GTECH 201

Session 08GPS

Global Positioning Systems

GPS is a Satellite Navigation System

GPS was originally funded by and controlled by the U. S. military.

GPS provides specially coded satellite signals that can be processed in a GPS receiver, enabling the receiver to compute position, velocity and time.

Four GPS satellite signals are used to compute positions in three dimensions and the time offset in the receiver clock.

The Satellites

The Satellites

The satellite orbits repeat almost the same ground track (as the earth turns beneath them) once each day. The orbit altitude is such that the satellites repeat the same track and configuration over any point approximately each 24 hours (4 minutes earlier each day). There are six orbital planes with four satellites in each equally spaced (60 degrees apart), and inclined at about fifty-five degrees with respect to the equatorial plane. This constellation provides the user with between five and eight satellites visible from any point on the earth.

GPS ReceiversGPS receivers convert the satellite signals into position, velocity, and time estimates. Four satellites are required to compute the four dimensions of X, Y, Z (position) and Time. Navigation in three dimensions is the primary function of GPS. Precise positioning is possible using GPS receivers at reference locations providing corrections and relative positioning data for remote receivers. Surveying, geodetic control, and plate tectonic studies are examples.

Standard Reception

Without further techniques, the accuracy is approximately   100 meter horizontal 156 meter vertical

The position of the receiver is where the signals from a set of satellites intersect.

Standard ReceptionThe position is determined from multiple measurements at a

single measurement epoch. The measurements are used together with satellite position estimates based on the precise orbital elements (the ephemeris data) sent by each satellite. This orbital data allows the receiver to compute the satellite 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-Centred, Earth-Fixed X, Y, Z (ECEF XYZ) coordinates. Three satellites 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. More satellites can provide extra position fix certainty and can allow detection of out-of-tolerance signals under certain circumstances.Position in XYZ is converted within the receiver to geodetic latitude, longitude and height above the ellipsoid. 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.

Y

ReceiverX, Y, Z

0, 0, 0

Equator

X

Z

SatelliteX, Y, Z

PrimeMeridian

Earth-Centred, Earth-Fixed X, Y, Z

Geodetic Latitudeat Point P

Semi Major Axis

Tangent to Ellipsoidat Point P

Point P

Geodetic Longitudeat Point P

EllipsoidSurface Semi Minor Axis

Pole

Equator

Geodetic Heightat Point P

Normal toEllipsoid atPoint P

Carrier Phase Tracking (Surveying)

• Accuracies of millimeters under special circumstances

• Ionospheric delay differences

• Two receivers be within about 30 km of each other

• Real-Time-Kinematic (RTK)

GPS Error Sources

GPS errors are a combination of noise and bias. Noise and bias errors combine, resulting in typical ranging errors of around fifteen meters for each satellite used in the position solution.

GPS Error Sources

Noise and bias errors combine, resulting in typical ranging errors of around fifteen meters for each satellite used in the position solution

Noise errors Bias errors

Ephemeris (orbital sphere) data errors

Tropospheric delays Ionosphere delays Multipath

Geometric Dilution of Precision (GDOP) and Visibility

GPS ranging errors are magnified by the range vector differences between the receiver and satellites.

The volume of the shape described by the unit-vectors from the receiver to the satellites used in a position fix is inversely proportional to GDOP.

Geometric Dilution of Precision

Poor GDOP, a large value representing a small unit vector-volume, results when angles from receiver to the set of satellites used are similar.

Geometric Dilution of Precision

Good GDOP, a small value representing a large unit-vector-volume, results when angles from receiver to satellites are different.

Geometric Dilution of Precision

GDOP is computed from the geometric relationships between the receiver position and the positions of the satellites the receiver is using for navigation. For planning purposes GDOP is often computed from Almanacs and an estimated position. Estimated GDOP does not take into account obstacles that block the line-of-sight from the position to the satellites. Estimated GDOP may not be realizable in the field.

Differential GPS Techniques

Relative to a known position

Differential corrections may be used in real-time or later, with post-processing techniques

Combined ErrorError source Typical range

errorDGPS (code) range error

< 100 km distanceClock 1 m  

Ephemeris 1 m  

Troposphere 1 m  

Ionosphere 10 m  

Pseudo-range noise

1 m 1 m

Receiver noise 1 m 1 m

Multipath 0.5 m 0.5 m

RMS error 15 m 1.6 m

Combined error 60 m 6 m

Differential Carrier GPS (Survey)

Remote receiver

Reference receiver

Orbit path

Satellite at t1

Satellite at t2