Performance Assessment of Recursive ARAIM with High-Integrity Time-Correlated Measurement Error Models
Elisa Gallon, Illinois Institute of Technology; Mathieu Joerger, Virginia Tech; Boris Pervan, Illinois Institute of Technology
Date/Time: Thursday, Sep. 22, 8:57 a.m.
In this paper, we develop a new Kalman-filter (KF)-based approach for GNSS positioning, fault detection, and integrity monitoring. The filter design integrates stochastic measurement error models developed and validated in prior work using multiple years of data [1-3]. These models account for uncertain measurement error time-correlation using power spectral density (PSD) bounding . They are used in this paper to provide a realistic performance assessment of recursively-implemented Advanced Receiver Autonomous Integrity Monitoring (ARAIM).
The modernization of GPS and the deployment of additional GNSS constellations have increased the number of redundant ranging signals, leading to heightened interest in the development of ARAIM for aircraft navigation. The baseline version of ARAIM uses ionosphere-free carrier smoothed code (CSC) measurements at one instant in time to provide a “snapshot” navigation solution [5-7]. Unlike conventional snapshot ARAIM, a recursive implementation of ARAIM is able to exploit changes in satellite geometry. The accumulated geometry variations of redundant satellites from multiple GNSS can be substantial. In , we showed that the additional exploitation of satellite motion over time could provide superior positioning performance and tighter protection levels (PLs) than baseline ARAIM. Recursive algorithms can therefore open the possibility to extend the scope of ARAIM applications beyond aircraft navigation, to rail, maritime/naval, or arctic operations.
However, to implement and evaluate recursive ARAIM, one must ensure that the error models in the KF properly account for measurement error time correlation. Dynamic models are needed for the three main GNSS error sources: satellite orbit and clock errors, tropospheric delay, and multipath. In prior work [1-3], multiple years of data were processed to derive bounding, time-correlated error models for each of these error sources. The bounding error models ensure fault-free integrity, but they will affect availability. This impact needs to be quantified in order to realistically assess the performance improvements brought by recursive ARAIM over snapshot ARAIM.
The first part of this paper outlines the specifics of our recursive ARAIM implementation. In particular, three aspects have a specific importance and are highlighted:
- Unlike snapshot ARAIM, which relies on dual-frequency, ionospheric-free carrier-smoothed-code measurements, recursive ARAIM mainly uses raw carrier phase measurements. Indeed, dual-frequency code phase measurement errors will be heavily influenced by antenna group delays, the dynamics of which cannot be modelled stochastically in a KF because they are deterministic; given choice of antenna and installed environment, the error changes only due to substantial platform reorientations (e.g., turns, banks) and satellite line of sight variation. In principle, the effect is calibratable, albeit not always easily for many platforms of interest, like civil transport aircraft. Although much the same can be said for multipath, in this case error dynamics are highly sensitive to small scale attitude motions and further complicated by a multiplicity of reflective surfaces on platforms with complex shapes, (again) like transport aircraft, making multipath far more amenable to stochastic modelling. We focus on raw carrier phase measurements because their platform/antenna dependent errors are restricted to by multipath and thermal noise, which can be modelled stochastically in a KF. Code phase measurements are used to aid in the initialization of floating carrier cycle ambiguities, but they will not otherwise be used (or needed) in the reclusive ARAIM KF.
- To detect faults, like baseline snapshot ARAIM, recursive ARAIM uses the Multiple Hypothesis Solution Separation (MHSS) method. In the recursive case, however, it becomes necessary to implement a bank of KFs running in parallel -- e.g., one using all satellites in view and the rest with one satellite removed. (In this first work on recursive ARAIM, we do not consider simultaneous satellite faults or fault exclusion.) Satellites coming in and out of view will be handled following the methodology described in . Anytime a satellite i goes out of sight, all sub filters remain affected by past-time measurements from satellite i. Unless fault modes associated with satellite i are monitored indefinitely, all sub filters must be re-initialized to eliminate the impact of potential past-time faults from satellite i. The re-initialization leads to temporary poor estimates and therefore causes low detection capability until the filters converge again. To avoid this issue, the “fading filter” approach developed in  is used. This approach relies on the temporary monitoring of prior faults associated with previously in-view satellites.
- Finally, to properly account for the time correlation of the errors present in the raw carrier measurements (satellite orbit and clock, residual tropospheric error, multipath, and thermal noise), bounding dynamic error models derived in our prior work [1-3] are used in this work. Most of these bounding models are first order Gauss-Markov processes incorporated into the KF by state augmentation.
The second part of this paper assesses the performance improvements provided by recursive ARAIM, using bounding dynamic error models, with respect to baseline snapshot ARAIM, using baseline snapshot models. We focus on two performance metrics: availability and integrity (protection levels).
The third and last part of this paper builds on the results of the second and third sections by allowing us pose two important questions: Can the performance improvement provided by recursive ARAIM outweigh the cost of modifying the now well-established snapshot ARAIM algorithm for aviation? Could these modifications help extend the scope of ARAIM applications beyond aircraft navigation, to high integrity rail, maritime/naval, or arctic operations?
 E. Gallon, M. Joerger, and B. Pervan, “Robust modeling of GNSS tropospheric delay dynamics,” IEEE Transactions on Aerospace and Electronic Systems, 2021.
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 E. Gallon, M. Joerger, B. Pervan, "Frequency-Domain Modeling of Orbit and Clock Errors for Sequential Positioning," Proceedings of Institute of Navigation GNSS+ Virtual Conference, Sep 2020.
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 M. Joerger, B. Pervan, “Multi-Constellation ARAIM Exploiting Satellite Motion“, NAVIGATION, Volume 67, Issue 2, pp 235 – 253, Summer 2020, doi: https://doi.org/10.1002/navi.334.
 C. Tanil, S. Khanafseh, M. Joerger, B. Kujur, B. Kruger, L. de Groot, B. Pervan, "Optimal INS/GNSS Coupling for Autonomous Car Positioning Integrity,” Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019)”, Miami, Florida, September 2019, pp. 3123-3140.
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