An Optimized Multiple Hypothesis RAIM Algorithm for Vertical Guidance

For several years, Receiver Autonomous Integrity Monitoring (RAIM) has been used successfully for horizontal positioning in the phases of flight with Protection levels on the order of several hundreds of meters. In the next years, there will be many more navigation satellites (Galileo, a renewed GLONASS constellation, Compass), all expected to have signals in at least two frequencies. This has raised the possibility of using RAIM for much more demanding phases of flight (LPV 200 or Cat. I, for example), and perhaps ultimately replacing integrity providers such as SBAS and GBAS. However, it is not possible to apply the assumptions that are made for RAIM today in studies for vertical approach availability. Among others, the definition of failure needs to be changed: because the expected accuracy will be better, the threshold for failure will be reduced; as a consequence, the prior probability of failures could be larger than what is used now. This, together with the fact that there will be many more ranging sources makes it necessary to consider the possibility of multiple simultaneous failures. There are several RAIM algorithms treating multiple failures. However, most of them present certain disadvantages: either the calculations required to compute the Protection Levels are very complex, or the link between these Protection Levels and the Probability of Hazardously Misleading Information is problematic (often because several approximations are necessary). In this paper, we give a detailed explanation of an optimized Multiple Hypothesis Solution Separation algorithm for RAIM. There are several advantages in the Multiple Hypothesis approach. First, the link between threat model, Protection Level and PHMI is a very easy and straightforward one; second, the calculation of the Protection Level does not involve complex steps. We will show how these advantages stem mostly from the fact that the algorithm works by computing a Protection Level that meets the PHMI requirement, rather than computing a probability of misdetection. One of the key points in this algorithm is the allocation of the PHMI to the different failure modes. In previous papers, the allocation was made heuristically, in this one we will show how to compute an optimal allocation. As an example, the algorithm will be applied to a single dual frequency constellation (GPS or Galileo) and a dual constellation. INTRODUCTION In the next years, several GNSS constellations are expected to become operative, such that users will have access to a large number of pseudoranges in two frequencies, which will allow receivers to cancel the ionosphere induced error. This has raised the possibility of using RAIM to provide worldwide coverage of vertical guidance (starting with LPV 200), with a reduced need for ground monitoring [1], [2], [3]. However, compared to the algorithms used currently for horizontal positioning, the RAIM algorithms will need to be updated such that they accommodate complex threats (in particular multiple failures with any number of satellites and different a priori probability of failure), have a rigorous proof of safety (Probability of Hazardously Misleading Information) while not being unnecessarily conservative. Generalizations of the slope based RAIM algorithm [5] to multiple failures have been devised [6], however the threat model is not clearly defined and the proof of safety still relies on approximations. The algorithm presented here is an improvement on the algorithm that has been described in [1], which in turn is a modification of the Multiple Hypothesis Solution Separation algorithm described in [4]. Also, the algorithm is bears several similarities with other RAIM algorithms based on solution separation [5]. The main features of the optimized MHSS RAIM algorithm are as follows. First, as long as one can provide a definition of the threat and an a priori probability, the algorithm can account for it. In particular, multiple failures with an arbitrary number of satellites can be included in a transparent way. Second, the algorithm has a simple proof of safety: the Probability of Hazardously Misleading Information (HMI) is computed by adding up the contribution of each failure, following a fault tree (as it is done in the Wide Area Augmentation System proof of safety [7]). Finally, The Probability of HMI is allocated dynamically to increase performance (by reducing the Protection Levels). Dramatic gains in performance can be obtained in the case of heterogeneous a priori probability of failure for different fault modes The paper starts by defining the threat model framework and describing the baseline MHSS RAIM algorithm. Then, the optimization of the integrity budget allocation is explained the original contribution of this paper. After that, we present a little-known formula linking slope based RAIM and solution separation RAIM. This formula allows us to compare slope based RAIM with solution separation RAIM. Finally, the optimized algorithm is used to assess the global coverage of vertical guidance using RAIM with high prior probabilities of failure.