IGS LEO orbit comparisons
IGS LEO orbit comparisons
Pairwise orbit error
Satellite orbit data is typically presented in the form of a series
of points that are sufficiently close to each other to allow for reliable
n-point
interpolation (usually n=8 or n=10). The reference frame
in which the coordinates are defined is usually Earth Centered Fixed (as
implicitly defined by the set of tracking station coordinates, e.g.
ITRF2000)
or inertial (J2000).
Other reference frames are occasionally used, but will then require coordinate
conversions that may introduce additional noise.
Orbits can be pairwise compared, which means that difference vectors are computed at densely spaced time intervals. If the sample intervals coincide with the available data points in both input orbits, interpolation can be avoided. Nonetheless, the SP3 comparison tool that is used at ESOC has been thoroughly tested also for cases where interpolations are inevitable, and no significant interpolation errors have ever been detected.
With N participating Centres, a total of N*(N-1)/2 pairwise comparisons becomes possible. The information provided by all these comparisons together provides good insight in the precision levels of each solution separately. The orbit error in a POD solution is typically defined as the RMS of differences between this orbit solution and the true satellite orbit, even if this true orbit is unknown. If two independent orbit solutions Aand B are considered, the combined orbit error signal follows from
In theory the combined error signal above is observed as the RMS of orbit differences in the orbit comparisons. However, most pairs of compared solutions are not fully independent, which means that there will be a common component in the orbit error signals RMS(A) and RMS(B). In that case the relation above is not valid, and the observed orbit difference RMS value will be lower than the actual pairwise orbit error RMS.
In summary: if two solutions are close to the true satellite orbit, they will inevitably be close to each other as well. If two solutions are dependent, they may be close to each other but not necessarily close to the true orbit. A low pairwise orbit error RMS is therefore a necessary but not sufficient condition for the two solutions to be accurate representations of the true satellite orbit.
Reference frame deficiencies
A typical source of error in orbit comparison results is caused by
minor differences between the two reference systems in which the orbits
are defined. To detect and correct reference frame deficiencies, the orbit
comparison program that is used for this analysis will compute a least
squares solution for the 7-parameter Helmert transform between the two
compared orbits (three rotations, three translations and a scale factor).
The comparison is then repeated after applying the estimated transform
to one of the orbits. In many cases, the results from this second comparison
will not be notably different from the first comparison, in which case
the two reference frames are probably identical. For LEO orbits based on
GPS data only, this is typically the IGS reference frame in which the GPS
reference orbits are defined. Sometimes a notable difference can be detected,
e.g. a shift in the Z-component of the geocenter.
Reference frames are implied by sets of tracking station coordinates. Via the tracking data to which the satellite orbit is adjusted, the orbit coordinates adopt the same implicit reference frame as the stations. Because tracking station coordinates are typically estimated on the basis of their own tracking data, it is imaginable that minor inconsistencies exist between station coordinate sets from different tracking types (i.e. SLR, DORIS, GPS, PRARE). Orbit comparison campaigns provide the unique means to analyse such reference frame deficiencies, as long as the satellite of interest operates various tracking instruments simultaneously. Examples of such satellites are TOPEX/Poseidon, ERS-2, Envisat, and JASON. An important aspect of the JASON-1 orbit campaign is therefore a reference frame collocation analysis.
Analysis tools
Two tools are used at ESOC for orbit conversions and for orbit comparisons.
The tools are made available for download via the links below, under the
usual contraints that ESOC can not accept any liability for the consequences
of correct or incorrect use of these programs. Both programs are provided
'as is' without further support. SP3comp has a README file that should
be sufficiently clear to use it. The SP3tool is in practice constantly
extended for whatever new use may become relevant. Its command line options
are more or less self-explanatory, but it is assumed that any user is sufficiently
familiar with orbit format terminology to sort out practical problems without
further support.
