IGS LEO JASON-1 orbit comparisons

Comparison summary
For the JASON orbit campaign all available solutions are pairwise compared by computing the difference vectors in 1441 sample points per day. This corresponds to a sample interval at 1 minute, including the final vector which is equal to the first vector of the next day. Because the daily SP3 files are typically provided in the form of points at 60 second steps, interpolations can be avoided in most cases. In total, the 29-day campaign period from day 152 to 181of 2002 provides  41761 equidistant sample points, which must be considered as a reliable basis for statistical analysis. in addition, a reference frame collocation analysis is performed.

Format conversions
The preferred campaign inputs are daily SP3 files with 2-hr overlaps at both ends. Most POD systems do not produce this kind of output for JASON, and typically a full repeat cycle is processed at once. To convert all solutions to the standard format used for the present analysis, either the originating center or the processing center (ESOC) must convert the input orbits into the desired daily SP3-files. The advantage in doing all format conversions at ESOC is that they can be done as consistently as possible. This is the main reason why the campaign proposal is not very strict on the required input format. Nonetheless, all such conversions must be done with great care. The following comments should justify the file manipulations that are done at ESOC for the current JASON campaign:

• POE files to SP3 files

The GEODYN / POE orbit data consists typically of three files, namely a header file, a file with UTC time offsets, and the actual ephemeris data file. The data is supposed to be interpolated with the NASA 10-point Hermite interpolation software, available from GSFC via anonymous ftp. These orbit vectors are provided in GEODYN inertial true of date and GEODYN Earth centered fixed, and in addition the instantaneous polar motion parameters are provided to allow for reference frame conversions.

At ESOC the Hermite software has been downloaded and implemented in a test program that creates SP3 vectors at desired time steps, which may be chosen in such a way that no interpolation is required. The normal ESOC SP3 tool has also been adapted to translate the POE ephemeris files into SP3 vectors directly (either with or without interpolations), using the Earth rotation parameters that come with the POE ephemeris. The two tools give SP3 files, one that uses the actual Hermite algorithm, and one that uses a Lagrange interpolator. Both tools can be configured to either interpolate at desired output intervals, or to just copy the input vectors to the output. This means that four different cases can be compared, namely, neither conversion tool interpolates, one of the two interpolates and the other does not, or both tools interpolate. These four cases were applied to a POE test file from CNES, covering JASON cycle 15. The table below shows the RMS of differences for the 4 pairwise comparisons (... using the same orbit comparison tool that is used for the JASON campaign itself).
 

RMS of comparisons over cycle 15	Hermite, without interpolations	Hermite, with interpolations
SP3 / Lagrange, without interpolations	0.068 mm	0.302 mm
SP3 / Lagrange, with interpolations	0.557 mm	0.728 mm

The least significant digit in the SP3 file format represents 1 mm in position, so that interpolations of SP3 files must be expected to introduce a noise at the level of 1 mm. The above figures show that perhaps the hermite interpolator is slightly superior to the 8-point Lagrange interpolation, but that the introduced noise levels are not disturbing for the campaign analysis. The three significant figures presented in the table results are in fact not realistic, and should probably be rounded to the level of 10^-1 mm or 1 mm.
 

• SP1 files to SP3 files

The SP3 format has arisen from various extensions to the SP1 format, but SP1 files essentially contain the same orbit information. If no interpolation takes place during the conversion, the output vectors are identical to the input vectors. If resampling is required the interpolation errors will be at the resolution level of the SP3 format, i.e. about truncated below 1 mm.
 
• SP3 files to SP3 files with different arc length or sample interval

The same applies as for the SP1 to SP3 conversions. Interpolations in SP3 files are inevitably inaccurate below the 1 mm resolution level of the SP3 files. For the JASON campaign comparisons the 0.1 mm truncation error can be considered as acceptable, although it would be good to have a resolution that was just one order of magnitude more precise.
 
• Numerical differentiation of the position to add velocity vectors to SP3 files.

Various AACs have requested velocity information to be introduced in the campaign analysis, but not all contributions provide velocity vectors. For adding velocity vectors to a position-only file, the ESOC SP3 tool interpolates two position vectors, one at t-0.05s and the other at t+0.05s. The difference between the two positions at 0.1 s separation provide a gradient vector that by very good approximation gives the velocity vector at t, after division by 0.1 s of course. This is because the orbit arc over such a short time interval will not deviate notably from a perfect circle segment, for which the computation would be exact. The same 1 mm resolution limit of the SP3 format applies to all these interpolations, i.e. the velocity error will be of order 0.1 mm / 0.1 s = 1 mm/s. Note that for missions like GRACE and GOCE this level of error in the velocity information may be unacceptable.

• Overlap comparisons between consecutive arcs of the same solution
• Overlap comparisons between consecutive arcs of two different solutions

Comparison results
The 29 daily SP3 files from any two solutions are pairwise, leading to 29 sets of daily statistics per comparison. For practical reasons associated with the reference frame collocation analysis, comparisons in both ways are available (i.e. orbit A minus orbit B, as well as orbit B minus orbit A). The following results can be accessed for each comparison pair, via links in the table below:

• Plots with daily values for mean, RMS, sigma, minimum and maximum value, for position and velocity and all relevant directions separately.
• Tables with the numerical values of all daily statistics.
• Geographical distribution plots of orbit differences in radial, along-track, cross-track directions
• geographical distribution plots for the absolute position difference and absolute velocity difference.
• Difference distribution curves for the entire comparison period, per solution. There are (N-1) curves for each solution because each of the N solutions is pairwise compared with the (N-1) other solutions.