IGS LEO precision estimates

IGS LEO precision estimates

*IGS LEO Homepage*	*Associate Analysis Centers*	*LEO Orbit Campaigns*	*SP3 and RINEX acronyms*	*Links*
		*CHAMP campaign* *JASON-1 campaign*
	*Orbit comparisons*	*Tracking data analysis*	*Precision estimates*
			*CHAMP precision* *JASON precision*

Introduction
The two complementary sources of information about the orbit solutions are the pairwise comparison results and the single-orbit tracking data residuals. In theory, this information provides the following limits to the orbit error in any orbit solution:

The pairwise comparisons set an upper limit to the orbit error of either solution, on the condition that the orbit solutions are independent.

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The tracking residuals set a lower limit to the orbit error, on the condition that the residuals are mainly caused by orbit error.

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In practice the both conditions tend to be compromised to some extent, but it is still reasonable to do an analysis of the absolute orbit precision based on the comparisons and residuals together.

Analysis
The orbit comparisons apply to a pair of two solutions, the residuals apply to one single solution. If the RMS of pairwise orbit differences is interpreted as the pairwsie orbit error, as explained on the comparisons page, it is reasonable to compute an equivalent pairwise RMS of tracking residuals from the RMS of residuals for the separate solutions, according to the same relationship for a pairwise RMS:

Again, this is only possible under the condition that the two solutions have independent RMS values for their tracking residuals, otherwise a common component would disappear from the pairwise RMS. This does not add a new condition, because the further analysis already required the two compared solutions to have independent error signals.

We can now consider the ratio D which is defined as the pairwise RMS of orbit error (= the RMS of orbit differences), divided by the pairwise RMS of tracking residuals as computed above. From elementary statistical analysis it follows that if this constant D is found to be constant for all compared pairs, the same constant will also define the ratio between the RMS of orbit error and the RMS of tracking residuals for a single solution.

Based on the results from the pairwise orbit comparisons and the pairwise tracking data residuals, the factor D can be computed for every compared pair of orbits. A separate factor D is of course required for every tracking data type that is considered in the campaign analysis. The ratio D turns out to be reasonably constant, and the mean factor D is then adopted as the 'Dilution of precision' factor for that tracking data type.

If both the orbit error and the tracking data error would have a perfectly homogenous three-dimensional distribution, the dilution factor D has a theoretical value of sqrt(3) = 1.73. The orbit campaigns do not use this theoretical ratio but rather derive an equivalent ratio from the actual behaviour of the orbits and tracking residuals. It is reasonable to assume that this will better account for the inhomogenous error distributions caused by asymmetrical tracking geometries, cut-off elevations and global coverage of tracking data.

Once that the factor D and its standard deviation are obtained from the total set of comparison pairs (excluding pairs that are suspected to be dependent), it can be used in combination with the single-orbit tracking data residuals to estimate the absolute orbit error in that solution. The credibility of this analysis will of course be better if two or more tracking data sets lead to consistent orbit error estimates, so that it is a good idea to analyse more than one tracking data set if possible.

The results of the precision estimates can be found on separate pages for each LEO campaign:

Go to the CHAMP precision estimates
Go to the JASON-1 precision estimates