Integrity Risk Minimisation in RAIM Part 2: Optimal Estimator Design

Abstract

This paper is the second part of a two-part research effort to find the optimal detector and estimator that minimise the integrity risk in Receiver Autonomous Integrity Monitoring (RAIM). Part 1 shows that for realistic navigation requirements, the solution separation RAIM method can approach the optimal detection region when using a least-squares estimator. This paper constitutes Part 2. It presents new methods to design Non-Least-Squares (NLS) estimators, which, in exchange for a slight increase in nominal positioning error, can substantially lower the integrity risk. A first method is formulated as a multi-dimensional minimisation problem, which directly minimises integrity risk, but can only be solved using a time-consuming iterative process. Parity space representations are then exploited to develop a computationally-efficient, near-optimal NLS-estimator-design method. Performance analyses for an example multi-constellation Advanced RAIM (ARAIM) application show that this new method enables significant integrity risk reduction in real-time implementations where computational resources are limited. K E Y WO R D S 1. RAIM.2. Risk Minimisation.

Exploiting Satellite Motion in ARAIM: Measurement Error Model Refinement Using Experimental Data

“…i T can be defined as: (27) where the function It is worth noting that this batch implementation is compatible with estimator optimization methods [2,7,9], which are specifically designed to minimize integrity risk while meeting continuity requirements. These methods will be investigated for batch ARAIM in future work.…”

“…Therefore, even using an optimized estimator, coverage using snapshot ARAIM is 9% lower than using batch ARAIM. Furthermore, the optimal estimator approach [2,7,9] is compatible with batch ARAIM, so that availability in Fig. 9 can be further improved.…”

“…Integrity risk is the probability of undetected faults causing unacceptably large positioning errors. Multiple research efforts have recently been conducted to design optimal estimators and detectors that minimize the integrity risk in ARAIM, while meeting specified continuity and accuracy criteria [7][8][9][10]. These methods have been employed in the 'ARAIM Milestone 2 Report' [2] to identify the circumstances under which dualfrequency GPS/Galileo could satisfy LPV-200 requirements globally.…”

“…In addition, the alert limit (i.e., the limit on acceptable positioning errors, which defines hazardous situations) is 35 meters for LPV-200, which is much larger than, for example, the Category II precision approach alert limit requirement of 10 meters [11]. Thus, given that the methods used in [7][8][9][10] reach the best achievable performance, 'snapshot' ARAIM algorithms cannot provide global service better than LPV-200.…”

Impact quantification of satellite outages on air navigation continuity

“…In particular, the role transition from backup to primary means of navigation has increased the significance of H‐ARAIM continuity as compared to conventional RAIM. Most prior ARAIM work focused on reducing integrity risk [11–13]. Only few investigated continuity, and in most cases, false alarm (FA) was considered the only source of LOC [14, 15].…”