Reference

Global Positioning System Overview
Peter H. Dana
Department of Geography, University of Texas at Austin.

• GPS is an artificial solar system

• the consistent and predictable paths and position of stars and planets were measured with crude instrurments (sextants) and a book of tables (the ephemeris) to triangulate an unknown position on the earth

• NAVSTAR (Navigation Satellite Timing and Ranging), the GPS developed by the US department of Defense (DoD)

• reached initial operational capacity in December, 1993

• has been fully operational since April 27, 1995

• consists of three segments

1. Space Segment: space vehicles (SVs)
   

   • 24 operational satellites (spares as well) orbit the Earth every 12 hours (i.e., not geosynchronous) at 20,200 km

   • six orbital planes inclination of 55 degrees to the equator

   • satellites appear 4 minutes earlier each day

   • spacing of satellites such that 5 satellites will be available (in view) to users worldwide (with PDOPs < 7)

   • two components of radio message transmitted by the satellites; one for timing purposes (pseudo random code) and one for satellite positioning (ephemeris)

2. Control Segment

• consists of four monitoring stations around the world close to the equator (Hawaii, Kwajalein, Ascension Island, Diego Garcia) and master control station in Colorado Springs

• twice daily information is uploaded to the satellites relating to navigation and ephemeris

3. User Segment

   • the users, including receivers, hardware, software, antennas, computers and data loggers

   • positioning, velocity and timing information

Satellite Trilateration

• 2D - require 3 known locations to determine a position
• 3D - require 4 know locations to determine a position

Satellite Ranging

• GPS receivers determine a range (distance between a GPS antenna and the satellite) by measuring the the travel time of a signal from the satellite by comparing the "pseudo random code" it generating with an identical code in the signal form the satellite
• the receiver "slides the code" code it is synchronous with the satellite code; the time required to synchronize the is the travel time of the signal

Timing

• clocks in the GPS receiver and on board the satellites must be synchronized
• GPS receivers have quartz clocks, satellites have atomic clocks
• timing is critical, since it is the basis for ranging

GPS Positioning Services

Authorized users (U.S. and Allied military, certain U.S. Government agencies, and selected civil users specifically approved by the U.S. Government) with specially equipped receivers use the Precise Positioning System

PPS Predictable Accuracy

• 22 meter Horizontal accuracy
• 27.7 meter vertical accuracy
• 100 nanosecond time accuracy

Standard Positioning Service (SPS)

Civil users worldwide use the SPS without charge or restrictions. Most receivers are capable of receiving and using the SPS signal. The SPS accuracy is intentionally degraded by the DOD by the use of Selective Availability.

SPS Predictable Accuracy

• 100 meter horizontal accuracy
• 156 meter vertical accuracy
• 340 nanoseconds time accuracy

GPS Satellite Signals

The SVs transmit two microwave carrier signals.

• L1 frequency (1575.42 MHz) carries the navigation message and the SPS code signals.
• L2 frequency (1227.60 MHz) is used to measure the ionospheric delay by PPS equipped receivers.

Three binary codes shift (modulate) the L1 and/or L2 carrier phase.

• The C/A Code (Coarse Acquisition), repeating 1 MHz Pseudo Random Noise (PRN), modulates the L1 carrier phase. There is a different C/A code for each SV. This code is the basis for the civil SPS.
• The 10 MHz P-Code (Precise) modulates both the L1 and L2 carrier phases. The P Code is the basis for the PPS.
• The Navigation Message also modulates the L1-C/A code signal. The Navigation Message is a 50 Hz signal consisting of data bits that describe the GPS satellite orbits, clock corrections, and other system parameters.

Selective Availability

• DoD randomly and intentionally limits the accuracy of the NAVSTAR GPS by transmitting a false signal (different time, different position)
• selective avallability will be turned off in nine years (perhaps by year 2000)
• this largest source of error but can be entirely corrected by differential correction
• 100 m error is a conservative estimate - most of the time it is closer to 50 m

Propagation Delays

• signal speed is theoretically at the speed of light but only true in a vacuum
• travel through the ionosphere and atmosphere and perhaps canopy delays are small (5 metres)
• and predicable
• corrected through dual frequency receivers (L1 & L2) that determine ionospheric delays

Dilution of Precision - DOP

• a function of the geometry of satellites
  • satellites are clustered - poor geometry - poor triangulation
  • satellites distributed across the sky - good geometry
• software on receiver can filter data with unacceptable DOPS
• numerous DOPs:
  • PDOP = Position Dilution of Precision (3-D), sometimes called Spherical DOP
  • HDOP = Horizontal Dilution of Precision (Latitude, Longitude)
  • VDOP = Vertical Dilution of Precision (Height)
  • TDOP = Time Dilution of Precision
• while each of these GDOP terms can be individually computed, they are formed from covariances and so are not independent of each other
• a high TDOP, for example, will cause receiver clock errors which will eventually result in increased position errors

Ephemeris and Clock Error on Satellites

• predicable orbits, precise clocks
• DoD monitors satellites
• small error (2 metres)

Receiver Error

• rounding
• resolving the pseudo random code
• depends on type of receiver (code, carrier, dual freq.)
• small error (1 metre)

Multipath

• signal deflected before it reaches the receiver's antenna
• range measurement becomes longer
• cannot correct for this error
• antenna design and position is important

Differential GPS

Differential positioning is used to corrects bias at one location with measured bias errors at a known position. A reference receiver, or base station, computes corrections for each satellite signal. These corrections are passed to the remote, or rover, receiver which must be capable of applying these individual pseudo-range corrections to each SV used in the navigation solution. both receivers have to be using the same set of SVs. Differential corrections may be used in real-time or later, with post-processing techniques. Real-time corrections can be transmitted by radio link. Many public and private agencies (e.g., Geomatics Canada) record DGPS corrections for distribution by electronic means.

To remove Selective Availability (and other bias errors), differential corrections should be computed at the reference station and applied at the remote receiver at an update rate that is less than the correlation time of SA. Suggested DGPS update rates are usually less than twenty seconds. DGPS removes common-mode errors, those errors common to both the reference and remote receivers (not multipath or receiver noise). Errors are more often common when receivers are close together (less than 100 km). Differential position accuracies of 1 - 10 meters are possible with DGPS based on C/A code SPS signals.

Carrier Phase Tracking (Surveying)

Carrier-phase tracking of GPS signals has resulted in a revolution in land surveying. All carrier-phase tracking is differential, requiring both a reference and remote receiver tracking carrier phases at the same time. In order to correctly estimate the number of carrier wavelengths at the reference and remote receivers, they must be close enough to insure that the ionospheric delay difference is less than a carrier wavelength. This usually means that carrier-phase GPS measurements must be taken with a remote and reference station within about 30 kilometers of each other. Special software is required to process carrier-phase differential measurements. Newer techniques such as Real-Time-Kinematic (RTK) processing allow for centimeter relative positioning with a moving remote receiver. This use of GPS requires specially equipped carrier tracking receivers.

The L1 and/or L2 carrier signals are used in carrier phase surveying. If tracked and measured these carrier signals can provide ranging measurements with relative accuracies of millimeters under special circumstances. Tracking carrier phase signals provides no time of transmission information. The carrier signals, while modulated with time tagged binary codes, carry no time-tags that distinguish one cycle from another. The measuremerts used in carrier phase tracking are differences in carrier phase cycles and fractions of cycles over time. At least two receivers track carrier signals at the same time. Phase difference changes in the two receivers are reduced using software to differences in three position dimensions between the reference station and the remote receiver. Problems result from the difficulty of tracking carrier signals in noise or while the receiver moves.