The BIOMASS mission from the European Space Agency (ESA) is designed to measurebiomass and carbon content in Earth’s forests. To account for phase changes caused byionospheric variations, a map-drift autofocus algorithm is developed, which utilises a phasescreen of the ionosphere to eliminate phase errors in the signal. In this development, a filteris employed to integrate and remove noise from the second-order derivative of the ionosphericphase screen. This thesis aims to analyse methods to implement this filter andcompare their efficiency.

Two filters are constructed using two methods, a Least Mean Square (LMS) filter and aWiener filter. Further emphasis is placed on the Wiener filter, and the most optimal way tocalculate it is explored in detail. The aim is to produce a filter that can integrate, lower theimpact of noise as much as possible and be computationally efficient. An implementationwas made in Python using simulated data of an ionosphere.

The conclusion is that the Wiener filter can yield improved results if a precise estimation ofthe autocorrelation function of the ionospheric phase screen can be determined, and thatlinear regression models might be a method to do so. There is also consideration taken tothe noise of the data, it is compensated for by utilising multiple data sources. Additionally,to enhance computational efficiency, a comparison of different solving methods for the linearsystem of equations that is the filter where made, showing a LU-decomposition method tobe efficient.