The application of nonlinear least-squares estimation algorithms in atmospheric density model calibration
Aircraft Engineering and Aerospace Technology
ISSN: 0002-2667
Article publication date: 20 May 2020
Issue publication date: 16 June 2020
Abstract
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.
Keywords
Acknowledgements
The study presented here was supported by the National Natural Science Foundation of China (no. 11771450, no. 41874028), by the Program of Equipment Investigation in Advance (no. 30505020402), and by the Foundation of Key Laboratory on Equipment Pre-research (no. 614221001060417).
Citation
Zhang, H., Gu, D., Duan, X., Shao, K. and Wei, C. (2020), "The application of nonlinear least-squares estimation algorithms in atmospheric density model calibration", Aircraft Engineering and Aerospace Technology, Vol. 92 No. 7, pp. 993-1000. https://doi.org/10.1108/AEAT-06-2019-0133
Publisher
:Emerald Publishing Limited
Copyright © 2020, Emerald Publishing Limited