Purpose

The purpose of this paper is to focus on the performance of three typical nonlinear least-squares estimation algorithms in atmospheric density model calibration.

Design/methodology/approach

The error of Jacchia-Roberts atmospheric density model is expressed as an objective function about temperature parameters. The estimation of parameter corrections is a typical nonlinear least-squares problem. Three algorithms for nonlinear least-squares problems, Gauss–Newton (G-N), damped Gauss–Newton (damped G-N) and Levenberg–Marquardt (L-M) algorithms, are adopted to estimate temperature parameter corrections of Jacchia-Roberts for model calibration.

Findings

The results show that G-N algorithm is not convergent at some sampling points. The main reason is the nonlinear relationship between Jacchia-Roberts and its temperature parameters. Damped G-N and L-M algorithms are both convergent at all sampling points. G-N, damped G-N and L-M algorithms reduce the root mean square error of Jacchia-Roberts from 20.4% to 9.3%, 9.4% and 9.4%, respectively. The average iterations of G-N, damped G-N and L-M algorithms are 3.0, 2.8 and 2.9, respectively.

Practical implications

This study is expected to provide a guidance for the selection of nonlinear least-squares estimation methods in atmospheric density model calibration.

Originality/value

The study analyses the performance of three typical nonlinear least-squares estimation methods in the calibration of atmospheric density model. The non-convergent phenomenon of G-N algorithm is discovered and explained. Damped G-N and L-M algorithms are more suitable for the nonlinear least-squares problems in model calibration than G-N algorithm and the first two algorithms have slightly fewer iterations.

中文翻译：

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非线性最小二乘估计算法在大气密度模型标定中的应用

目的

本文的目的是关注大气密度模型校准中三种典型的非线性最小二乘估计算法的性能。

设计/方法/方法

Jacchia-Roberts大气密度模型的误差表示为关于温度参数的目标函数。参数校正的估计是一个典型的非线性最小二乘问题。三种用于非线性最小二乘问题的算法，即高斯-牛顿（GN），阻尼高斯-牛顿（阻尼GN）和Levenberg-Marquardt（LM）算法，被用来估计Jacchia-Roberts的温度参数校正，以进行模型校正。

发现

结果表明，GN算法在某些采样点上不收敛。主要原因是Jacchia-Roberts与温度参数之间存在非线性关系。阻尼的GN和LM算法在所有采样点都收敛。GN，阻尼GN和LM算法将Jacchia-Roberts的均方根误差分别从20.4％降低到9.3％，9.4％和9.4％。GN，阻尼GN和LM算法的平均迭代分别为3.0、2.8和2.9。

实际影响

这项研究有望为大气密度模型校准中非线性最小二乘估计方法的选择提供指导。

创意/价值

该研究分析了三种典型的非线性最小二乘估计方法在大气密度模型校准中的性能。发现并解释了GN算法的非收敛现象。阻尼GN和LM算法比GN算法更适合模型校准中的非线性最小二乘问题，并且前两种算法的迭代次数略少。