IGS Analysis Center Workshop - IGS - NASA

applied to the solution in order to avoid possible numerical problems associated with a 3-rank deficiency.s It is also important to keep the free network within a few meters ofconvention (ITRF) so that linear transformations can still be applied to the networksolution. The rank deficiency is removed only after all solutions are combined into one,otherwise we would be faced with the difficult situation where solutions submitted bydifferent agencies have different a priori constraints. For the routine production of orbitsand EOP parameters, global analysis centers can save a lot of processing time if they firstproduce the loosely constrained solution to extract the “fiducial-free” network and EOPestimates; then fix a subset of stations to recommended coordinates, and extract the orbitsand EOP in the standard frame.Loose Constraints.G Loose constraints are applied in the form of a nominal value with an apriori standard deviation. “Loose” is defined such that the observable quantities that wecare about (e.g., baseline lengths) are negligibly affected by the constraint. This raises twoissues: (i) How good should the nominal values be? (ii) How “loose” should the a prioristandard deviations be? In answer to the first question, only loosely constrain those stationcoordinates that are known to at least an order of magnitude better than the applied a prioristandard deviation. In answer to the second question, what is relevant is the ratio of a priorivariance to the variance computed in the absence of constraints. We note that the locationof the network with respect to the geocenter (a net translation) can be particularly sensitiveto indiscriminate application of a priori constraints, so we place a note of caution here. Forexample, if an a priori constraint of 10 cm is applied to all coordinates of a 25 stationnetwork, this effectively constrains the net translation to 10/~= 2 cm, which may becomparable to the formal standard deviation computed using the data alone (with no a prioriconstraints), thus significantly biasing the solution towards the nominal geocenter. Wetherefore simply recommend that (i) at least 3 stations (but e 100) be loosely constrainedwith a 10 meter a priori standard deviation, and that constraints should only be applied tostations whose nominal values are consistent with ITRF to better than a meter..Re~ional Anal@. For regional network estimation where station coordinates are allestimated, the scale, orientation, and origin are defined by fixing the supplied orbits andpolar motion. However, the network is not well tied to the origin for regional sizednetworks since a net translation is strongly correlated with the satellite clock parameters.’One way to deal with this problem is to use the globally determined clock parameters, andnot estimate the satellite clocks. However, this method is not likely to ever be as precise asincluding a station whose position is routinely estimated in global analyses (a “common”station). In addition, we recommend at least 3 common stations so that network orientationand scale can be monitored and corrected, and so that network distortions caused byremaining orbit errors can be corrected to first order.g In practice, a regional center canimmediately produce a solution for it’s own purposes by constraining the coordinates of the3 common stations to the ITRF. From the IGS point of view, it is important to receive thefiducial-free regional solutions because the common station coordinates themselvesimprove in time as more global solutions accumulate, and it is important to properlypropagate those changes into the regional solutions. It is also important that the IGS5A 1-rank deficiency is ~au~ by ~~~~t ~orr~]~tio~ betw~n s~tion longitude and the ascending node Of thesatellite orbits, and an additional 2-rank deficiency is caused by a perfect correlation between the X and Ypole parameters and a global rotation of station coordinates about the X and Y axes.6Actually, no-constraints should be applied if solutions are represented by normal equations or SRIFmatrices, as will be discussed in section 3.3.7An equivalent point of view is that in the limit of short baselines, the direction to the satellites is thesame for both stations, hence both stations can move together without significantly affecting singledifferencedobservations from the same satellite.8 9common station coordinates give 3 origin parameters+ 1 scale + 3 orientation angles + 2-dim. strain.73