A fast and efficient integrity computation for non-precision approach performance assessment

Abstract

The level of safety to be expected from global positioning system (GPS) must be known in order to use it to support safety critical operations such as air navigation. This is captured by the navigation performance parameter of integrity which includes the ability of the navigation system to deliver a warning to the user in the event of a significant failure and within a specified time-to-alert. Given the high percentile requirement associated with integrity, assessment of expected system performance both in the nominal case and during failure events, requires the application of analytical techniques. This paper identifies the weaknesses of the current methods for assessing the level of performance to be expected of GPS for non-precision approaches and proposes ways to address them including a novel application of a mathematical integration technique that greatly reduces the computational load associated with integrity performance calculations. Results based on computation times show that the new method reduces computational load by a factor of 500? with a high accuracy and associated high level of confidence. It is shown that in some cases, the technique presented is able to improve GPS RAIM availability beyond the gains achieved by measurement weighting.

Integrity Risk Minimisation in RAIM Part 2: Optimal Estimator Design

“…Determining the worst-case f i is achieved using a line-search process, also implemented in Lee (1995), Milner and Ochieng (2010) and Jiang and Wang (2014). The line search can be avoided using the alternative approach given in Section 3.…”

Integrity Risk Minimisation in RAIM Part 1: Optimal Detector Design

“…Multiple implementations of SS and χ 2 RAIM have been derived, for example, regarding the treatment of the worst-case fault magnitude as explained in Lee (1995), Milner and Ochieng (2010) and Jiang and Wang (2014). In order to establish fair grounds for analysis, the approach pursued in this paper is based on a common, tight integrity risk bound defined in Section 2.…”

“…The worst-case fault magnitude f i , which maximizes the integrity risk given H i , is found using a straightforward line search algorithm (e.g., used in Lee (1995), Milner and Ochieng (2010) and Jiang and Wang (2014)). For the fault-free case (i = 0), the following notation is used: f 0 = 0.…”

A New Approach to Calculate the Horizontal Protection Level

“…THE PROBABILITY OF THE HORIZONTAL POSITION ERROR. Two methods to calculate the exact probability P PE are studied: the Imhof approach (Imhof, 1961) and the DJ approach (DiDonato and Jarnagin, 1961;Milner and Ochieng, 2010). They are chosen in consideration of the ability to control error tolerance for high accuracy, which is set at 10 −9 for both implementations.…”

“…Milner (2009) as well as Milner and Ochieng (2010) to improve the computational efficiency. But since the two loops impose a considerable computational burden, such improvement is less obvious than the Iterative B method in this test.…”