Abstract
The Global Positioning System (GPS) is a satellite based navigation system. Since safety is the main concern for aircraft navigation, various means of monitoring the integrity (certainty of position) have been developed. This is an important area of research in the GPS community. In the following, it will be shown how some numerical linear algebra techniques can be applied to this interesting application. A typical model is presented. A uniform approach to derive the statistics for fault detection and isolation by orthogonal transformations is given. It is shown that the diagonal elements ω ii 2 of the orthogonal projection matrix onto the residual space are fundamental to the theory and understanding of integrity. ω ii can, for example, have a drastic effect on integrity when they are small. The sensitivity of related problems in this area are discussed.
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