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

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