Carrier Phase-based RAIM Algorithm Using a Gaussian Sum Filter

Carrier phase measurements are used to provide high-accuracy estimates of position. For safety-of-life navigation applications such as precision approach and landing, integrity plays a critical role. Carrier phase-based Receiver Autonomous Integrity Monitoring (CRAIM) has been investigated for many years (Pervan et al, 1998 ; Feng et al, 2007 ). Assuming that the carrier phase error has a Gaussian distribution, conventional CRAIM algorithms were directly derived from the Pseudorange-based RAIM (PRAIM). However, the actual carrier phase error does not exactly follow the Gaussian distribution, hence the performance of the conventional CRAIM algorithm is not optimal. To approach this problem, this paper proposes a new CRAIM algorithm that uses Gaussian sum filters. A Gaussian sum filter can deal with any non-Gaussian error distribution and accurately present the posterior distributions of states. In this paper, a new method of making a Gaussian mixture model, which follows the true error distribution, is introduced. Additionally an integrity monitoring algorithm, using a Gaussian sum filter, is described in detail. The simulation results show that the proposed algorithm can have about 18% smaller Minimum Detectable Bias (MDB) and generates about 20% lower protection levels than those of the conventional CRAIM algorithm. In other words, by considering a non-Gaussian carrier phase error distribution, the new algorithm can improve the accuracy and the availability.