A Generalized Variable Projection Algorithm for Least Squares Problems in Atmospheric Remote Sensing

Adelina Bärligea (), Philipp Hochstaffl and Franz Schreier
Additional contact information
Adelina Bärligea: DLR-German Aerospace Center, Remote Sensing Technology Institute, 82234 Oberpfaffenhofen, Germany
Philipp Hochstaffl: DLR-German Aerospace Center, Remote Sensing Technology Institute, 82234 Oberpfaffenhofen, Germany
Franz Schreier: DLR-German Aerospace Center, Remote Sensing Technology Institute, 82234 Oberpfaffenhofen, Germany

Mathematics, 2023, vol. 11, issue 13, 1-20

Abstract: This paper presents a solution for efficiently and accurately solving separable least squares problems with multiple datasets. These problems involve determining linear parameters that are specific to each dataset while ensuring that the nonlinear parameters remain consistent across all datasets. A well-established approach for solving such problems is the variable projection algorithm introduced by Golub and LeVeque, which effectively reduces a separable problem to its nonlinear component. However, this algorithm assumes that the datasets have equal sizes and identical auxiliary model parameters. This article is motivated by a real-world remote sensing application where these assumptions do not apply. Consequently, we propose a generalized algorithm that extends the original theory to overcome these limitations. The new algorithm has been implemented and tested using both synthetic and real satellite data for atmospheric carbon dioxide retrievals. It has also been compared to conventional state-of-the-art solvers, and its advantages are thoroughly discussed. The experimental results demonstrate that the proposed algorithm significantly outperforms all other methods in terms of computation time, while maintaining comparable accuracy and stability. Hence, this novel method can have a positive impact on future applications in remote sensing and could be valuable for other scientific fitting problems with similar properties.

Keywords: separable least squares; nonlinear optimization; python; inverse problems; trace gas retrieval; atmospheric composition; carbon dioxide; infrared spectroscopy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/13/2839/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/13/2839/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:13:p:2839-:d:1178394

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().