Gaussian‐Pareto overbounding of DGNSS pseudoranges from CORS

Larson, Jordan; Gebre-Egziabher, Demoz; Rife, Jason

doi:10.1002/navi.276

Cited by 14 publications

(14 citation statements)

References 17 publications

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“…Non-Gaussian methods lead to tight overbounds, revealing the trend of the entire underlying distribution. At present, instances of such approaches include the stable overbound [26] and the Gaussian-Pareto overbound (GPO) [27]. Unfortunately, these two methods have defects in their mathematical properties.…”

Section: Previous Work On Single-frequency Overboundsmentioning

confidence: 99%

An Error Overbounding Method Based on a Gaussian Mixture Model with Uncertainty Estimation for a Dual-Frequency Ground-Based Augmentation System

et al. 2022

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To ensure the integrity of a ground-based augmentation system (GBAS), an ionosphere-free (Ifree) filtering algorithm with dual-frequency measurements is employed to make the GBAS free of the first-order ionospheric influence. However, the Ifree algorithm outputs the errors of two frequencies. The protection level obtained via the traditional Gaussian overbound is overconservative. This conservatism may cause false alarms and diminish availability. An overbounding framework based on a Gaussian mixture model (GMM) is proposed to handle samples drawn from Ifree-based GBAS range errors. The GMM is employed to model the single-frequency errors that concern the uncertainty estimation. A Monte Carlo simulation is performed to determine the accuracy of the estimated GMM confidence level obtained by using the general estimation approach. Then, the final GMM used to overbound the Ifree error distribution is analyzed. Based on the convolution invariance property, vertical protection levels in the position domain are explicitly derived without introducing complex numerical calculations. A performance evaluation based on a real-world road test shows that the Ifree-based vertical protection levels are tightened with a small computational cost.

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Section: Previous Work On Single-frequency Overboundsmentioning

confidence: 99%

An Error Overbounding Method Based on a Gaussian Mixture Model with Uncertainty Estimation for a Dual-Frequency Ground-Based Augmentation System

et al. 2022

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“…1 remains a bound-in other words, the probability of the actual VPE exceeding VPL H0 is no greater than P ffmd . Note that, while standard models for σ pr_gnd n exist (e.g., see RTCA 2004), they are not guaranteed to sufficiently bound actual errors for every ground station installation, so this must be validated with specialized analysis and data (Blanch et al 2019;Larson et al 2019).…”

Section: Vertical Protection Level Computationmentioning

confidence: 99%

Ground-Based Augmentation Systems Operation in Low Latitudes - Part 1: Challenges, Mitigations, and Future Prospects

Marini-Pereira

Pullen

Moraes

et al. 2021

J. Aerosp. Technol. Manag.

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Ground-based augmentation systems (GBASs) were designed to support civil aviation precision approach and landing with safety and integrity. It has several advantages over traditional navigation aids, allowing airspace usage optimization and reduction of fuel consumption. However, in low-latitude regions such as Brazil, this technology is still not operational due to the strong influence of ionospheric variability. Considering the increased interest in deploying a GBAS station in Brazil along with efforts toward this goal over the last decade, this paper is the first of a two-part series that provides an overview of the key aspects of this technology and the challenges posed when using it in low-latitude regions. The context in which GBAS operates today in midlatitudes is presented along with its fundamental principles and methods of guaranteeing sufficient accuracy, continuity, and integrity for precision operations, particularly those dealing with threatening ionospheric conditions. Finally, the evolution of GBAS to include multiple Global Navigation Satellite System (GNSS) satellite constellations and signal frequencies are discussed with respect to their ability to mitigate ionospheric effects. The conclusion is that the use of these new elements of GBAS seem to be the most viable solution for operating GBAS in low latitudes with high availability.

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“…Future work will also explore the application of our overbounding methods to SDM and broader GNSS data sets. A forthcoming study combines our overbounding methods with extreme value theory to perform a statistical characterization of distribution far tails .…”

Section: Future Workmentioning

confidence: 99%

Comparing Geometric Approximations of Heavy-Tail Effects for Chi-Square Integrity Monitors

Rife

Parker

2018

J Inst Navig

Self Cite

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This paper considers the verification of integrity monitors used commonly in safety‐of‐life navigation systems. The paper compares three conservative bounds (also known as overbounds) that can be used to compute missed‐detection performance for nominally chi‐square integrity monitors subject to random noise with non‐Gaussian heavy tails. The three overbounds rely on simple geometric shapes – cones, cylinders, and spheres – to ensure that missed‐detection probability can be computed conservatively, reliably, and efficiently. The overbounds provide conservative estimates of missed‐detection performance even when the exact form of the noise distribution is not known, so long as the noise CDF is spherically symmetric. Monte Carlo simulations suggest that, for moderate and large faults, the spherical overbound performs best, but for small faults, the cylindrical overbound performs best, at least in the case of a two‐dimensional vector space. © 2018 Institute of Navigation

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Gaussian‐Pareto overbounding of DGNSS pseudoranges from CORS

Cited by 14 publications

References 17 publications

An Error Overbounding Method Based on a Gaussian Mixture Model with Uncertainty Estimation for a Dual-Frequency Ground-Based Augmentation System

An Error Overbounding Method Based on a Gaussian Mixture Model with Uncertainty Estimation for a Dual-Frequency Ground-Based Augmentation System

Ground-Based Augmentation Systems Operation in Low Latitudes - Part 1: Challenges, Mitigations, and Future Prospects

Comparing Geometric Approximations of Heavy-Tail Effects for Chi-Square Integrity Monitors

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