Evaluating Integrity and Continuity Risks of Cycle Resolution in the Presence of Receiver Faults

S. Khanafseh, S. Langel, M. Joerger and B. Pervan

Abstract:	This paper introduces a method to compute an upper bound on the integrity risk of cycle resolution in the presence of receiver faults. In high accuracy aviation applications such as shipboard landing and autonomous airborne refueling, differential carrier phase navigation algorithms are used, and carrier phase cycle ambiguities must be estimated and resolved as integers (or ‘fixed ambiguities’). In applications that also demand high integrity, the cycle resolution process must comply with integrity risk requirements. Under normal measurement error conditions, fault-free integrity risk can readily be quantified using existing cycle resolution methods; this is true even in the presence of known measurement biases. However, other contributors to integrity risk exist, most notably GNSS receiver faults, referred to as H1 events in the GNSS aviation community. In these situations, risk can potentially be mitigated by equipping with redundant receivers. In this work, we develop a method using multiple receivers to quantify and minimize H1 integrity risk in cycle resolution. The fault-free integrity risk is typically defined as the probability that the position error exceeds predefined alert limits. In applications where integrity and accuracy requirements are stringent, it is necessary to quantify the impact of the cycle resolution process on position domain integrity. In this context, the bootstrap fixing method is used as a baseline for cycle resolution because it provides an a priori success rate (probability of correct fix and probability of incorrect fix). Using the probability of correct fix, several simple methods can then be used to upper-bound fault free integrity risk of the cycle resolution process. But these methods are conservative because they assume that incorrect fixes always result in position estimate errors that exceed integrity containment requirements (alert limits). In recent years, new methods have been developed to compute much tighter bounds on fault free integrity risk by also evaluating the impact of incorrect fixes on the position estimates. Examples of such algorithms are the Enforced Position-domain Integrity-risk of Cycle resolution (EPIC) method [1], and the Geometric Extra Redundancy Almost Fixed Solution (GERAFS) method [2]. Two separate types of probabilities must be calculated when evaluating the integrity risk of cycle resolution. The first is the probability of correct fix (and also probability of incorrect fix for the EPIC and GERAFS methods). The second probability is computed from the conditional distribution of the position estimate error for the fixed solution. Both of these probability types are strongly influenced by rare-event measurement faults. Several publications address the computation of the probability of correct fix in the presence of measurement biases (for example, see [3]). However, these methods are only applicable if the bias on the measurement error is exactly known. In previous work [4] we developed a method to compute an upper bound on cycle resolution integrity risk in the presence of bounded measurement errors and faults. For example, in the case of atmospheric anomalies, the magnitude of the measurement is never exactly known, but it can often be physically bounded [5]. In contrast, reference receiver faults have no established threat models and therefore, cannot be bounded. As already noted, integrity risk due to receiver faults can potentially be mitigated by equipping with redundant receivers. For example, various approaches to utilize redundant carrier phase measurements from multiple reference receivers in differential carrier phase systems are described in [6]. In that work, the measurements from all reference receivers are coupled with airborne measurements in the range domain and used to estimate a unified solution. Although the literature provides specific solution for H1 integrity for some navigation systems (such as GBAS), the necessity of estimating and resolving the cycle ambiguities is the main challenge in bounding H1 integrity risk for high accuracy carrier phase navigation applications. In this paper, we derive a method to simultaneously account for the effects of reference receiver failures on position estimate error and cycle ambiguity fix error probabilities. This derivation directly leads to two approaches to bounding integrity and continuity risk: the first is simpler to implement, but provides loose bound; the second approach, although more complex, provides a much tighter bound. We quantify the performance of the two bounding methods as measured by availability on an example autonomous shipboard landing application. [1] S. Khanafseh and B. Pervan, “A New Approach for Calculating Position Domain Integrity Risk for Cycle Resolution in Carrier Phase Navigation Systems,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 46, No. 1, January 2010, pp. 296-307. [2] S. Wu, S. Peck, R. Fries, "Geometry Extra-Redundant Almost Fixed Solutions: A High Integrity Approach for Carrier Phase Ambiguity Resolution for High Accuracy Relative Navigation," Proceedings of IEEE/ION PLANS 2008, Monterey, CA, May 2008, pp. 568-582. [3] P. Teunissen, “Integr Estimation in the Presence of Biases,” Journal of Geodesy, No. 75, 2001, pp. 399-407. [4] Khanafseh, S., Joerger, M., Pervan, B., "Integrity Risk of Cycle Resolution in the Presence of Bounded Faults," Proceedings of IEEE/ION PLANS 2012, Myrtle Beach, South Carolina April 2012, pp. 664-672. [5] Khanafseh, Samer, Joerger, Mathieu, Pervan, Boris, Von Engeln, Axel, "Accounting for Tropospheric Anomalies in High Integrity and High Accuracy Positioning Applications," Proceedings of the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, September 2011, pp. 513-522. [6] S. Khanafseh and B. Pervan, “Detection and Mitigation of Reference Receiver Faults in Differential Carrier Phase Navigation Systems”, IEEE Transactions on Aerospace and Electronic Systems, Vol. 47, No. 4, 2011, pp. 2391-2404.
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	2583 - 2591
Cite this article:	Khanafseh, S., Langel, S., Joerger, M., Pervan, B., "Evaluating Integrity and Continuity Risks of Cycle Resolution in the Presence of Receiver Faults," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 2583-2591.
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