ION GNSS 2009
Session C3: Galileo Integrity, Multi-constellation RAIM

Title: Using Kriging to Optimize WAAS Performance Over the Entire Solar Cycle
Author(s): N. Pandya, F. Sheng, O. Castaneda, H. Jeong, N. Haveman, D. Goble, Raytheon Company
Date/Time: Thursday, September 20, 2012, 9:20 a.m.
Room: Room 102/103/104

The ionospheric delay is the primary source of errors for single-frequency Global Positioning System (GPS) receivers. The Wide Area Augmentation System (WAAS) measures ionospheric slant delays using dual frequency receivers in a network of reference stations throughout North America to compute and broadcast ionospheric vertical delays at Ionospheric Grid Points (IGPs) on a thin-shell at a 350 km altitude. Along with each IGP vertical delay, a safety-critical integrity bound called the Grid Ionospheric Vertical Error (GIVE) is also broadcast. The GIVEs are used in receiver computations to determine Vertical Protection Levels (VPLs) for the users, which determine the availability of the navigation service. Since the Initial Operating Capability (IOC) in July 2003, WAAS has computed the vertical delay estimate and the integrity bound at each IGP using a planar fit based on neighboring measurements. In a recent WAAS release, fielded in October 2011, the vertical delay estimates and the GIVEs at the IGPs are computed using kriging, a type of minimum mean square estimator adapted to spatial data using a distance dependent decorrelation. Various tunable ionospheric model parameters exist in the kriging algorithm. These parameters needed to be optimized over the full range of possible ionospheric behaviors. This paper documents the methodology, implementation, and analysis for a trade study that optimized kriging algorithm performance for the range of ionospheric behaviors over the entire solar cycle. A final set of kriging parameters was determined through the trade study that dramatically improved system availability performance and increased system robustness against storm ionospheric activity while maintaining nominal ionospheric performance.

The GIVEs must be large enough to protect against two categories of ionospheric gradients: sampled and undersampled. For sampled ionospheric gradients, the GIVE algorithm implements a chi-squared goodness-of-fit dependent inflation factor. To protect against ionospheric conditions that are not being sampled by WAAS but may be sampled by a user of WAAS, the GIVE algorithm includes an undersampled threat model. The threat model is a set of terms used in the GIVE computation designed to protect a user from the ionospheric gradient threats that the network of reference stations may not have sufficiently sampled. A set of days with high ionospheric activity is used to determine the magnitude of the undersampled ionospheric gradient threat bounding terms used in the GIVE computation. The ionospheric threat model is computed to bound both spatial and temporal threats. In order to provide additional availability while maintaining integrity, the GIVE algorithm implements an irregularity detector at each IGP and the system-wide Extreme Storm Detector (ESD), either of which can set the GIVE to its safe maximum monitored GIVE broadcast value. These two detectors, both of which are driven by metrics dependent on the chi-squared goodness-of-fit statistic, determine when the ionosphere does not match the assumed ionospheric model. All of these components - undersampled threat model, irregularity detector thresholds, and Extreme Storm Detector (ESD) thresholds - had been previously determined for the planar fit algorithm and had to be recomputed for each of the kriging models used in the trade study. The kriging models are defined by a set of ionospheric correlation parameters. For each set of parameters, a trade over a range of irregularity detector trip thresholds was conducted to obtain the best setting for this parameter. If the irregularity detector trips too often, availability will suffer. If it trips too seldom, the undersampled threat model may increase too much, also leading to a loss of availability.

The trade study optimized over a wide range of ionospheric behavior: non-solar maximum nominal ionosphere, moderate ionospheric storms, strong ionospheric storms, severe ionospheric storms, extreme ionospheric storms, solar maximum strong storms, and solar maximum nominal ionosphere. (Note: the ionospheric behavior description uses the nomenclature for geomagnetic storms in the National Oceanic and Atmospheric Administration (NOAA) Space Weather Scales.) In order to determine behavior in the low latitude region during solar maximum, data from the previous solar maximum (when WAAS did not have stations in Mexico) was supplemented with external Mexico data to measure performance of the expanded WAAS system during solar maximum periods. The performance of the system was optimized over the full range of ionospheric behavior to determine the selected kriging parameters.

An undersampled ionospheric gradient threat model was generated for each set of parameters used in the trade study using the Raytheon Threat Model (TM) tool using historical ionospheric storm data. Using the WAAS 3rd Generation Safety Prototype (W3SP) or WAAS 3rd Generation Prototype (W3P) and the Raytheon Service Volume Model (SVM), availability performance was computed over a set of four coverage regions: CONUS, Alaska, Mexico, and North America. Performance was computed for Localizer Performance with Vertical Guidance (LPV) and Localizer Performance with Vertical Guidance with a 200 foot decision altitude (LPV200) aviation service at the 100%, 99%, and 95% availability levels. Historical system data over the full range of ionospheric behavior during the entire solar cycle were used for the trade study.

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