For the investigation of the correlation between the ASM-VFM scalar residuals with:
scalar calibrations have been performed co-estimating scaling coefficients (for x and z components of the VFM) for 2-3 of the above parameters. δsTsensor is always included in the paramter estimation ("calibration") whereas δsTeu and sbeta are either included exclusively or both. A moderate, homogeneous regularisation have been applied to suppress too high fluctuations; "homogeneous" implies the scaling coefficients are regularized according to the standard deviation of the corresponding parameter (i.e. there are no preferred coefficient imposed by the regularisation). The calibrations has been performed for all three Swarm satellites.
The scalar residuals of the estimations using the different parameter sets are plotted below with δsTeu exclusively in blue, sbeta exclusively in red and both parameters in green. Inbetween are shown the differences between both parameters solutions and the "exclusive" solution. The plots of these "differences", δΔF, in some sense show the improvement of adding the other parameter. For Alpha, sbeta seems to do the job, whereas for Bravo, sbeta is (possibly) not sufficient. For Charlie, the situation is not entirely clear although δsTeu exclusively is not appealing.
The following plots show the estimated, effective scalings as function of time. For models with all three parameters, they are split into the three contributors and their sum; also plotted are the scalings of the "exclusive" solutions using dotted lines. The top plots show the VFM x-axis scaling, the bottom plots the z-axis scaling. For the z-axis scaling δsTeu is dominating whereas for the x-axis the split between δsTeu and sbeta varies between the satellites. As expected, the exclusive solutions closely follow the sums (in brown) of the "full" solutions.
The estimated scaling coefficients are as follows:
| Alpha | Bravo | Charlie | |||||||
| Full | no sbeta | no δsTeu | Full | no sbeta | no δsTeu | Full | no sbeta | no δsTeu | |
| δsTsensor [10-9/°C] |
-16.4 11.1 38.9 |
-135.5 -57.4 20.5 |
27.9 -10.3 -48.0 |
4.1 37.4 70.7 |
-63.7 4.7 72.6 |
117.5 177.7 239.0 |
-30.0 -48.1 -66.0 |
-115.7 -123.3 -131.4 |
-20.7 27.2 75.9 |
| δsTeu [10-9/°C] | 238.2 -10.8 -482.4 |
839.5 -9.3 -371.0 |
- | 665.0 -5.5 -1,013.1 |
1,021.5 8.6 999.3 |
- | 115.9 -0.5 1,015.2 |
723.5 -0.3 1,493.2 |
- |
| sbeta [10-9/deg] |
-98.2 -5.1 -18.8 |
- | -132.3 -2.4 49.9 |
-57.5 -9.3 2.2 |
- | -154.3 -10.9 -145.5 |
-100.7 0.0 -70.5 |
- | -117.6 0.3 -213.0 |