The parameter estimation package PARFIT implements a multiple-shooting based boundary value problem (BVP) approach for the numerical solution of a very general class of inverse problems, using a generalization of the Gauß-Newton method, which appears to be particularly adequate for this purpose, as it is not attracted to statistically instable local solutions and stable against small measurement perturbations.

Various flavors of PARFIT have evolved during the last four decades, from original Fortran77 implementations up to C++ versions. The original version [1] comes with several specially adapted initial value problem solvers (e.g. METANB, DIFSYS), which are also available in newer implementations. PARFIT supports least-squares (ℓ2) objectives, delivering a maximum-likelihood estimate for unknown quantities from measurements with normally distributed error. Also, other objectives are available, e.g. ℓ1 fitting objectives for robustification against outliers. Furthermore, PARFIT is perfectly able to handle constraints and non-differentiabilities (switches). Accurate derivatives and sensitivities are computed using the principle of Internal Numerical Differentiation (IND).

Recently [2], in a collaboration with the European Space Operations Centre (ESOC), PARFIT was successfully used to retrieve and determine orbits of satellites that where unsuccessfully launched into unforeseen orbits.

PARFIT is also used as parameter estimation tool by our experimental design software VPLAN (Link zu VPLAN).

[1] Hans Georg Bock: Numerical Treatment of Inverse Problems in Chemical Reaction Kinetics. In: Modelling of Chemical Reaction Systems (pp.102-125), Springer, DOI: 10.1007/978-3-642-68220-9_8. Online: https://link.springer.com/chapter/10.1007/978-3-642-68220-9_8

[2] Simon M. Lenz, Hans Georg Bock, Ekaterina A. Kostina, Johannes P. Schlöder: Multiple Shooting Method for Initial Satellite Orbit Determination. Journal of Guidance Control and Dynamics 33(5):1334-1346, DOI: 10.2514/1.48929, September 2010. Online: https://arc.aiaa.org/doi/10.2514/1.48929