Optimal Positioning for Advanced Raim

In the next decade, several important developments will have a major impact on civil aviation: the deployment of Galileo and Compass, the modernization of GPS, and the fact that all these core constellations will broadcast navigation signals in two distinct frequencies that fall in the L1/E1 and L5/E5, which fall in the Aeronautical Radio Navigation Satellite Service (ARNSS) space. As a consequence, even under conservative assumptions, the ranging sources will more than triple. In addition, the ionospheric delay will be estimated and removed by receivers using dual frequency. These developments can be exploited in all satellite navigation systems for aircraft. In particular, the increased redundancy and accuracy could dramatically improve the performance of Receiver Autonomous Integrity Monitoring (RAIM). In Advanced RAIM (ARAIM), they could help enable worldwide vertical guidance. For horizontal RAIM, it could help achieve worldwide coverage of lateral navigation down to fractions of a mile. It is therefore useful to evaluate which RAIM algorithms offer the best performance. As shown in [1], [2] the performance of RAIM can be improved by optimally allocating the integrity budget and the continuity budget across the fault modes – in order to minimize the Protection Levels. The approach in [1] and [2] assumes that the position is centered at the most accurate all-in-view position. This approach guarantees the best accuracy under nominal conditions. However, it is possible to reduce the Protection Levels by choosing a position solution that minimizes it – therefore degrading accuracy. This approach has been exploited in NIORAIM within the framework of slope-based RAIM, where single faults are assumed [3] and accuracy constraints are not considered. It has also been exploited in the case of a simplified threat model where only constellation faults are assumed in [4]. The contribution of this paper consists on simultaneously optimizing the integrity allocation and the position solution, in taking into account additional constraints when generating the position solution for example the accuracy, but not only -, and in doing it for any threat model (in particular multiple faults). This is done by casting the problem as a convex optimization problem. We will evaluate this algorithm by comparing its performance with algorithms where the position solution is not optimized, and showing how it could help achieve worldwide coverage of vertical guidance (LPV-200) under different sets of assumptions. INTRODUCTION Advanced RAIM (ARAIM) [5] performance is a function of the threat model, the constellation strength, and the user algorithm. The objective of this paper is to present a potential improvement on the ARAIM user algorithms within the solution separation ARAIM algorithms presented in [1] and [2], and more generally, on any form of RAIM (like horizontal RAIM). The objective of the user algorithm is to maximize availability while meeting the integrity and continuity requirements. We will first give an overview of ARAIM and a summary of the user algorithm, which is based on solution separation [1], [2]. Then, we will show how to decrease the Protection Levels by adjusting the all-in-view position, while staying within the same framework. Finally, we will evaluate the performance of the algorithm for vertical guidance. ADVANCED RAIM OVERVIEW In this section we give a short description of the ARAIM concept. For more details on this description, the reader should refer to [5]. Advanced RAIM definition The provision of integrity for vertical guidance using mainly airborne monitors is referred to as Advanced RAIM to distinguish it from RAIM as it is used today for horizontal navigation [7], [8]. The increased level of integrity for vertical guidance requires a higher level of scrutiny in the generation of the Protection Levels. In turn, this results in expanded threat models, airborne algorithms that can handle the expanded threat models, and a ground monitoring system that can update the assumptions used by the airborne algorithms. Requirements for vertical guidance (LPV-200) At least six conditions must be met for LPV-200: the Vertical Protection Level (VPL) must be below 35 m, the Horizontal Protection Level (HPL) must be below 40 m, the Effective Monitor Threshold (EMT) must be below 15 m, the false alarm rate must be below 8 x 10 per approach, the 95% vertical accuracy must be below 4 m, and the 10 bound on the fault free vertical error must be below 10 m. A definition of these different figures of merit and guidance on how to compute them is given in [5]. With the above thresholds, whenever the VPL is met, the HPL is almost always met; in addition, the objective of minimizing the EMT is almost the same as the objective of minimizing the VPL; finally, the two last requirements have been determined to be formally very similar. For these reasons, in this paper we will focus on two of the requirements: the VPL and the accuracy. As will be seen, the false alarm rate requirement is taken into account in the VPL calculation. Nominal error models As discussed in [5] the different requirements target different probability levels and different levels of hazard severity. For this reason, there are at least two different pseudorange error models. One error model, which will be labeled the integrity nominal error model, is applied for the requirements that are in the Hazardous category. This error model is only used in the PL terms that guarantee the integrity of the error bound. The other error model, which will be labeled the accuracy nominal error model, is applied in the requirements that are in the Major category (which require less scrutiny). This error model is used to compute the terms in the PL that only affect continuity (the false alert rate), the EMT requirement, and the accuracy. Both errors are characterized by a Gaussian overbound with a maximum nominal bias. For a given geometry, the covariance of the measurements will be designated by Cint for the integrity error model and by Cacc for the accuracy error model. Both covariances are diagonal, and the formulas to compute each term is given in [1]. The maximum biases are designated by bint and bacc respectively. However, within this paper, we will assume bacc to be zero. Failure modes In this paragraph we generalize the description of the failure modes beyond what was described in [2] and [5], so that known correlations between satellite faults can be exploited. In the fault free case, we have: