The Covariance Matrix for Variable Projection with Multiple Right Hand Sides

In this article, I explore how to efficiently calculate the covariance matrix of the best fit parameters for global fitting problems that use the variable projection (VarPro) algorithm. It’s a very niche topic, but I do need it for my open source library so I might as well write it down. It might be helpful for people looking to gain a deeper understanding of the math behind VarPro.