DETERMINATION OF PSEUDORANGE AND CARRIER PHASE MULTIPATH
1. Introduction
Pseudorange multipath is mainly governed by the following factors:

the location of the antenna: is a ground plane or choke ring available, are
higher conducting obstacles nearby,

the quality of the antenna: does the antenna have low sensitivity for low
elevation signals,

the quality of the receiver: do the tracking algorithms of the receiver channels
poses multipath reduction techniques.
For a reference station the location can be optimized, a high quality antenna
with a choke ring can further minimize multipath. The user however can often
not optimize location and antenna type. It is therefore advantageous to know
the multipath behavior of antenna/receiver under optimal conditions,
and under the normal usage conditions. Estimates can then be made for the
antenna contribution and for the receiver contribution.
2. Pseudorange multipath.
Pseudorange multipath is fairly easy to determine. The following recipe can
be used.

Set up the receiver and antenna for either optimal or normal usage. Power
up the receiver and start downloading of pseudoranges and carrier phases.
Record data for several hours at a rate of once per second, until the full
range of satellite elevations has been covered.

Convert pseudoranges and carrier phases to length units (usually pseudoranges
are already in meters, but carrier phases in cycles. To convert from cycles
to meters multiply by the speed of light (c = 299792458 m/s) and divide by
the L1 frequency (1575.42 MHz).

Subtract for each satellite and for each moment the carrier range from the
pseudorange. This cancels common errors, such as satellite clock error, satellite
position error, tropospheric error, and receiver clock error. Remaining errors
are: twice the ionospheric error, pseudorange multipath error, carrier phase
multipath error, receiver pseudorange noise, receiver carrier phase noise
and the carrier phase ambiguity. The carrier phase multipath and noise are
very small compared to pseudorange multipath and noise respectively, and
can be neglected. As long as the receiver remains in track (no cycle slips)
the carrier phase ambiguity is a constant number.

Select per satellite time slices of about 15 minutes, which are free from
cycle slips. Remove the ambiguity and the double ionospheric error by fitting
a second order polynomial through the data and subsequently subtracting the
second order curve. The thus obtained residuals contain to a large extend
the pseudorange multipath, some pseudorange noise and possibly a small and
slowly varying residual iono term.

Determine the average elevation for the satellite in the 15min time slice.

Determine the standard deviation of the residuals and subtract the pseudorange
noise contribution (as earlier determined for that elevation, see the
"noise" page) using the propagation law
S_{mul} = sqrt(S_{residual}^{2} 
S_{noise}^{2}).

Finally plot the multipath as a function of the elevation.
3. Carrier phase multipath.
Carrier phase multipath is very difficult to determine. However, this form
of multipath is only important to users who want to use the receiver in the
differential carrier mode (with one or more reference receivers) and thus
determine position differences (or 'baselines') to the cm, or even mm level.
In the following recipe, a procedure is described which gives a rough idea
only of the carrier phase multipath for normal usage conditions.

Find a friend with an identical receiver, or a receiver of whom the multipath
is known, and preferably low.

Connect one receiver to an antenna with at least a proper ground plane (a
circular plate of 50 cm diameter), or better a choke ring ground plane, and
connects the other receiver to the 'normal' antenna installation. Locate
the ground plane antenna in a flat area with no obstacles protruding above
this antenna. Locate the other antenna close by, preferably about 10 m.

Connect both receivers to PC's. Power up and start downloading carrier phases.

Record data for a couple of hours until the full range of satellite elevations
have been covered.

Form carrier phase double differences (DD's) for 15 min time slices with
the highest satellite as reference satellite. This cancels common errors
such as satellite clock error, satellite position error, ionospheric error,
tropospheric error, and receiver clock error. Remaining errors are the combined
receiver noise, the combined multipath and the combined carrier phase ambiguity.

Select 15 minute time slices, which contain no cycle slips. In these time
slices the combined carrier phase ambiguity is a constant. Remove this constant
and the effect of the changing satellite  receiver geometry by fitting a
second order polynomial through the DD's and subsequently subtracting
the second order curve. The residuals contain the combined multipath and
noise. If we assume the multipath contribution of the reference satellite
for both receivers low (a reasonable assumption since only low elevation
(less than 40 deg) satellites may show significant multipath), the residual
is largely made up by the multipath of the 'normal' receiver's carrier phase
measurement to the other (not the reference) satellite.

Determine the average elevation for the 15 min time slice.

Determine the standard deviation of the residuals and subtract the DD carrier
phase noise contribution (as earlier determined for that elevation, see the
"noise" page) using the propagation law
S_{mul} = sqrt (S_{DDmul}^{2} 
S_{DDnoise}^{2}).

Finally plot the multipath as a function of elevation.
If the above obtained noise remains below a few (let's say 3) cm, ambiguity
fixing becomes a real option.
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