Analysis of GNSS Constellation Performance for Advanced RAIM

Juan Blanch, Xinwei Liu, Kaz Gunning, Todd Walter

Abstract: As its name implies, ARAIM is an evolution of Receiver Autonomous Integrity Monitoring (RAIM) which has been used by aircraft for many years to support horizontal navigation [1, 2, 3]. RAIM is limited to GPS-only, L1-only measurements. It was developed in the 1990’s before the Satellite Based Augmentations Systems (SBASs) and the Ground Based Augmentations Systems (GBASs). These later augmentations developed much more detailed descriptions of potential threats to satellite ranging accuracy as well as more sophisticated analysis techniques for describing and bounding errors. ARAIM harmonizes the threat models with these augmentation systems and leverages their advanced techniques to analyze and mitigate the threats. ARAIM also supports the combination of signals on multiple frequencies and from other constellations in addition to GPS. A significant part of the ARAIM concept is to provide a transparent method to validate key integrity parameters and to transmit their numerical values to users through an Integrity Support Message (ISM). The parameters in this ISM convey the level of performance and trust that can be put into the system. In this paper, we describe the methodology used to evaluate these ISM parameters and to ensure that they conform to requirements [4, 5, 6]. The ISM parameters include 5 key elements. These are: P_sat – The probability that an individual satellite is in a faulted state at any given time P_const – The probability that multiple satellites are in a faulted state at any given time Alpha_URA – A multiplier to obtain the integrity overbound of the uncertainty on the SIS error b_nom – An overbound on the magnitude of the SIS long-term/deterministic bias error MFD – The Mean Fault Duration or average time that a satellite stays in a faulted state The paper will develop the following points: Signal-In-Space Range Error Estimation. The estimated instantaneous SISREs must accurately represent the effects of satellite orbit and clock errors (as well as other random components of other SISRE error sources) affecting the user’s pseudorange errors [7]. This could fail to happen in four primary ways: - Incorrect broadcast clock and ephemeris data - Incorrect precise clock and ephemeris data - Missing data (particularly during anomalous event) - Data is processed incorrectly We will briefly go over the methods to address these issues, as well as the use of precise orbits, and clock estimates. Long-Term System Behavior. The purpose of the ISM parameters is to describe expectations on future performance. Therefore, it is imperative to establish that operational behaviors will be maintained and not become worse than described. We will describe a set of analyses to measure the long term behavior. For GPS, these analyses confirm that the performance has steadily improved. Specific Risk Evaluation. It is important to identify predictable and/or repeatable behavior so that risk may be properly characterized. Averaging risk across different conditions is not safe to do if those conditions have significantly different levels of risk. The events associated with higher risk will be erroneously assessed to have better integrity than they actually do. We therefore consider the question of how to aggregate the data for this evaluation, and propose a set of partitions including: - Individual satellites - Satellite block type (including clock type) - Time (by year, by season, by month, or by day) - Satellite age - Age of navigation data Probability Overbounding. We will go over the steps involved in the overbounding process, as well as the different techniques and tools available to determine gaussian overbounds (symmetrical unimodal gaussian bounding and paired bounding) [8, 9, 10, 11]. Error Correlation. The overbounding results in the range domain depend on an assumption of independence. However, there are mechanisms that can impact the clock and ephemeris estimates such the errors are correlated, as, for example, the time transfer across the monitoring receivers, correlated errors at the monitoring stations etc. We therefore need to ensure that the errors can be treated as if they were independent and still end up with conservative error bounds. To demonstrate that the errors can be treated as if they were independent, we will examine the statistics of the sum of square normalized residuals for each vector errors affecting a user. Fault Rate Estimation. We will review methods to estimate upper limits of the fault rates (from which the probabilities Psat and Pconst can be derived) [12]. This will include the identification of faults (based on the definition of a fault for each constellation), their validation, and the estimation of the rate based on Poisson distributions. For each of these points we present the corresponding results for GPS and Galileo (whenever possible). REFERENCES [1] Working Group C, ARAIM Technical Subgroup, Milestone 3 Report, February 26, 2016. Available at: http://www.gps.gov/policy/cooperation/europe/2016/working-group-c/ http://ec.europa.eu/growth/tools-databases/newsroom/cf/itemdetail.cfm?item_id=8690 [2] Working Group C, ARAIM Technical Subgroup, Milestone 2 Report, Issue 1.0, February 11, 2015. Available at: http://www.gps.gov/policy/cooperation/europe/2015/working-group-c/ http://ec.europa.eu/growth/tools-databases/newsroom/cf/itemdetail.cfm?item_id=8191 [3] Working Group C, ARAIM Technical Subgroup, Interim Report, Issue 1.0, December 19, 2012. Available at: http://ec.europa.eu/enterprise/newsroom/cf/_getdocument.cfm?doc_id=7793 http://www.gps.gov/policy/cooperation/europe/2013/working-group-c/ARAIM-report-1.0.pdf [4] ICAO, Annex 10 to the Convention on International Civil Aviation, Aeronautical Telecommunications, Volume I Radio Navigation Aids, Seventh Edition, July 2018 [5] GPS Standard Positioning Service (SPS) Performance Standard. 5th Edition, April 2020. [6] “Proposed amendments to Annex 10, Volume I: Galileo system provisions” ICAO working paper presented at the sixth meeting of the Navigation Systems Panel, 2-13 November 2020 [7] Walter, Todd, Gunning, Kazuma, Phelts, R. Eric, Blanch, Juan, "Validation of the Unfaulted Error Bounds for ARAIM", NAVIGATION, Journal of The Institute of Navigation, Vol. 65, No. 1, Spring 2018, pp. 117-133. [8] Perea, S., Meurer, M., Rippl, M., Belabbas, B., and Joerger, M. (2017) URA/SISA Analysis for GPS and Galileo to Support ARAIM. J Inst Navig, 64: 237– 254. doi: 10.1002/navi.199. [9] Blanch J., Walter, T., and Enge, P., “Gaussian Bounds of Sample Distributions for Integrity Analysis”. IEEE Transactions on Aerospace and Electronic Systems.” PP. 1-1. 10.1109/TAES.2018.2876583. [10] DeCleene, B. “Defining Pseudorange Integrity - Overbounding,” Proceedings of the 13th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2000), Salt Lake City, UT, September 2000, pp. 1916-1924 [11] J. Rife, T. Walter, and J. Blanch, “Overbounding SBAS and GBAS error distributions with excess-mass functions,” Proceedings of the 2004 International Symposium on GPS/GNSS, Sydney, Australia, 6-8 December, 2004. [12] Walter, T., Blanch, J., Gunning, K., Joerger, M., & Pervan, B. (2019). Determination of Fault Probabilities for ARAIM. IEEE Transactions on Aerospace and Electronic Systems, 55(6), 3505-3516. [8684918]. https://doi.org/10.1109/TAES.2019.2909727
Published in: Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021)
September 20 - 24, 2021
Union Station Hotel
St. Louis, Missouri
Pages: 1410 - 1434
Cite this article: Blanch, Juan, Liu, Xinwei, Gunning, Kaz, Walter, Todd, "Analysis of GNSS Constellation Performance for Advanced RAIM," Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021), St. Louis, Missouri, September 2021, pp. 1410-1434. https://doi.org/10.33012/2021.18148
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