Course Notes: Overview of GPS
Global Positioning System (GPS) - a radio navigation
facility
- Developed by DoD.
- $12 billion system.
- 24 operational satellites.
- IOC achieved on Dec. 8, 1993 (Block I, II & IIA).
- FOC will be declared when 24 Block II & IIA satellites are operational.
- Civilian users have access to Standard Positioning Service (SPS) »
100 m (95%) accuracy.
- Precise Positioning Service is available to authorized users (military).
Satellite Signals
- L1-1575.42 MHz modulated w/two codes and navigation messages
- L2 - 1227.6 MHz
- C/A - codeÞ SPS
- P-code Þ PPS
- Current level of SPS follows from an intentional degradation of the full C/A - code
capability -- termed Selective Availability (SA).
- SA - falsification of the satellite clock (SA-dither) and
broadcast satellite ephemeris (SA-epsilon).
- On Jan. 31, 1994 antispoofing (AS) was permanently implemented. As is used to encrypt
the P-code, thereby making it unavailable to non-authorized users.
- Encrypted P-codes is referred to as the Y-code.
Observables
- Pseudorange - distance from the satellite to the receiver plus
small corrective terms for clock errors, the ionosphere, the troposphere, and multipath.
Given the geometric positions of the satellites (satellite ephemeris), four
pseudoranges are sufficient to compute the position of the receiver and its clock error.
Pseudoranges are a measure of the travel times of the codes (C/A, P or Y).
- Carrier phase - the difference between the received phase and
the phase of the receiver oscillator at the epoch of measurement.
- Receivers are programmed to make phase observations at equally spaced epochs.
- Receivers keep track of the number of complete cycles received since the beginning of
the measurement.
- Epoch - fixed point in time that is the basis for all
computations.
Classical Navigation
- One receiver observes satellites to determine geocentric position. Positions are
computed for each epoch (SPS, or PPS).
Surveying and Geodesy
- Relative positioning (differential) is used to cancel or reduce common mode errors
(i.e., SA).
- With the initial development of GPS there were significant differences between
navigation and surveying. Today these applications are one and the same. Both applications
employ Differential GPS (DGPS).
Capabilities
- Carrier phase can be measured to 1/100 of a cycle.
- L1 & L2 frequency penetrate the ionosphere well.
- Time delay of ionosphere is inversely proportional to square of frequency -- phase
observations at both frequencies can be used to eliminate this error.
- GPS satellites are stable because of their high altitudes (»
11,000 miles) and therefore atmospheric drag is eliminated.
- Impact of sun and moon on orbits is significant, but can be accurately predicted.
- Remaining problems include solar radiation pressure on satellites, tropospheric delay
and multipath effects on propagated signals.
- Processing of single, double and triple differences yields the relative position between
co-observing receivers.
Example
- Speed of light - 186,000 mi/s
- Frequency of LI - 1575.42 MHz
- >2.04 cm when using carrier phase.
- See Table 1.1 for summary of GPS development to date!
Elements of Satellite Surveying
- Because satellites move in space we must be able to relate space-fixed to earth-fixed
coordinate systems.
- Geocentric Coordinate Systems
Space-Fixed: motion of earth's rotation axis in space on the
basis of a rigid earth model being driven by gravitational pull of sun and moon.
It is now necessary to model the earth as an elastic shell with liquid core.
The current set of nutations (mathematical expressions describing the position of the
earth's rotation axis in space as a function of time) is the "1980 IAU Theory of
Nutation". This theory includes all externally forced motions of the earth's axis.
Earth-fixed: division of earth's lithosphere (solid outer 100 km) into 20 nearly rigid
plates that seem to move independently complicates definition of earth-fixed reference
system.
- Precision and Nutation
Precision refers to long period motions of the earth's axis of rotation in space.
- Nutation are small periodic motions of the earth's axis.
- CEP - celestial ephemeris pole (New Standard!).
- NEP - North ecliptic pole
Celestial Coordinate System:
Figure Missing!
Sphere of Directions
- The sphere of directions allows one to visualize the CEP versus NEP. Distances are not
relevant, only the directions or angles. Translation of one sphere relative to another is
not important.Planes of the ecliptic and equator are normal to the NEC and CEP,
respectively. They are shifted parallel so as to contain the center of the sphere and
intersect the sphere at two distinct great circles.
- The intersection of the ecliptic and equator defines the direction of the vernal
equinox, g ,
- The angle e between the ecliptic and equator is called the
obliquity.
- The directions and planes thus define the celestial (fixed-space) coordinate system.
- Let S denote the direction of an object, such as a star. The plane define by arc S-CEP
and the center of the sphere intersects the sphere in another great circled called the
hour circle.
- The position of the star can now be defined by the right ascention a
and declination d .
- Ascention - angle measured from vernal equinol
counterclockwise in the equatorial phase.
- Declination - angle above or below the equator measured in the
great circle plane, positive angles are in the Northern hemisphere while negative angles
are in the Southern.
- The position of the object can also be given by ecliptic longitude l
and ecliptic latitude b .
- If the center of the direction sphere is located at the center of the sun the position
of the celestial object is termed "heliocentric".
- Measurements from the center of the earth are geometric, and from the earth's surface
are topocentric.
- Unfortunately, the ecliptic latitude and longitude, and the right ascension and
declination are functions of time -- the NEP and CEP are not fixed in space.
- Motion of NEP is called planetary precision.
- Motion of the CEP exhibit long periodic (1 unisolar precision) and many short periodic
motions (nutations).
- This motion is caused by the ever-changing gravitational attraction of the sun, moon,
and other planets.
- Changes in gravitational pull occur as a result or orbits -- the distance between
objects changes continually. These changes are periodic.