Estimating ionospheric delay using kriging: 1. Methodology

The Wide Area Augmentation System (WAAS) is an augmentation of the Global Positioning System (GPS) that provides safe and reliable use of GPS signals for airline navigation over much of North America. Ever since WAAS was first commissioned in July of 2003, the vertical delay estimate at each node in the WAAS ionospheric grid has been determined from a planar fit of slant delay measurements, projected to vertical using an obliquity factor specified by the standard thin shell model of the ionosphere. In a future WAAS upgrade (WAAS Follow-On Release 3), however, the vertical delay will be estimated by an established, geo-statistical technique known as kriging. When compared to the planar fit model, the kriging model is generally found to match better the observed random structure of the vertical delay. This paper presents the kriging methodology to be used to estimate the vertical delay and its uncertainty at each ionospheric grid point. In addition, it provides examples of the improvement in delay accuracy achieved. Under disturbed conditions, the implementation of kriging reduces the magnitude of the root mean square fit residual by up to 15%.