GPS World, February 2014

Algorithms Methods INNOVATION Ionospheric Modeling Using GPS Greater Fidelity Using a 3D Approach Wei Zhang Attila Komjathy Simon Banville and Richard B Langley MAY YOU LIVE IN INTERESTING TIMES So goes the purported Chinese proverb and curse When it comes to the ionosphere an interesting time might indeed be a curse for most users of GPS The ionosphere that region of the upper atmosphere where free electrons exist in sufficient numbers to affect the propagation of radio waves owes its existence primarily to the extreme ultraviolet EUV and x ray photons emitted by the sun They ionize atoms and molecules in the upper atmosphere freeing the outer electrons Mostly the ionosphere is well behaved but it can get quite interesting when it is disturbed by space weather events such as solar flares or coronal mass ejections The signals from the GPS satellites are perturbed as they transit the ionosphere Pseudorange measurements are increased in value an additional delay and carrier phase measurements are decreased a phase advance If not fully modeled or otherwise INNOVATION INSIGHTS with Richard Langley Ionospheric perturbations can decrease the accuracy of GPS accounted for the perturbations can decrease the accuracy of GPS positioning navigation and timing PNT For highest PNT accuracies observations are made at the two frequencies transmitted by all GPS satellites and because the ionospheres effect on radio signals is dispersive a linear combination of the measurements removes almost all of the ionospheric perturbations On the other hand the ionospheres effect on single frequency observations must be corrected using a model Most commonly the model assumes that all of the electrons in the ionosphere can be compressed into a thin shell at a certain height above the receiver This permits the computation of an estimate of the vertical ionospheric delay Then a mapping function is used to predict the slant delay the delay contributing to a GPS measurement The approach works reasonably well particularly if near real time values of vertical delay can be provided to users as is done by the Wide Area Augmentation System and other satellite based augmentation systems However this two dimensional approach ignores the fact that the electron content of the ionosphere is actually spread out in the vertical direction and so has certain inaccuracies which can increase when the ionosphere is disturbed In an effort to improve ionosphere modeling with potential application to singlefrequency GNSS users a couple of my current graduate students together with a former student have investigated a three dimensional approach to ionospheric modeling using empirical orthogonal functions or EOFs to describe the vertical structure of the ionosphere EOFs reduce the dimensionality of a data set or an empirical model consisting of a large number of interrelated variables while retaining as much of the variance present in the data set as possible This is achieved by transforming to a new set of variables the orthogonal functions which are uncorrelated orthogonal and which are ordered so that the first few retain most of the variation present in all of the original variables Only three functions are required to account for more than 99 percent of the variability in the International Reference Ionosphere 2007 for example In this months column we look at the performance of this 3D approach to modeling the ionosphere including times when the ionosphere is particularly interesting Innovation is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering University of New Brunswick He welcomes comments and topic ideas To contact him see the Contributing Editors section on page 4 I onospheric modeling plays an important role in improving the accuracies of positioning and navigation especially for current civil aircraft navigation and mass market single frequency users Measurementdriven models are considered to be among the best candidates for real time single frequency positioning owing to their real time applicability and relatively higher accuracy compared to empirical models such as the GPS broadcast also known as Klobuchar and NeQuick models A good example of a real time positioning application is satellite based augmentation systems SBAS including the Wide Area Augmentation System WAAS the European Geostationary Navigation Overlay Service EGNOS the Japanese MSTAT Satellite based Augmentation System MSAS and the Indian GPS Aided Geo Augmented Navigation system GAGAN Because the ionosphere can be the largest error source in single frequency positioning the accuracy of ionospheric modeling is critical for single frequency applications Several organizations have been routinely providing ionospheric products to correct errors caused by the ionosphere in the form of ionospheric maps that is vertical total electron content vTEC at grid points including regional and global products such as those from WAAS and the International GNSS Service IGS with various processing time delays ranging from near real time to a couple of weeks Among the earliest works of ionosphere modeling the University of New Brunswick Ionospheric Modeling Technique UNB IMT was developed in the mid 1990s This technique was demonstrated to effectively derive both regional and global total electron content TEC maps However most of the models including the current www gpsworld com February 2014 GPS World 59