GPS Navigation Using Three Satellites and a Precise Clock

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. INTRODUCTION The NAVSTAR Global Positioning System (GPS) is a satellite-based radionavigation system intended to provide highly accurate three dimensional position and precise time on a continuous global basis. When the system becomes fully operational in late 1988, it will consist of 18 satellites in six orbital planes inclined at 55”. Each plane will contain three satellites spaced 120” apart in 12-hour orbits. The relative phasing of the satellites from one orbital plane to the next is 40”. Each satellite will continually transmit navigation signals at Ll = 1575.42MHz and L2 = 1227.6MHz consisting of the P-code ranging signal (10.23MBPS), the C/A code ranging signal (l.O23MBPS), and 50BPS data providing satellite ephemeris and clock bias information. Navigation using GPS is accomplished by passive triangulation. The GPS user equipment measures the pseudorange to four satellites, computes the position of the four satellites using the received ephemeris data; and processes