【英文博士2003】USING KRIGING TO BOUND SATELLITE RANGING ERRORS

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Title:USING KRIGING TO BOUND SATELLITE RANGING ERRORS DUE TO THE IONOSPHERE
Author:   Juan Blanch
Year:  2003
Degree:  PHD
Adviser: Per Enge
Abstract:
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.
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, a type of minimum mean square estimator adapted to spatial data, is optimal. More importantly kriging provides an estimation variance at each location that can be easily translated to a confidence bound. However, this method must be modified for two 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 which are needed to apply kriging. I will show how these two obstacles can be overcome.
The algorithm presented here provides up to 40% reduction in the confidence bound corresponding to the ionospheric delay. This reduction in the ionospheric error results in a 20% 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.

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插值的最优算法KRIGING