A New Approach to Calculate the Vertical Protection Level in A-RAIM

Jiang, Yiping; Wang, Jinling

doi:10.1017/s0373463314000204

Cited by 18 publications

(17 citation statements)

References 11 publications

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“…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.…”

Section: N T E G R I T Y R I S K M I N I M I S At I O N I N R a I Mmentioning

confidence: 99%

“…To simplify the calculations in the upcoming derivation, a tight integrity risk bound is given by: where, as defined in Part 1, P Hi is the prior probability of occurrence of hypothesis H i (i.e., fault on measurement subset i ), and f i is the single-Satellite Vehicle (SV) fault magnitude under H i . 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.…”

Section: Non-least-squares Estimator Design To Minimise Integrity Riskmentioning

confidence: 99%

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Integrity Risk Minimisation in RAIM Part 2: Optimal Estimator Design

2016

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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.

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Section: N T E G R I T Y R I S K M I N I M I S At I O N I N R a I Mmentioning

confidence: 99%

Section: Non-least-squares Estimator Design To Minimise Integrity Riskmentioning

confidence: 99%

Integrity Risk Minimisation in RAIM Part 2: Optimal Estimator Design

2016

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“…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.…”

Section: Introduction Receiver Autonomous Integrity Monitoring (Raim)mentioning

confidence: 99%

“…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.…”

Section: Introduction Receiver Autonomous Integrity Monitoring (Raim)mentioning

confidence: 99%

Integrity Risk Minimisation in RAIM Part 1: Optimal Detector Design

et al. 2016

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This paper describes the first of a two-part research effort to find the optimal detector and estimator that minimise the integrity risk in Receiver Autonomous Integrity Monitoring (RAIM). In this first part, a new method is established to determine a piecewise linear approximation of the optimal detection region in parity space. The paper presents examples suggesting that the optimal detection boundary lays in between that obtained using chi-squared residual-based RAIM, and that provided by Solution Separation (SS) RAIM, as one varies the alert limit requirement. In addition, these examples indicate that for realistic navigation requirements, the SS RAIM method approaches the optimal detection region. The SS RAIM detection tests will be employed in the second part of this work, which focuses on the design of non-least-squares estimators to reduce the integrity risk in exchange for a slight increase in nominal positioning error. K E Y WO R D S 1. RAIM.2. Risk minimisation.

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“…But it is observed that the iterative method is not able to control the accuracy of the results with uncertainty caused by the number of steps, and is computationally heavy with two search loops. Therefore, a new approach is proposed here to improve these two performance criteria based on the method in Jiang and Wang (2014) for the Vertical Protection Level (VPL) computation. A new iterative method with one search loop is designed with results showing that it has higher computational efficiency, but the accuracy of the results is still uncertain.…”

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confidence: 99%

A New Approach to Calculate the Horizontal Protection Level

Jiang

Wang

2015

J. Navigation

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A method to compute the minimum Horizontal Protection Level (HPL) using the test statistic of normal distribution, which will exploit advances in computational power to meet the requirement of Time to Alert (TTA), is proposed to improve service availability. To obtain the minimum solution, two approximations used in traditional algorithms need exact solutions: the distribution of the horizontal position error and the determination of the worst case to ensure that the resulting HPL is able to accommodate all possible bias. This is validated with results such that the optimal solution is achieved with a pre-defined accuracy and sufficient computational efficiency. Also, the new HPL is used to determine if current approximated methods are conservative, where one of the methods does not meet the integrity requirement with given test statistics, error model and integrity risk definition. K E Y WO R D S 1. HPL.2. RAIM. GPS

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A New Approach to Calculate the Vertical Protection Level in A-RAIM

Cited by 18 publications

References 11 publications

Integrity Risk Minimisation in RAIM Part 2: Optimal Estimator Design

Integrity Risk Minimisation in RAIM Part 2: Optimal Estimator Design

Integrity Risk Minimisation in RAIM Part 1: Optimal Detector Design

A New Approach to Calculate the Horizontal Protection Level

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