TLE Orbital Determination Based on Simplex Method
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摘要: TLE数据库是目前公开获得轨道信息的唯一来源，其包含的空间目标将持续增加.利用TLE数据库获得精确的定轨结果已成为研究重点.由于TLE数据本身精度未知且存在波动，需要利用历史TLE数据对参考时刻的TLE状态进行轨道确定.常用方法为最小二乘法，但是该方法具有局限性，需要较为精确的初始值，且误差评估不可靠，解易产生发散.为克服现有方法的局限性，本文提出了一种局部搜索算法——单纯形调优法来实现TLE轨道确定.为避免构建的初始单纯形搜索得到的最优解属于局部最优，引入蒙特卡罗方法对初始单纯形进行采样，获得一系列解的统计分布，通过求该分布的期望和方差获得最终结果.研究结果表明，将单纯形调优法获得的结果用于传播预报可显著降低位置和速度误差.Abstract: TLE database is the only public source available to orbital information, and many spatial researchers use the database to obtain an accurate orbit determination result. In the future, the number of spatial objects classified by TLE database will continue to increase. Due to the unknown and fluctuation precision of TLE data, it is necessary to use historical TLEs data to determine the orbit of TLE state at reference time. The least square method is often used to get a precise result but has its own shortcomings, such as the need for more accurate initial value, unreliable error evaluation, solution divergence. To overcome the shortcomings of the existing methods, another local search algorithm, i.e., simplex method is proposed to solve the problem of TLE orbit determination. Monto-Caro method is introduced to produce a series of initial simplex to obtain a series of local optimum solutions and avoid the local optimum solution obtained by an initial simplex. The final global optimum solution is obtained by calculating the expectation and variance of the local-optimum solution distribution. The research shows that results obtained by the simplex method can significantly reduce the position and speed errors.
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Key words:
- Simplex method /
- Orbital determination /
- TLE
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