[IGSMAIL-7411] Combined orbits and clocks from the IGS 2nd reprocessing

[Griffiths, Jake]

Author: Jake Griffiths

Dear Colleagues,

As announced in IGS Mail #7399, the IGS will soon adopt IGS14/igs14.atx as the
basis of its products.  Some users have accumulated results in the old
framework, and are looking to begin their own reprocessing back to 1994 using
the IGS14 framework and compatible IGS products.  Combined IG2 orbits and clocks
have been generated, along with an accumulated ERP file generated in the orbit
and clock combination process.  This ERP file, like in IGS operations, should
only be used for comparison with the definitive ERPs provided by the Reference
Frame Combination Center (see IGS Mail #7055).  As with the IG1 reprocessed
products, the full suite of IG2 orbit and clock combination products are
available only for the GPS satellites including:

- ig2[wwww][d].sp3            : daily GPS orbit SP3c files
- ig2[wwww][d].clk            : daily station and GPS 5-min clk RINEX files
- ig2[wwww][d].cls            : daily clk combination summary files
- ig2[wwww]7.erp              : daily ERPs in weekly concatenated files
- ig2[wwww]7.sum              : weekly orbit, clock, ERP combination summary
- ig215p01.erp                : accumulated ERP file from orbit & clock combo

and that last file is in addition to:

- ig215p02.erp                : definitive accumulated ERP file from SINEX combo

where,

wwww is GPS week ranging from 0730...1831, and
d is day-of-week ranging from 0...6

Note: there will not be an IG2 timescale; the IG2 clock products are aligned to
GPST via the broadcast clocks.

The above IG2 products will be submitted to the IGS Data Centers in time for the
transition to IGS14/igs4.atx.


QUALITY OF THE IG2 ORBITS AND CLOCKS
Griffiths and Ray presented a poster at the 2016 AGU Fall Meeting in December
summarizing the IG2 orbit and clock combination results, along with an
assessment of their quality using PPP and a recently refined version of their
day-boundary orbit discontinuity analysis [e.g. Griffiths and Ray, 2009&2013].
That poster is available online at the IGS Analysis Center Coordinator website,
and can be downloaded using this URL:

http://acc.igs.org/repro2/griffiths_ig2.pdf

In addition to the analysis in the AGU poster, estimates of IG2 orbit precision
have since been accumulated.  These estimates are derived from a long-arc
analysis of each weekly set of orbits, where 7 days of Analysis Center and
combined SP3c files are fit for a single orbit state vector and the 9 terms
of the CODE solar radiation pressure model.  Then the RMS, WRMS, and MEDIAN of
residuals are computed on a daily basis.  These statistics are reported in the
companion *.sum files noted above. This procedure is identical to that used
for the operational Finals summaries.

Below is a table containing the average and standard deviation of the daily
WRMS and MEDIAN statistics from the long-arc analysis.  These averages and
standard deviations are computed over the full repro2 time span (GPS Wks 0730
thru 1831, or 1994.003 thru 2015.121).

                       WRMS   [mm]        MEDIAN [mm]
                  IG2  43.5 (+/- 28.9)    26.5 (+/-  8.9)
                IG1/F  41.6 (+/- 30.1)    24.4 (+/- 11.6)

The averages and standard deviations of the WRMS and MEDIAN are taken to
represent the internal long-term precision of the IG2 and IG1/F orbits.  The
question is whether the precision of IG2 is significantly different from that of
IG1/F.  A z-test comparing the average WRMS from IG2 and IG1/F indicates that
the precision of the two solution series is indeed significantly different at
the 99.9% confidence interval, and that IG2 is less precise than IG1/F.  The
same conclusion is drawn when repeating the z-test for the MEDIAN values from
above.

The root of the square differences is computed to approximate the magnitude in
the loss of precision for IG2:

   RDS_wrms = 8.99 mm = sqrt(abs(IG2_wrms^2 - IG1/F_wrms^2))/sqrt(2)
   RDS_medi = 7.31 mm = sqrt(abs(IG2_medi^2 - IG1/F_medi^2))/sqrt(2)

This is an interesting result, especially when compared to a feature of the
companion day-boundary orbit discontinuity results.  While there was no space
for a plot of the IG1/F orbit discontinuity spectra in the AGU poster, it is
worth noting that the white noise floors for the 1D total discontinuties are:

           1D WN floor [mm]
     IG2   27.1
   IG1/F   25.8

The similarity with the long-arc MEDIAN statistics is striking, and supports
the use of the long-arc process for measuring orbit precision.

What caused the loss in precision? The time series of WRMS of residuals from the
orbit combination (Panel 3 of AGU poster) indicates that about half of the
precision loss for IG2 is attributable to not having a contribution from the
National Geodetic Survey (NGS) operational Analysis Center.  The remaining half
is due to other errors in other highly weighted AC repro2 orbits.

Of course, there is a question as to whether the CODE 6+9 model is appropriate
for the IG2 long-arc analysis given changes in some AC orbit models that were
adopted for repro2 (e.g., ESA).  That is, perhaps the CODE 6+9 model is simply
more consistent with the IG1/F orbits, and so the differences in the long-arc
statistics largely reflect model inconsistency.  It is assumed that the 6+9
model has sufficient degrees-of-freedom to adequately represent the IG2 orbits
for this analysis.


RECOMMENDATIONS ON THE USAGE OF IG2 ORBITS AND CLOCKS
Based on the analyses in the AGU poster and the precision estimates provided
above, the IG2 clocks should not be used for long-term PPP reprocessing
campaigns.  The IG2 orbits are compatible with IGS14/igs14.atx framework and can
be used for long-term reprocessing.  While less precise than IG1/F, there are
at least two potential advantages to using the IG2 orbits for long-term
reprocessing:
  * internally consistent over the full history
  * large rotational offsets of the orbital frame prior to GPS Wk 1702 have
    been eliminated for IG2
Plus, the effects of having poorer precision may be reduced in solutions where
double-differencing is used.


RECOMMENDATIONS TO IGS FOR NEXT REPROCESSING
* Need improved orbit modelling and participation
* Forego clock submission/combination if number and quality of submissions is
  insufficient for robust combined product
* Need improved models for sub-daily variations in Earth orientation due to
  ocean tides [Griffiths and Ray, 2013&2016]
* Understand and mitigate (if possible) source of errors at the Mf/Mf' direct
  tidal frequencies [Rebischung et al, 2015&2016; Griffiths and Ray, 2016]
* Full implementation of IERS Conventions by all ACs (with changes below)
* Modify IERS mean pole model to older linear form (to agree with Wahr et al.,
  2015)
* Adopt model for seasonal variations of the low-degree geopotential terms,
  preferably in agreement with ILRS and IDS
* Enforce a common attitude model for all ACs, ideally an improved version
* Require full consistency with IGS and updated IERS Conventions by all ACs
* Establish well-defined analysis standards and reject non-compliant AC
  solutions


Best regards,

Dr. Jake Griffiths
Naval Research Laboratory
4555 Overlook Ave SW
Washington, DC 20375