This paper derives geometric formulations for computing dilutions of precision (DOPs), such as GDOP, PDOP, and HDOP. These formulations are in terms of volumes, areas, and lengths determined by the unit vectors pointing from the receiver to the satellites. They often result in very efficient computer algorithms for computing the DOP quantities. The underlying methods easily generalize to any dimension for DOPs involving any number of transmitters.
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Massatt et al. (1990) studied this question.