Chapters 1-4 are the lecture notes of my course "Real Algebraic Geometry I" from the winter term 2020/2021. Chapters 5-8 are the lecture notes of its continuation "Real Algebraic Geometry II" from the summer term 2021. Chapters 9-10 are the lecture notes of its further continuation "Geometry of Linear Matrix Inequalities" from the winter term 2021/2022.Because of the COVID-19 pandemic, I produced a series of accompanying screencasts of varying length where go in detail through the material. These can be found within a playlist of my Youtube Channel https://www.youtube.com/channel/UCcsp7yAQjJQHx3SN3aL_r1AOther material like the exercise sheets are available somewhere on my website:

No abstract

No abstract

Successful GPS on‐the‐fly (OTF) carrier phase ambiguity resolution for precise positioning at the centimetre level has already been demonstrated. This has usually been in good observation conditions, e.g. over short distances, lots of satellites, P‐code pseudoranges available, and small unmodelled errors. In order for GPS to fulfil the rigorous ICAO Cat. III precise landing navigation requirements centimetre‐level accuracy must also be obtained in more realistic conditions, e.g. A‐S on, high‐unmodelled errors and less than six satellites. Integrating GPS with other sensors, e.g. INS, is likely to aid ambiguity resolution in such conditions, but there are limitations. After discussing critically the OTF methods, approaches are examined which will provide the precise accuracy, reliability and integrity required. Combining GPS with one, or more, pseudolites to provide an extra geometrical constraint to aid ambiguity resolution is described. Flight tests using different configurations of pseudolites are carried out and analysed.

The project Integrity of Satellite Navigation (ISAN) investigates the potential of GNSS (GPS and/or GLONASS) as part of a hybrid GNSS Landing System (GLS) for precision approach and landing down to Category (CAT) III. Specifically, accuracy, integrity, continuity of function, and availability are considered. The accuracy and continuity of function of the GLS were demonstrated in more than 400 flight tests in a commuter aircraft, and landing trials with a Boeing 757 aircraft during the Boeing Autoland Program. These flight tests demonstrated that the navigation system provides sufficient accuracy to perform landings according to suggested FAA requirements of CAT I to III. The present objectives of ISAN are the analysis and improvement of the system availability and establishment of a method to approve system integrity standards. A combination of GPS/GLONASS is considered for the GLS availability improvement. For reasons of integrity monitoring, satellite anomalies, atmospheric effects, and multipath problems on the signal‐in‐space, as well as GPS receiver failures, are taken into account in a GLS Closed Loop Simulation Test Bed installation, including a GPS Simulator to validate the system integrity in defined test scenarios.