Doug Bade wrote:
[snip] ... sub-centimeter GPS's for Surveying, and these measurements are possible... OK... We have discussed that the GPS signal received as displayed is at the antenna.... Where is
that little millimeter of antenna to which the sub-centimeter reading refers too???
and Russ, KB0TVJ replied
...The reference point for the position measurement is the focal point of the antenna. This is the point, generally located a short distance behind the antenna aperture, which the far field spherical wave fronts are centered about. Our antennas come from the manufacturer with this point precisely characterized in the documentation. This information is usually determined by measurements in a near field antenna range.
Sorry to be late in answering Doug, but I was in Alaska on business and just got back. These antenna-related issues refer to something that is one of my specialties. Russ is nearly correct in what he says, but "focal point" is the wrong terminology --- the correct words should have been "phase center".
The sub-cm measurements that Doug asks about are achieved by logging the phase of the 1575 MHz L1 signal (and for some applications also the 1227 MHz L2 signal) for each of the satellites in view at two or more stations. The L1 microwave frequency corresponds to a 19 cm (~7.5 inch) wavelength, so the carrier phase repeats (i.e. is ambiguous) every 19 cm. With the signal- to-noise achieved in practice, this 19 cm long "ruler" can be split into ~100 parts, i.e. it can be resolved to ~2 mm, albeit with a 19 cm ambiguity. The difference phase measurement between the two sites constitutes an interferometer.
The interferometric phase measurement has a geometric contribution due to the desired vector measurement baseline plus the satellite geometry, and has some instrumental biases. The satellite geometry part is taken care of by either using the ephemerides broadcast by the satellites in realtime (which put the satellites into a ~20 meter box ~10,000 km away), or more precise orbits (~20 cm box) available a day later from the IGS (http://igscb.jpl.nasa.gov or http://cddisa.gsfc.nasa.gov).
The instrumental biases arise from phase delays in the antennas (more on this later), coaxial cables, and internally in the GPS receivers. But all the N satellites in view share these biases, so there are N-1 bias-free observables available.
To crunch the data and eliminate the 19 cm carrier phase ambiguities, you make use of the fact that the baseline-satellite geometry is constantly changing. Satellites rise, move across the sky and then set with a 12 hour periodicity. The earth rotates under the satellite constellation every 24 hours. The changing pattern for the combination of all visible satellites "fits" the ambiguous observations for a unique point if you have gathered enough data.
Now back to the antenna part of this process. If the two stations in the interferometric baseline have identical antennas, and if they are close enough so that the satellite az/el is nearly the same at both ends, then the antenna's phase properties will cancel out and be irrelevant. And the location of the real phase reference "point" doesn't matter as long as you assume it is the same at both ends of the baseline.
The geometric point within the antenna where the signals are collected
is called the "phase center". Unfortunately, for a real antenna, the phase
center is not a single point and it moves around depending on:
- the elevation of the satellite
- the azimuth of the satellite
- the signal frequency
- multipath in the vicinity of the antenna
- diffraction by structures near the antenna.
For a description of some of these effects, I refer you to a paper by Bruce Schupler and me "How Different Antennas Affect the GPS Observable" in GPS World, Nov.91, page 32. And for a lot of details on specific antennas, see out paper "GPS User Antennas", Navigation 41, pp278-295, Fall 1994. Bruce and I continue to work in this field and have a number of subsequent papers with details on a lot of more modern antennas. We do our "absolute" measurements on a precision indoor antenna range at NASA Goddard, and then verify them in the field at my IGS site (GODE) near Goddard.
You can see some of the activities at the anechoic chamber in the JPEG
pictures at ftp://aleph.gsfc.nasa.gov/GPS/antennas/
-- specifically see
ftp://aleph.gsfc.nasa.gov/GPS/antennas/6_choke_ants.jpg to see six nearly identical choke-ring antennas from 4 manufacturers collected for a range session last October. You might also note the file ftp://aleph.gsfc.nasa.gov/GPS/antennas/gode-ant.jpg to see my GODE GPS + VLBI station near Goddard. [The other stuff in this directory includes photos of my home-brew L1 choke-ring antenna and info on Matjaz (S53MV)'s quadrifilar helix antenna.]
[As an aside to Russ -- the phase center values that the manufacturers
paste on their products are in general guesses, and assume no elevation
dependence. They really rely on the interferometeric phase differences
to achieve their specs. We are constantly deluged with requests from
the manufacturers to measure (and by implication to "certify") their
newest, greatest products in the GSFC anechoic chamber.]
There can be several ways that the "same at both ends" assumption may be violated:
(1) If the antenna has a non-uniform azimuth phase response (i.e. a non-symmetric pattern), then the antennas need to be mounted so that their "Norths" coincide. All manufacturers provide a "North" mark to guard against such biases. And the manufacturers work hard to make antennas with very uniform azimuthal responses.
(2) If the antennas are not level, then the tilt will cause any elevation-dependent
biases to have an azimuthal contribution. Proper GPS surveying requires
that the antennas be properly
(3) If the manufacturer does not exercise good manufacturing configuration
control, his product may vary from unit to unit. We have a lot of
cases where one production lot is centimeters
from another lot of similar antennas. And if the antennas are of a different style, you can bet there will be differences. And if an antenna is mistreated in the field, it will affect the
measurements. A careful surveyor will periodically recheck a 5-10 meter reference baseline to make certain that his antennas are still "good"!
(4) If the baseline is more than ~100 km long, then the antenna az/el at the two ends will start to differ (111 km = 60 nmi = 1 degree of latitude) by enough to be of concern. At that point, careful users introduce a detailed phase map (like those produced by Bruce & me) into their data analysis.
(5) The local multipath and effects of the antenna tripod/pier are quite
real, but its beyond the scope of this note for me to comment!
In conclusion -- if you are using GPS at levels of 5-10 cm, then the
effects aren't too important. As your requirements push down into the millimeter
range, then they become more and more and more important!