A Method of Over Bounding Ground Based Augmentation System (GBAS) Heavy Tail Error Distributions

2005 ◽  
Vol 58 (1) ◽  
pp. 83-103 ◽  
Author(s):  
Ronald Braff ◽  
Curtis Shively
Keyword(s):  
Local Area ◽  
Tail Probability ◽  
Heavy Tail ◽  
General Interest ◽  
Local Area Augmentation ◽  
Model Distribution ◽  
Tail Distribution ◽  
Error Distributions ◽  
Navigation Error ◽  
Normal Inverse Gaussian

The purpose of this paper is to describe a statistical method for modelling and accounting for the heavy tail fault-free error distributions that have been encountered in the Local Area Augmentation System (LAAS), the FAA's version of a ground-based augmentation system (GBAS) for GPS. The method uses the Normal Inverse Gaussian (NIG) family of distributions to describe a heaviest tail distribution, and to select a suitable NIG family member as a model distribution based upon a statistical observability criterion applied to the FAA's LAAS prototype error data. Since the independent sample size of the data is limited to several thousand and the tail probability of interest is of the order of 10−9, there is a chance of mismodelling. A position domain monitor (PDM) is shown to provide significant mitigation of mismodelling, even for the heaviest tail that could be encountered, if it can meet certain stringent accuracy and threshold requirements. Aside from its application to GBAS, this paper should be of general interest because it describes a different approach to navigation error modelling and introduces the application of the NIG distribution to navigation error analysis.

scholarly journals Optimal heavy tail estimation – Part 1: Order selection

2017 ◽  
Vol 24 (4) ◽  
pp. 737-744 ◽  
Author(s):  
Manfred Mudelsee ◽  
Miguel A. Bermejo
Keyword(s):  
Time Series ◽  
Heavy Tails ◽  
Characteristic Exponent ◽  
Tail Probability ◽  
Heavy Tail ◽  
Infinite Variance ◽  
Accurate Estimation ◽  
Monte Carlo Experiment ◽  
River Elbe ◽  
Tail Estimation

Abstract. The tail probability, P, of the distribution of a variable is important for risk analysis of extremes. Many variables in complex geophysical systems show heavy tails, where P decreases with the value, x, of a variable as a power law with a characteristic exponent, α. Accurate estimation of α on the basis of data is currently hindered by the problem of the selection of the order, that is, the number of largest x values to utilize for the estimation. This paper presents a new, widely applicable, data-adaptive order selector, which is based on computer simulations and brute force search. It is the first in a set of papers on optimal heavy tail estimation. The new selector outperforms competitors in a Monte Carlo experiment, where simulated data are generated from stable distributions and AR(1) serial dependence. We calculate error bars for the estimated α by means of simulations. We illustrate the method on an artificial time series. We apply it to an observed, hydrological time series from the River Elbe and find an estimated characteristic exponent of 1.48 ± 0.13. This result indicates finite mean but infinite variance of the statistical distribution of river runoff.

Technical and Programmatic Features of the FAA's LAAS

1999 ◽  
Vol 52 (2) ◽  
pp. 217-234
Author(s):  
R. Swider ◽  
K. Kaser ◽  
V. Wullschleger ◽  
J. Warburton ◽  
R. Braff
Keyword(s):  
Field Testing ◽  
Federal Aviation Administration ◽  
Local Area ◽  
Initial Development ◽  
Technical Aspects ◽  
Local Area Augmentation ◽  
The Us ◽  
Status Information ◽  
Local Area Augmentation System ◽  
The Government

The US Federal Aviation Administration (FAA) is developing and planning to field the Local Area Augmentation System (LAAS). LAAS is a Ground-Based Augmentation System (GBAS) to GPS, and is designed to serve all categories of precision approach. The purpose of this paper is to provide the latest technical and status information on the LAAS programme. The technical aspects of the LAAS specification are discussed, followed by a description of specification validation field testing and results. Institutional and programmatic aspects are then summarized along with a chronology of events leading up to the Government Industry Partnership (GIP) for the initial development and fielding of LAAS.

scholarly journals Large Cliques in a Power-Law Random Graph

2010 ◽  
Vol 47 (4) ◽  
pp. 1124-1135 ◽  
Author(s):  
Svante Janson ◽  
Tomasz Łuczak ◽  
Ilkka Norros
Keyword(s):  
Random Graph ◽  
Power Law ◽  
High Probability ◽  
Simple Algorithm ◽  
Heavy Tail ◽  
Degree Sequences ◽  
Constant Size ◽  
Tail Distribution ◽  
Law Degree ◽  
Large Clique

In this paper we study the size of the largest clique ω(G(n, α)) in a random graph G(n, α) on n vertices which has power-law degree distribution with exponent α. We show that, for ‘flat’ degree sequences with α > 2, with high probability, the largest clique in G(n, α) is of a constant size, while, for the heavy tail distribution, when 0 < α < 2, ω(G(n, α)) grows as a power of n. Moreover, we show that a natural simple algorithm with high probability finds in G(n, α) a large clique of size (1 − o(1))ω(G(n, α)) in polynomial time.

scholarly journals Analysis of Peak Flow Distribution for Bridge Collapse Sites

Water ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 52 ◽  
Author(s):  
Fahmidah U. Ashraf ◽  
Madeleine M. Flint
Keyword(s):  
Peak Flow ◽  
Flow Distribution ◽  
Heavy Tail ◽  
Flood Frequency ◽  
Return Periods ◽  
Peak Flows ◽  
Tail Distribution ◽  
Bridge Collapse ◽  
Flood Magnitude ◽  
Distribution Parameters

Bridge collapse risk can be evaluated more rigorously if the hydrologic characteristics of bridge collapse sites are demystified, particularly for peak flows. In this study, forty-two bridge collapse sites were analyzed to find any trend in the peak flows. Flood frequency and other statistical analyses were used to derive peak flow distribution parameters, identify trends linked to flood magnitude and flood behavior (how extreme), quantify the return periods of peak flows, and compare different approaches of flood frequency in deriving the return periods. The results indicate that most of the bridge collapse sites exhibit heavy tail distribution and flood magnitudes that are well consistent when regressed over the drainage area. A comparison of different flood frequency analyses reveals that there is no single approach that is best generally for the dataset studied. These results indicate a commonality in flood behavior (outliers are expected, not random; heavy-tail property) for the collapse dataset studied and provides some basis for extending the findings obtained for the 42 collapsed bridges to other sites to assess the risk of future collapses.

US Satellite Navigation Program Status

1999 ◽  
Vol 52 (3) ◽  
pp. 303-312
Author(s):  
Carl McCullough
Keyword(s):  
Federal Aviation Administration ◽  
Satellite Navigation ◽  
Local Area ◽  
The United States ◽  
Civil Aviation ◽  
National Airspace System ◽  
Local Area Augmentation ◽  
The Us ◽  
Navigation Program ◽  
Wide Area Augmentation System

This, and the following paper, were first presented during the European GNSS98 Symposium held at the Centre de Congrès Pierre Baudis, Toulouse, France, from 20 to 23 October 1998; however, both authors have provided updated scripts for use in this Volume of the Journal.This paper provides an update of the development and implementation of the United States of America Federal Aviation Administration (FAA) Wide Area Augmentation System (WAAS) and Local Area Augmentation Systems (LAAS). It also addresses FAA efforts to implement these satellite navigation technologies into the US National Airspace System (NAS), as well as interoperability efforts concerning Satellite Based Augmentation Systems (SBAS) between the FAA and other worldwide Civil Aviation Authorities.

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