GPS Navigation Using Three Satellites and a Precise Clock

 

MARK A. STURZA
Litton Aero Products, Canoga Park, Ca.

 

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.

 

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 processessional user position and precise time.

There are situations where the user only has three satellites available and still wishes to utilize GPS. This can be accomplished by equipping the user with a precise clock. Three situations where three satellite and a precise clock GPS navigation would be desirable are discussed in the following section.

 

THREE SATELLITE SITUATIONS

 

Poor Geometry

The lgsatellite GPS constellation described above has been shown’ to exhibit areas of poor four satellite geometry at certain times. A user relying on four satellite GPS navigation in these outage areas will experience extremely poor navigation performance. Four outage areas occur at the same time and repeat at the same location twice a day. The outages disappear and a new set of four appear 40 minutes later at other locations. Thus, there are a total of 72 outage
areas on the earth at various times. The duration of the outages ranges from 5 to 30 minutes with an average of 10 minutes.

 

Satellite Failure

Failure of a GPS satellite in orbit would result in periods of only three satellite coverage of approximately 30-minute duration over large geographic areas2. It may require months for a replacement satellite to be launched.

 

Constellation Build-up

Five GPS satellites will be maintained in orbit during the 1983 to 1986 time period. This will result in 4 to 12 hours per day of three satellite coverage depending on location. From 1986 to 1988, the number of satellites in orbit will be increased from 5 to 18 satellites. This will increase the area and time of three satellite coverage. By the end of 1987, three satellite coverage will be essentially continuously global.

 

 

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