From jimr@maia.usno.navy.mil Tue Mar  9 08:07:08 EST 1999
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From: Jim Ray (USNO 202-762-1444) 
Message-Id: <199903091304.IAA16429@maia.usno.navy.mil>
Subject: Discontinuities in clock estimates
To: gpst@maia.usno.navy.mil
Date: Tue, 09 Mar 1999 8:04:33 EST
X-Mailer: Elm [revision: 212.4]
Status: RO

DISCONTINUITIES IN CLOCK ESTIMATES AT DAY BOUNDARIES
====================================================
   J.R. Ray, M.S. Carter, and J.R. Rohde
   (U.S. Naval Observatory)


SUMMARY
-------
Discontinuities in GPS-based clock estimates at day boundaries are an
inevitable consequence of the standard strategy of processing the 
observational data in 24-hour batches.  However, the discontinuities 
should be consistent with the standard errors of the clock estimates,
normally about 0.2 ns, for realistic error estimates.  We have observed
that larger than expected discontinuities are sometimes obtained in
global network solutions, at about the 1-ns level.  It appears that
these can usually be associated with a specific station rather than
global causes (e.g., satellite orbits).  The source(s) of such station-
related discontinuities has not been positively identified although
changes in local multipath environment seem the likeliest candidate.

OBSERVATIONS
------------
As part of our participation in the IGS/BIPM GPS timing project, the
IGS Associate Analysis Center at USNO posts clock solution results at
the Web site http://maia.usno.navy.mil/gpsclocks/index.html.  Plots
of differential clock variations are provided for our "Rapid" solutions
submitted for the IGS combined Rapid products; plots and RINEX-type
solution files are provided for our "Final" clock solutions.  The two
types of analysis strategies are described at the above Web site.
This report describes results from our Final clock solutions, which
use the IGS Final orbits without adjustment.  Unless unavailable, the
IGS station "USNO" is always used as the fixed clock reference in our
analyses.

GPS week 0987 (06-12 December 1998) is interesting in showing two
distinct day-boundary discontinuities for all the usable H-maser
stations.  The magnitudes of the discontinuities at the midnight
boundaries between adjacent days are shown in the table below:


ESTIMATED CLOCK DISCONTINUITIES (all units ns)
   standard error estimates shown in ()
==========================================
                      GPS Week 0987
               51157/51158     51158/51159
               -----------     -----------
ALGO - USNO   -0.70 (0.20)    -0.97 (0.19)
DRAO - USNO   -0.89 (0.20)    -0.88 (0.19)
IRKT - USNO   -1.32 (0.21)        ---
KOKB - USNO   -1.82 (0.23)    -1.21 (0.26)
MATE - USNO   -1.75 (0.20)    -0.70 (0.22)
NLIB - USNO   -1.08 (0.20)    -0.96 (0.19)
PIE1 - USNO   -1.64 (0.20) *  -0.84 (0.20) * odd tails at day-starts
TID2 - USNO   -2.05 (0.20)    -0.31 (0.21) * rapid variation near boundary
USNB - USNO   -1.02 (0.19)    -0.82 (0.19)
WES2 - USNO   -1.20 (0.20)     0.03 (0.19)
------------------------------------------
 mean (RMS)   -1.33 (0.45)    -0.72 (0.37)
                              -0.83 (0.24) * excluding WES2
==========================================


Because "USNO" is common to all these differences, the ~1-ns
discontinuities can be attributed mostly to that station rather than
all the others.  This expectation has been empirically demonstrated
by reprocessing the Final clock solutions for week 0987 using "DRAO"
as clock reference rather than "USNO".  The results are available in
the subdirectory http://maia.usno.navy.mil/gpsclocks/finals/0987/drao/.
There it can be seen that the day-boundary discontinuities decrease
by about the mean offsets: -1.3 ns for 51157/51158 and -.8 ns for
51158/51159.  The residual discontinuities are then approximately
consistent with the error estimates except for WES2 at 51158/51159,
which could be another example of station-specific effects.  "DRAO"
itself is associated with another discontinuity of ~1 ns at 51156/51157.

STATION-SPECIFIC CAUSES
-----------------------
While we cannot offer a definitive explanation for the observed
discontinuities, the evidence strongly indicates that they are
associated specifically, in this case, with the station "USNO" rather
than with a more general cause, such as orbit error or analysis
strategy.  The orbit error required would be ~30 cm averaged over the
full constellation, compared with typical internal consistencies for
individual IGS orbits at the 5 cm level or better.  Moreover, if orbit
errors were responsible then we would expect the effect to be nearly
identical for "USNO" and "USNB" (the Swiss GeTT/Ashtech system
temporarily deployed at USNO), which is not the case.  These clock
discontinuities are also similar for the USNO Rapid solutions (for the
common stations), for which the satellite orbits are adjusted
simultaneously with the clocks.

Another possible general cause could be a defect in the analysis strategy.
However, USNO results for satellite clocks and other estimated parameters
generally compare very favorably with the other IGS Analysis Centers in
the IGS Rapid combination reports.  The USNO clock residuals have a
typical RMS of about 0.2 ns, compared with the IGS combined satellite
clocks.  Since receiver clock products are not yet compared within the IGS,
it is possible that analysis defects exist which affect ground-based clock
estimates much more than satellite clocks.  However, this seems unlikely.

The simplest explanation seems to be that the discontinuities are
station specific.  A receiver-based effect is possible, particularly
considering that "USNO" uses an AOA TurboRogue SNR-12 receiver while
"USNB" uses a modified Ashtech Z-XII receiver.  The tracking
performance is quite different for these two, especially at L2 and
at low elevation angles.  However, it is difficult to imagine how ~1 ns
(~30 cm) of clock difference could be obtained without affecting other
geodetic parameters unless the problem were restricted to receiver
"clock" circuitry.  In the latter case, there is no reason to expect the
effects to show up preferentially at midnight epochs.

While we cannot demonstrate this, we believe that changes in the local
multipath environment are probably the best explanation.  In the geodetic
method, the precision of clock variations is derived from the carrier
phase observables.  However, the "absolute" value for the clocks is
derived from the time-averaged pseudorange observables, which are
required in order to permit simultaneous estimation of the phase bias
parameters.  The pseudorange data are less precise and much more sensitive
to multipath than the carrier phase data.  Whether time-averaged daily
differences in multipath at the 1-ns level are reasonable is unclear to
us, although shorter term pseudorange variations at this level are common.

Even if the underlying cause is local multipath, the analysis strategy
could be changed to attenuate the day-boundary discontinuities.
Obviously, if the data were processed as a continuous stream or if
constraints between 24-hour arcs were applied, the day-boundary shifts
could be largely eliminated.  However, such approaches would only be
expected to redistributed the underlying error among other parameters
rather than remove it.  Implementation of phase cycle ambiguity
resolution, which is not done in any of the USNO solutions, might be
expected to be useful.  However, that procedure essentially fixes the
phase bias parameter at their estimated values and depends on the
pseudorange data in the same way.  The main benefit should be an
improvement in clock precision, not accuracy.

Week 0987 (and neighboring weeks) was checked because of concerns about
mechanical work being done on the roof of the building near the GPS
antenna during that period (see IGS Mail #2150).  At various times,
significant amounts of sheet metal and other metal pieces have been
moved around near the antenna.  However, we have no specific records of
these events to verify particular multipath circumstances.  The week was
unseasonably warm so there was no snow accumulation; there was significant
rain on 08 December (51155) and 12-13 December (51159-51160) but not
around the day-boundaries in question.

We invite comments from other groups who have investigated these or
related effects.