Hysteresis in RAIM

Absolute RAIM algorithms proposed for vertical guidance are based on a snapshot approach. At a given time, each satellite has a probability of being in a faulted state which does not depend on how long the satellite has been in view. This approach greatly simplifies the proof of safety. Both the threat model and the algorithm are simple enough so that the Probability of Hazardously Misleading Information can be shown to be below the required level for vertical guidance, even in the multiple failure case. However, this approach neglects the observation history of the satellites. A faulty satellite that has been in view for several hours has more chances to be detected and excluded from the position solution than a satellite that has just risen. This distinction is absent in the snapshot approach, therefore ignoring useful information -even though snapshot RAIM will have hysteresis in the exclusion function. In the Absolute RAIM (ARAIM) architecture proposed in [1] it is assumed that a failure could have started at any point in a defined period of time, which is unrelated to the time the satellite has been in view for the user. This period of time is the time it will take the GNSS provider to either flag the satellite or correct it. The goal of this paper is to define a threat model and a user algorithm that takes into account the satellite observation history so that performance can be increased. The threat model must be such that it includes all reasonably possible failures, without being overly optimistic - this is very important as even small deviations from the nominal behavior can be problematic for vertical guidance. The introduction of the time aspect in the threat model makes it much more complicated than in the snapshot approach. The failure of one satellite needs to be divided into several possibilities depending on when the failure started. Even within a given satellite failure at a given time, the failure is an error profile, not a given scalar (like in snapshot RAIM). All of this is also complicated by the fact that nominal errors are correlated in time. The algorithm must be practical, and most importantly, must allow a clear evaluation of the Probability of Hazardously Misleading Information. We propose a threat model that conservatively describes the possible threats in the time domain and an algorithm that mitigates this threat model. Once the algorithm is defined we will evaluate the gain in performance for worldwide vertical guidance