USNO Global VLBI Solution crf2009b
Presented here is the U.S. Naval Observatory's crf2009b global solution. Parametrization of this solution follows that of the International Celestial Reference Frame (ICRF) solution (Ma et al. 1998, AJ, 116, 516) and its extensions (Fey et al. 2004, AJ, 127, 3587) but includes several analysis changes, the most important of which are 1) using the Niell Mapping Function to model the troposphere, 2) more frequent estimation of troposphere gradients (once every 6 hours instead of once every 24 hours as was done for the ICRF), 3) a priori mean gradients computed from a GSFC Data Assimilation Office model for meteorological data from 1990-95, and 4) 5 degree elevation cutoff (versus 6 degree cutoff as was done for the ICRF). The solution also includes the most recent data and about 12 years of VLBA RDV experiments (RDV01 to RDV72).
Similar to the ICRF solution, the primary geodetic parameters, the station positions, were estimated separately for each session in the solution. Station motions within a day, from solid Earth tides and ocean loading, were derived from unadjusted a priori models. The adjusted "arc" parameters (i.e., parameters that depend only on the data from an individual experiment and are estimated separately for each epoch of observation) included: positions of sources with identified excessive apparent motion or random variation; celestial pole offsets in ecliptic longitude and obliquity to account for errors in the standard precession/nutation models; positions of the stations; the rate of UT1 relative to a good a priori time series; twenty-minute piecewise linear continuous troposphere parameters; tropospheric gradients in the east-west and north-south directions, linear in time, estimated once every 6 hours; quadratic clock polynomials for the gross clock behavior; sixty-minute piecewise linear continuous clock parameters; and necessary nuisance parameters such as clock jumps and baseline clock offsets. The remaining parameters, including source positions, were adjusted as invariant, or "global," quantities (i.e., parameters that are dependent on all data sets and are carried from step to step resulting in a single estimate derived from the combined data of all experiments in the solution).
The resultant global SOLVE solution includes most available VLBI observations at 8.4 GHz (X-band) and 2.2 GHz (S-band) from 1979 August 3 through 2009 April 8. This includes a total of 4455 diurnal sessions encompassing 6, 021, 326 measurements of group delay and delay rate. The weighted root-mean-square residuals of the solution were 22.995 ps in delay and 83.719 fs/s in delay rate. The SOLVE batch control file crf2009b_02.cnt.gz was used to generate this solution with an output spool file crf2009b_02.spl.gz (~24 MByte). Tabulated below are the global and session values for the solution.
Source and Station Positions
Positions of 997 sources were estimated as global parameters. Positions for an additional 221 sources (including several radio stars) were estimated for each session independently as "arc" parameters. A total of 121 sources with less than three good (group delay) measurments or with bad data were excluded from the solution. Positions of 130 stations were estimated as local (session) parameters.
*Note: the complete set of 1218 source positions can be obtained by down-loading these two files. The positions for the local sources are weighted mean positions. The position uncertainties for the local sources are the weighted root-mean-square deviations from the weighted mean positions.
Earth Orientation Parameters
Daily nutation offsets in longitude and obliquity were estimated for each session separately.
Shown below are comparisons of the USNO crf2009b source positions with the ICRF, ICRF-Ext.1, ICRF-Ext.2 and USNO crf2008b source positions. The weighted rms differences are at the end of the difference tables. In the vector difference plots, green indicates a less than 3-sigma position difference, orange indicates a 3-5 sigma difference and red indicates a greater than 5-sigma difference. Note that the sigmas are based on the inflated errors for the ICRF and ICRF-Ext.1 comparisons. The sigmas are based on the formal errors for the ICRF-Ext.2 and the USNO frame comparisons.
Tabulated data and plots.
Position Time Series
To assess the position stability of the sources observed in more than one session, eight additional solutions were made with identical parameterization and data. In each of these solutions, one eighth of the sources were estimated as "arc" parameters. The remaining sources were treated as "global." The SOLVE BATCH control files for these additional solutions are available here ( crf2009b_01_pts1.cnt.gz, crf2009b_01_pts2.cnt.gz, crf2009b_01_pts3.cnt.gz, crf2009b_01_pts4.cnt.gz, crf2009b_01_pts5.cnt.gz, crf2009b_01_pts6.cnt.gz, crf2009b_01_pts7.cnt.gz, crf2009b_01_pts8.cnt.gz ).
Daily nutation offsets in longitude and obliquity were estimated for each session separately. Nutation offsets are presented in the following tables.
Position time series plots and associated statistics tables are presented below. In the plots, green indicates a less than 3-sigma difference from the weighted mean position, orange indicates a 3-5 sigma difference and red indicates a greater than 5-sigma difference. The blue curves in the plots represent a 1-year running weighted average (boxcar smoothing).
Tabulated statistics and plots.
Below is a comparison of the source "arc" positions with their global positions. The weighted rms differences are at the end of the difference table. In the vector difference plot, green indicates a less than 3-sigma position difference, orange indicates a 3-5 sigma difference and red indicates a greater than 5-sigma difference. Note that the sigmas are based on the formal errors.