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The quality of world-wide GPS navigation service is frequently described by plotting on a world map background 2-dimensional regions (latitude, longitude) on the Earth's surface where navigation is degraded for some period of time, over the span of a day. Such depictions provide little information concerning when such navigation degradations occur or their duration. Computationally efficient algorithms are presented for computing the locations in space and time of these navigation degradations. Quick geometric formulas are presented for calculating the dilutions of precision. A data base is generated with this approach on a mainframe computer and then post-processed on a high resolution color graphics workstation to produce 3-dimensional plots (latitude, longitude, and time) which insightfully characterize GPS navigation service and its evolution in time. Degradation regions are readily isolated with their time of occurrence, duration, and location clearly defined. Also given are 2-dimensional plots which display location and time of poor coverage permitting an analysis of the quality of coverage from another perspective. Results are provided for the current 7 operational Block 1 satellites, a 9 satellite constellation projected for 1989 when 4 Block 2 SVs will have been added, the GPS baseline 21 SV constellation, and a revised 21 SV constellation under consideration.