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, thanks to satellite based augmentation systems (SBAS). SBAS systems, including the United State's Wide Area Augmentation System (WAAS), provide corrections and hard bounds on the user errors. The ionosphere is the largest and least predictable source of error. The only ionospheric information available to WAAS is a set of range delay measurements taken at reference stations. From this data, the master station must compute a real time estimate of the ionospheric delay and a hard error bound valid for any user. The variability of the ionospheric behavior has caused the confidence bounds corresponding to the ionosphere to be very large in WAAS. These ranging bounds translate into conservative bounds on user position error. These position error bounds (called protection levels) have values of 30 to 50 meters. Since these values fluctuate near the maximum tolerable limit, WAAS is not always available. In order to increase the availability of WAAS, we must decrease the confidence bounds corresponding to ionospheric uncertainty while maintaining integrity.; In this work, I present an ionospheric estimation algorithm based on kriging. I first introduce a simple model of the Vertical Ionospheric Delay that captures both the deterministic behavior and the random behavior of the ionosphere. Under this model, the kriging method is optimal. More importantly kriging provides an estimation variance that can be translated into an error bound. However, this method must be modified for three reasons; first, the state of the ionosphere is unknown and can only be estimated through real time measurements; second, because of bandwidth constraints, the user cannot receive all the measurements and third there is noise in the measurements. I will show how these three obstacles can be overcome.; The algorithm presented here provides a reduction in the error bound corresponding to the ionospheric delay that results in up to a 40% reduction in Vertical Protection Levels across the United States. This is achieved without any changes in the hardware and without significantly increasing the complexity of the algorithm.