Schlüsselwort: Gaussian Mixture Model

Abstract: Integrity for satellite navigation solutions is becoming increasingly important as the application of satellite navigation is expanding. Also, the amount of measurement data is constantly increasing due to the use of multi-GNSS-constellation. The simultaneous consideration of several GNSS constellations, such as GPS and Galileo or Glonass, increases the availability, especially in urban scenarios, since shading by buildings can typically be expected. A disadvantage of current integrity algorithms is the exponentially increasing required computational power with each additional satellite. This is primarily due to there working principle, which is often based on a derivative of the solution separation algorithm. In this thesis an integrity algorithm is proposed which scales linearly with increasing number of satellites. It is based on the recognition of distribution patterns in the residuals, resulting from the solved satellite navigation equation system. For this purpose, a detailed analysis of the residuals and their influencing factors is carried out. Starting at the source of the GNSS signal, the satellite, along the transmission path to the receiver, the respective influence on the measured pseudo range is analytically characterized and quantized. It can be shown that noise, which originates from different sources along the signal path, is one of the primary factors. In addition, the noise can be characterized as normally distributed. This characteristic is transferred on to the residuals. However, this only applies to the nominal state if there is no Hazardously Misleading Information (HMI) present. If a soft error like an unsynchronized atomic clock on one of the satellites occurs, the measured pseudo range of this satellite changes as well as the associated residual. The totality of the residuals then no longer follows a normal distribution but forms groups. Using pattern recognition based on a Gaussian Mixture Model, the groups are identified, parameterized and their relationships to one another are analyzed. As a result, an estimate of the integrity and of the potential disturbance in terms of quantity and type can be carried out. In addition, a Protection Level (PL) is derived for the navigation process, which can be used operationally together with the Alert Limit (AL). The proposed algorithm is then verified by means of a Monte Carlo simulation and evaluated in a Stanford diagram.