Calibrating antenna phase centers: a tale of two methods

GPS World, Feb, 2005 by Boussaad Akrour, Rock Santerre, Alain Geiger

The calibration of GPS antennas is of the utmost importance in GPS baseline determination, especially when millimeter precision is required for applications such as the monitoring of engineering structures or for GPS attitude determination. For these applications, even correcting for the mean phase center is not enough. To fully meet the precision requirements of these applications, the phase-center variation must also be taken into account.

In relative GPS positioning, both antennas are set up and centered on the two ends of the baseline that is to be measured. The geometric center of each antenna is used to determine the offset in relation to the geodetic point above which the antenna is installed. However, a GPS receiver determines the coordinates of the antenna's electrical phase center. The phase center is defined as being the point where the satellite signal is collected. The offset between the mean phase center and the geometric center of an antenna can range from a few millimeters to several centimeters.

The observation error due to the offset between the instantaneous and the geometric phase centers is represented by the amount of two projections on the antenna-satellite vector (see Figure 1): (1) the mean phase-center error ([epsilon][[PHI].sub.m]), and (2) the phase-center variation ([epsilon][[PHI].sub.r]) that is the difference between the mean phase center and the instantaneous phase center.

This article presents two methods for the calibration of GPS antenna phase centers. The first one is carried out in the field in a relative mode using an antenna-support calibration beam. The second method relies on observations made in an anechoic chamber. A comparison of both methods in relative mode was performed with regard to the components of the mean phase center and the phase-center variations. The results show that the differences between the two methods do not exceed 2 millimeters, even though they use completely different approaches.

Calibration Beam

The first GPS antenna calibration method investigated in our study has been carried out in relative mode using a calibration beam on which a pair of antennas is mounted. That is to say that a slave antenna is calibrated with reference to another one considered as the reference (master) antenna.

The calibration beam was built by the metrology-geodesy laboratory of Universite Laval. It is made of aluminum, with an approximate length of one meter, and it has two antenna mounts with forced-centering bolts. The distance between the centers of the two mounts was accurately measured in the laboratory using an interferometer. A theodolite is permanently installed at the center of the beam in order to define its orientation with a back-sight toward another geodetic point. The sighting axis of the theodolite is perpendicular to the axis formed by the forced-centering bolts of both antenna mounts. To ensure the beam is level in both longitudinal and transversal directions, two tubular bubble levels are perpendicularly mounted on the beam.

The main advantage of the calibration beam over a baseline formed by two arbitrary geodetic reference points is convenience while maintaining a high accuracy in determining the beam azimuth.

The calibration of both antennas, in relative mode, is carried out by using two geodetic points, as follows. The calibration beam was installed on a pillar (PEPS) on the Universite Laval campus and oriented perpendicularly to the direction to another pillar (NORD) by means of the beam's theodolite. Figure 2 illustrates the calibration beam installation on the PEPS pillar.

The length of the calibration beam ([L.sub.B]) is known from laboratory measurements and the beam is leveled and oriented in the field so that the three-dimensional baseline components [DELTA][N.sub.B], [DELTA][E.sub.B], and [DELTA][h.sub.B], are known.

Temperature Compensation. The length of the beam was measured in the laboratory at a temperature of 20[degrees]C. During an antenna calibration session, the beam length gets shorter or longer depending on the ambient temperature. If the ambient temperature exceeds 20[degrees]C, the nominal length of the beam is longer than when calibrated in the laboratory. When the temperature is below 20[degrees]C, the nominal length is shorter. Knowing the thermal expansion coefficient of aluminum (23 parts per million per [degrees]C), the beam length variation and its corrected length are given by the following equations:

[DELTA][L.sub.B] = 23 X [10.sup.-6] X [L.sub.B] X [DELTA]t (1)

[L.sub.Bc] = [L.sub.B] [DELTA][L.sub.B] (2)

where

[DELTA][L.sub.B] is the beam-length variation resulting from aluminum thermal expansion (meters);

[DELTA]t is the difference between the field and calibration temperatures--field minus laboratory ([degrees]C);

[L.sub.B] is the beam length during laboratory calibration (meters);

[L.sub.Bc] is the beam length corrected for thermal expansion (meters).

For example, for an outside operating temperature of -20[degrees]C, the beam length would be shorter than that in the laboratory by almost 1 millimeter.