Research project This project aims at combining linear estimation theory with non-linear optimization theory to solve non-linear estimation problems found in Photogrammetry and Space Physics.
Many measurement problems of real-world phenomena are solved using linear least squares methods. However, real-world problems are often non-linear, and linear estimation methods generally lack strong convergence properties, something necessary to obtain a solution. On the other hand, non-linear optimization theory, whose methods do guarantee a solution, usually ignore the statistical properties of the problem, something necessary to estimate the quality of the obtained solution. By combining theories from both fields, methods with superior convergence and statistical properties can be constructed. Two application examples are position measurement in images used in photogrammetry and measurements of current sheets in magnetospherical data.