Mathematical Solution for the attitude of Phoenix lander’s radar (rapport de stage)

I was very lucky to go to the United States and finally get this kind of internship because I had been given the opportunity to work in one of the most productive scientific pole of the country: The California Institute of Technology. This American college is one of the research centres of the NASA, so this internship is very representative of the American way of working: Everything is put at the researcher's disposal no matter the cost. The only thing that matters is productivity. A solution has to be found and as soon as possible. So the laboratories are impressive and equipped with latest fashion hardware.

I worked in the mathematics department of the University, which is just a succession of offices, it was obvious that the only tools used there were mathematicians 'brains and laptops. I did not have my own office but I had to work in the professor Haddad's office who lent me a laptop that I just used to communicate with the professor when I was not in the office. Indeed, I just used papers and a pen to do the work I was assigned.
The professor spent one afternoon with me; he wanted to know more about my mathematics background to see if I was able to make it. Of course I did not know some of the notions I would have to use but the professor told me he will explain in due course those complex notions I never learned.
I have already heard about the phoenix Mars lander mission and I knew that the general purpose was to find out if life was possible in Mars, but I didn't know the whole concept: It is a Mars lander that has to take samples and to find frozen water in order to study the history of water in Mars.
After presenting me the mission, Ziad Haddad showed me what was the problem with phoenix. The spaceship has to land vertically because if it is not the case it won't be able to take off and go back to Earth with the samples.
The problem is that the radar is not perfectly equipped to measure the three components of the velocity during the landing, and by solving a mathematics problem it will be possible to know to what extend the measured components are reliable.

After a general presentation of the mission and the work setting, the mathematics part will be explained: My contribution to this project and the solution will be developed.