Using kriging to bound satellite ranging errors due to the Ionosphere

The Global Positioning System (GPS) has the potential to become the primary navigational aid for civilian aircraft. GPS, however, lacks a fundamental feature for a safety critical system: it does not provide hard bounds on the position inaccuracy. Although most of the time the accuracy is excellent, the position error can become very large without any warning to the user. Consequently, satellite based augmentation systems (SBAS) for GPS have been developed to provide corrections and hard bounds on the user errors. Among the sources of error to GPS positioning, the ionosphere is the largest and least predictable. The only ionospheric information available to the United State’s SBAS, termed the Wide Area Augmentation System (WAAS), at any given time is a set of slant range delay measurements taken at reference stations distributed across the continent. From this limited and randomly scattered data, the master station must compute in real time an estimate of the ionospheric delay and a hard bound valid for any user within range of the reference stations. The variability of the ionospheric behavior and the stringent integrity requirements have caused the confidence bounds corresponding to the ionosphere to be very large in WAAS, on the order of 10 meters of delay. In the position domain, these conservative ranging bounds translate into conservative bounds on vertical position error. These position error bounds are called protection levels and take values of 30 to 50 meters. Since these values fluctuate near the maximum tolerable, WAAS is not always available. In order to increase the availability of WAAS, we need to decrease the confidence bounds corresponding to ionospheric uncertainty while maintaining integrity.