GPS Navigation Using Three Satellites and a Precise Clock

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Abstract
Navigation using GPS generally requires that the user track four satellites to resolve his 3-D spatial position and time bias. There are several reasons why it is desirable to navigate while tracking only three satellites: —The proposed 18 satellite GPS constellation will exhibit substantial periods of poor four satellite geometry over large geographic areas several times a day. —Failure of a GPS satellite in orbit will result in periods of only three-satellite availability over large geographic areas. —During establishment of the operational GPS constellation, there will be long periods of three-satellite GPS coverage. Three-satellite GPS navigation can be accomplished by equipping the user with a precise clock. The required stability of the clock is a function of the maximum allowable PDOP (Position Dilution of Precision) and the time interval between updates of the clock. Clock updates can be accomplished by tracking four GPS satellites, tracking one GPS satellite from a known location, or conventional time transfer methods. This paper presents a formula for computing PDOP and its components, HDOP (Horizontal DOP) and VDOP (Vertical DOP), as a function of three-satellite geometry and clock stability. This formula is used to plot HDOP and VDOP versus time for representative high quality quartz crystal and low-cost rubidium clocks for two scenarios of satellite geometry. The stability and environmental sensitivity of high quality quartz crystal and low-cost rubidium clocks are discussed.

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