. In this paper semiparametric regression is presented to solve the problem, moreover the algorithm is given. It is an iterative process between linear estimation and nonlinear estimation. The linear estimation is LS estimation and the nonlinear estimation is a wavelet denoising process of residual. In contrast to conventional LSE and Kalman filtering, the algorithm has higher performance in precision orbit determination. Moreover the algorithm is tested by simulation data and real observed data, and the computing results show that the algorithm is very effective.
传统的轨道控制一般基于两种方法，一种是代数优化方法，这种方法与卫星的轨道几何特性相结合进行分析，将轨道的几何特性和优化指标用代数方程的形式表示出来进行求解，这种方法主要用于冲量式控制。但在多指标的要求下，这种方法难以求得最优解；另一种方法是应用Pontryagin最大值原理解决有限推力最优控制问题，但对复杂的或者含有不确定因素的系统往往难以奏效。本文用智能控制的方法来解决轨道控制中某些用经典控制难以求解的问题：用进化算法解决轨道转移的时间-能量优化问题，用模糊控制方法解决相对运动方程有限推力控制问题。
本文首先对一般的进化算法进行了研究，对SPEA方法(一种多目标进化算法)进行了改进：引入多体交叉和Cauchy变异来代替两体交叉和正态变异，并对SPEA进行了收敛性分析。然后分别用一般的进化算法和改进的SPEA方法解决轨道转移的时间-能量优化问题，对于相对运动方程有限推力控制问题，本文用模糊控制的方法加以解决。
轨道确定的传统估计算法是最小二乘算法和Kalman滤波。当观测数据含有非线性因素时，它们的估计性能比较差，而这些非线性因素在实际当中往往是不可避免的。本文提出的半参数回归方法较好的解决了上述问题，并给出了相应的算法：这是一种线性估计和非线性估计相互迭代的方法，线性估计是最小二乘法，而非线性估计是基于小波对残差去噪的方法。本文提出的这种算法比经典的最小二乘算法或Kalman滤波方法具有更高的定轨精度，仿真数据和实际观测数据的计算结果证实了算法的有效性。
With the diversification and complication of space mission requirements, it is necessary for orbital control and orbital determination to meet these requirements. However classical methods could not meet these requirements in some cases. This paper improved these methods based on the requirements 0
There are two methods for conventional orbital control: one is algebra method which deals with the problems by optimization based on orbit geometry characteristics The first method is applied when we adopt impulsive control, but in the multiobjective cases the method has its limitation. The other method is Pontryagin maximum value principle dealing with low thrust control problem. However when the system is very complex, especially when the system contains uncertain factors, the method is not effective. In this paper we introduce some intelligent control methods to solve them.
Firstly the paper introduces evolutionary algorithms(EA), presents the improved SPEA, which adopts multiple-chromosome crossover and Cauchy mutation instead of bi-chromosome crossover and norm mutation, also gives convergence analysis of SPEA. Then the paper applies EA and SPEA to an orbital transformation problem.- time-energy optimization o The paper also solve low thrust control problem of relative motion using fuzzy logic.
The classical algorithms for orbital determination are least square estimation (LSE) and Kalman filtering. But when the observing data contains nonlinear factors, which is always encountered in practice, the performance of the algorithms is very poor. In this paper semiparametric regression is presented to solve the problem, moreover the algorithm is given. It is an iterative process between linear estimation and nonlinear estimation. The linear estimation is LS estimation and the nonlinear estimation is a wavelet denoising process of residual. In contrast to conventional LSE and Kalman filtering, the algorithm has higher performance in precision orbit determination. Moreover the algorithm is tested by simulation data and real observed data, and the computing results show that the algorithm is very effective.
引文
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