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Covariance analysis of Lambert's problem via Lagrange's transfer-time formulation

机译：通过Lagrange转移时间公式对Lambert问题进行协方差分析

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摘要

An analytical linear covariance prediction is formulated for Lambert's boundary value problem with navigation errors. The required initial velocity impulse in orbit targeting problems is computed under the initial and final position vector errors, the initial velocity vector error and the transfer time error. These errors are assumed to satisfy Gaussian distributions. The uniqueness of our approach is that first-order partial derivatives of the outputs (boundary velocity vectors) are derived with respect to the Lambert inputs (boundary position vectors and transfer time) using the Lagrange's transfer-time formulation and the Lagrangian F&G solution. This allows establishment of a direct relationship between the partial derivatives for boundary value problems and classical state transition matrix for initial value problems. Then linear covariance matrices of terminal position and velocity vectors are derived. The case of hyperbolic transfer is also studied. Numerical simulations are presented to illustrate and verify the proposed analytical linear covariance technique using Monte Carlo error distributions. (C) 2018 Elsevier Masson SAS. All rights reserved.
机译：针对具有导航误差的兰伯特边值问题制定了解析线性协方差预测。在初始和最终位置矢量误差，初始速度矢量误差和传递时间误差的情况下，计算了轨道瞄准问题所需的初始速度冲量。假定这些误差满足高斯分布。我们方法的独特之处在于，使用Lagrange的传递时间公式和Lagrangian F＆G解决方案，相对于Lambert输入（边界位置矢量和传递时间）得出了输出的一阶偏导数（边界速度矢量）。这允许在用于边值问题的偏导数和用于初始值问题的经典状态转移矩阵之间建立直接关系。然后得出终端位置和速度矢量的线性协方差矩阵。还研究了双曲线传递的情况。提出了数值模拟，以说明和验证使用蒙特卡洛误差分布的拟议分析线性协方差技术。 （C）2018 Elsevier Masson SAS。版权所有。

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