[time-nuts] Sub mm measurements with gps timing antennas?

J. Forster jfor at quikus.com
Wed Apr 25 17:53:14 UTC 2012


>From a friend:

Yes, emphatically!  It was established more than twenty years ago, by
theory and experiment, that simple GPS receiving antennas yield position
determinations with errors of many millimeters, and time-synchronization
errors of equivalent magnitude (i.e., many millimeters multiplied by the
speed of light), for two reasons:

(1) The locus of constant phase of the antenna's received-signal output is
not spherical, even when the antenna is in an anechoic environment.  In
other words, the antenna has no well-defined phase-center.  The apparent
phase center is typically a strong function of the elevation angle, and
also varies substantially with the azimuth, from which a signal is
received.

(2) In the real world, an antenna's received-signal output is a
superposition of the desired signal (received directly from a satellite
via free-space TEM propagation) and one or more undesired signals,
received via reflection and/or scattering from surfaces/objects near the
antenna.  The strongest of these undesired signals has usually been
reflected from the ground.  The phase of the composite signal, i.e., the
superposition of desired and undesired signal components, differs from the
phase of the desired signal.  The magnitude of the difference can be
greater than a radian, and can vary so slowly, or so _systematically_,
that time-averaging fails to eliminate its effects.

An ideal GPS receiving antenna would respond to signals received directly
from satellites without introducing direction-dependent phase variation;
and would NOT respond to reflected or scattered signals.  A highly
directive antenna such as a well-designed parabolic "dish" reflector with
very low sidelobes could do this for just one satellite at a time, but
simultaneous observations of multiple satellites are required to cancel
receiver-related errors; so the antenna that's usually regarded as ideal
has a "upper-hemispheric" gain pattern.  That is, its gain (both magnitude
and phase) is uniform for the whole sky, but its gain is zero below the
horizon.

The gain must be nil below the horizon because it is practically
impossible to prevent reflection from the surface of the ground, and
because ground-reflection effects cannot be modeled and accounted for
theoretically unless the electromagnetic properties of the ground
material(s) can be characterized and the topography determined at the
millimeter level.  In some GPS geodetic measurements, sub-millimater
accuracy has been achieved by covering the actual ground with a usefully
large sheet of metal that was planar and horizontal within a small
fraction of one millimeter.  However, a sufficiently large and precise
artificial "ground plane" is expensive and cumbersome, so it is seldom
used.  Artificial ground-planes having diameters less than a meter are not
uncommon, but careful experiments have shown that they are not
satisfactory for submillimeter work.

In antenna theory there is a well-known Fourier-transform relation between
an antenna's gain as a function of direction, and the spatial distribution
of RF current on the surface of the antenna.  It follows from
Fourier-transform properties that, for the gain of an antenna to cut off
very sharply at the horizon, the antenna must be spatially large.  Sharp
horizon-cutoff is most efficiently achieved by extending the antenna
vertically (perpendicular to the horizon plane).  Sharp horizon-cutoff can
also be achieved by extending the antenna horizontally for all azimuths,
in other words, by making the antenna in the form of a very large,
circular, disk.  One-dimensional, vertical extension requires less
material (mass, weight, and cost) than two-dimensional, horizontal
extension.

The referenced "bullet" antenna you mention has small extent both
vertically and horizontally; so it is effectively useless for
millimeter-level work.


Best,

-John

===============









>
> You are not going to get anywhere near sub-mm levels without doing L1/L2
> measurements with a geodetic grade receiver and thermally stabilized
> antenna (and receiver/cable).   With a patch antenna (which is in a lot of
> timing antenas) on a geodetic L1/L2 receiver you can see 1 meter errors!
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