This thesis aims to assess how different convex penalty functions can be used in orbit determination methods and to design an algorithm to test them under different conditions.
Most traditional Precise Orbit Determination (POD) algorithms use the Least-Squares (LSQ) method to minimise the misfit between a set of modelled and actual measurements. The approach followed in this research is to investigate other convex penalty functions for this purpose in order to achieve better results than the traditional LSQ method, while maintaining the overall quality and robustness of the former.
To simplify the application of convex optimisation methods, an external toolbox was used to implement the different convex cost functions. The testing environment included a Precise Orbit Propagator (POP), measurement generating and processing functions, the POD algorithm itself, and data processing functionalities for the representation of the results. All the different components integrated in the final algorithm were validated before their application.
Tests to assess different aspects of the implemented penalty functions were run, regarding both computational aspects and solution performance. The traditional method was observed to present suboptimal results when the noise present in the observations included unprocessed outliers. In addition, cases where the observations were highly sparse yielded a suboptimal estimation of the trajectory.
After that, the L1-Norm was implemented as penalty function, alongside with Huber’s penalty function, which represents a combination of both LSQ and L1-Norm.
The use of the L1-Norm in the orbit determination algorithm outperformed the traditional method in the cases where it lacked performance, such as in the presence of unprocessed outliers or sparse observation sets. However, in other tests run, the LSQ algorithm was able to reach higher accuracy levels than the L1-Norm. Huber’s penalty function, conversely, proved to be a great candidate for both purposes, closely resembling the results obtained by the best penalty function for each test and even improving it on occasions, at the cost of a higher computational effort.
Finally, the designed algorithms were applied to a real-world study-case making use of GOCE data provided by TU Delft. These applications demonstrated satisfactory performance for each of the methods that were implemented and provided an important validation of the work.