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Pseudo-Range Navigation
- The position of the receiver is where the pseudo-ranges from a set of SVs intersect.
- Position is determined from multiple pseudo-range measurements at a single measurement epoch. The pseudo range measurements are used together with SV position estimates based on the precise orbital elements (the ephemeris data) sent by each SV. This orbital data allows the receiver to compute the SV positions in three dimensions at the instant that they sent their respective signals.
- Four satellites (normal navigation) can be used to determine three position dimensions and time. Position dimensions are computed by the receiver in Earth-Centered, Earth-Fixed X, Y, Z (ECEF XYZ) coordinates.
ECEF X, Y, and Z Refer Diagram Page5
- Time is used to correct the offset in the receiver clock, allowing the use of an inexpensive receiver clock.
- SV Position in XYZ is computed from four SV pseudo-ranges and the clock correction and ephemeris data.
- Receiver position is computed from the SV positions, the measured pseudo-ranges (corrected for SV clock offsets, ionospheric delays, and relativistic effects), and a receiver position estimate (usually the last computed receiver position).
Pseudo-Range Navigation
Solution Example
Ephemeris Data Set Used in Pseudo-Range Navigation Solution Example
- Three satellites could be used determine three position dimensions with a perfect receiver clock. In practice this is rarely possible and three SVs are used to compute a two-dimensional, horizontal fix (in latitude and longitude) given an assumed height. This is often possible at sea or in altimeter equipped aircraft.
- Five or more satellites can provide position, time and redundancy. More SVs can provide extra position fix certainty and can allow detection of out-of-tolerance signals under certain circumstances.
Receiver Position, Velocity, and Time
- Position in XYZ is converted within the receiver to geodetic latitude, longitude and height above the ellipsoid.
Geodetic Coordinates refer page 4
ECEF XYZ to Geodetic Coordinate Conversion refer page 17
Geodetic to ECEF XYZ Coordinate Conversion refer page 17
- Latitude and longitude are usually provided in the geodetic datum on which GPS is based (WGS-84). Receivers can often be set to convert to other user-required datums. Position offsets of hundreds of meters can result from using the wrong datum.
Geodetic Datum refer pages 1- 22
- Velocity is computed from change in position over time, the SV Doppler frequencies, or both.
- Time is computed in SV Time, GPS Time, and UTC.
- SV Time is the time maintained by each satellite. Each SV contains four atomic clocks (two cesium and two rubidium). SV clocks are monitored by ground control stations and occasionally reset to maintain time to within one-millisecond of GPS time. Clock correction data bits reflect the offset of each SV from GPS time.
- SV Time is set in the receiver from the GPS signals. Data bit subframes occur every six seconds and contain bits that resolve the Time of Week to within six seconds. The 50 Hz data bit stream is aligned with the C/A code transitions so that the arrival time of a data bit edge (on a 20 millisecond interval) resolves the pseudo-range to the nearest millisecond. Approximate range to the SV resolves the twenty millisecond ambiguity, and the C/A code measurement represents time to fractional milliseconds. Multiple SVs and a navigation solution (or a known position for a timing receiver) permit SV Time to be set to an accuracy limited by the position error and the pseudo-range error for each SV.
- SV Time is converted to GPS Time in the receiver.
SV Time to GPS Time
Data Bits
GPS Time is a "paper clock" ensemble of the Master Control Clock
and the SV clocks. GPS Time is measured in weeks and seconds from 24:00:00,
January 5, 1980 and is steered to within one microsecond of UTC. GPS Time
has no leap seconds and is ahead of UTC by several seconds.
GPS Week Number Rollover Comments
- Time in Universal Coordinated Time (UTC) is computed from GPS Time using the UTC correction parameters sent as part of the navigation data bits.
- At the transition between 23:59:59 UTC on December 31, 1998 and 00:00:00 UTC on January 1, 1999, UTC was retarded by one-second. GPS Time is now ahead of UTC by 13 seconds.
UTC from GPS Time
Sample UTC Parameters refer page 27
Carrier Phase Tracking (Surveying)
- Carrier-phase tracking of GPS signals has resulted in a revolution in land surveying. A line of sight along the ground is no longer necessary for precise positioning. Positions can be measured up to 30 km from reference point without intermediate points. This use of GPS requires specially equipped carrier tracking receivers.
- The L1 and/or L2 carrier signals are used in carrier phase surveying. L1 carrier cycles have a wavelength of 19 centimeters. 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 measurements 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. Ionospheric delay differences at the two receivers must be small enough to insure that carrier phase cycles are properly accounted for. This usually requires that the two receivers be within about 30 km of each other.
- Carrier phase is tracked at both receivers and the changes in tracked phase are recorded over time in both receivers.
- All carrier-phase tracking is differential, requiring both a reference and remote receiver tracking carrier phases at the same time.
- Unless the reference and remote receivers use L1-L2 differences to measure the ionospheric delay, they must be close enough to insure that the ionospheric delay difference is less than a carrier wavelength.
- Using L1-L2 ionospheric measurements and long measurement averaging periods, relative positions of fixed sites can be determined over baselines of hundreds of kilometers.
- 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. High accuracy range difference measurements with sub-centimeter accuracy are possible. Problems result from the difficulty of tracking carrier signals in noise or while the receiver moves.
- Two receivers and one SV over time result in single differences.
- Two receivers and two SVs over time provide double differences.
- Post processed static carrier-phase surveying can provide 1-5 cm relative positioning within 30 km of the reference receiver with measurement time of 15 minutes for short baselines (10 km) and one hour for long baselines (30 km).
- Rapid static or fast static surveying can provide 4-10 cm accuracies with 1 kilometer baselines and 15 minutes of recording time.
- Real-Time-Kinematic (RTK) surveying techniques can provide centimeter measurements in real time over 10 km baselines tracking five or more satellites and real-time radio links between the reference and remote receivers.
all about global positioning system page: 1,2,3,4,5,6,7,8.9.10,11,12