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Two-Dimensional Model for Estimating the Efficiency of Angular Measurements in Elliptic Orbits
Journal of Computer and Systems Sciences International ( IF 0.6 ) Pub Date : 2021-04-28 , DOI: 10.1134/s1064230720060027
A. M. Anufriev , Yu. A. Goritsky , D. G. Tigetov

Abstract

Orbits that are unfavorable for the observer, whose plane passes near the orbital plane, are considered. Replacing the observer’s motion with an approximately equivalent motion in the orbital plane leads to a simple two-dimensional model to measure the motion. The Rao–Cramer bounds for the estimates of the orbital parameters are determined. The observation elevation angles are related to true anomalies and orbital parameters by nonlinear equations. Differentiating the equations with respect to the orbit’s parameters gives the Jacobi matrix of single angular measurements, and then the Fisher information matrix, which is the base for the accuracy analysis. The most difficult part of determining the Fisher matrix is calculating the derivatives of the true anomalies with respect to the orbit’s parameters; this part is based on the numerical solution of a differential equation expressing Kepler’s second law. Examples of calculating the boundaries of the accuracy of estimates in a wide range of practical velocities and angles of incidence are given. The results show that it is possible to obtain an accuracy that is of practical interest in some parameters from the angular measurements.



中文翻译:

估计椭圆轨道角测量效率的二维模型

摘要

考虑其平面在轨道平面附近通过的对观察者不利的轨道。将观察者的运动替换为在轨道平面中的近似等效运动会导致一个简单的二维模型来测量运动。确定轨道参数估计值的Rao–Cramer界线。观测仰角通过非线性方程与真实的异常和轨道参数有关。根据轨道参数对方程进行微分,得到单角度测量值的Jacobi矩阵,然后给出Fisher信息矩阵,这是精度分析的基础。确定费舍尔矩阵最困难的部分是计算相对于轨道参数的真实异常的导数。此部分基于表示开普勒第二定律的微分方程的数值解。给出了在各种实际速度和入射角范围内计算估计精度边界的示例。结果表明,可以从角度测量中获得某些参数具有实际意义的精度。

更新日期:2021-04-29
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