Calibration in the MBW of simulated GOCE gradients aided by ground data M. Veicherts, C. C....
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Calibration in the MBW of simulated GOCE gradients aided by ground data M. Veicherts, C. C. Tscherning, Niels Bohr Institute, University of Copenhagen, Denmark J. Bouman, SRON National Institute for Space Research, Utrecht The Netherlands Data Processing Flowchart Abstract. The GOCE gravity gradients will be calibrated using external gravity field data. While the GOCE gradients will have the minimal noise level within the Measurement Band-Width (MBW) from 5 to 100 mHz, they suffer from a 1/f error below the MBW. It is therefore required to band-pass filter the gradients to suppress the 1/f error on the one hand, while keeping the signal in and possibly below the MBW. The gradients are initially calibrated using a global gravity field model (GGM). Both time series of GOCE gradients and GGM derived gradients are identically filtered and scale factors for each component are determined. In order to verify this calibration result, the GGM has been enhanced using gradients computed by combining the model with ground gravity in four regions with good quality gravity data. Scale factors were determined for the gradients on each track passing through the area, and it could be concluded that the scale factors could be determined track-wise with results not significantly different from those obtained using the GGM only. Using 1 month of 1 s simulated data we have tested different procedures for extracting data in the MBW. Gradient Examples GOCE G ravity G radients G ravity M odel data Statevec tor A ttitude quater nions FTRANS/ M ATLAB Extracting the M BW partof gradients FTRANS/ M ATLAB Extracting the non-M BW part ofgradients PSO_EXTRACT Scriptof SP3_ext,overla pper,concat ROT_MAKES C oordinates to geodetic and rotation m atrix FILIN Thinning out data and file m erge MERGER A dding G OCE M BW w ith m odelnon- M BW and testing GEOCOL R eduction w ith m odeldata (EG M 96 d/o 25) GEOCOL G radient prediction in GOCE positions SCALE C alculating the scale factors MAKE_AUX_ CAL G enerate output validation files AUX_CAL _2I Terrestrial G ravity Data The accuracy of the SF determination naturally depends on the number of GOCE measurement points or maybe rather the ‘length’ of the crossing. In the figure below the scale factors are plotted against the number of points in the crossing and improvement is obvious as the number of points increase untill a certain point where the ‘minimum’ conditions for the estimation are fulfilled. However it is equally obvious that the quality of the scale factor estimates decrease significantly with only a small decrease of the number of points compared to the number of points in a ‘full’ crossing. Gradient Validation Areas Estimated Scale factors 890520000 890560000 890600000 T im e (s e c o nds) -1 4 00 -1 3 60 -1 3 20 -1 2 80 -1 2 40 Eu M easured E rro r fre e Figure 1: Time series of "true" and measured VXX GG. Figure 2: PSD of VXX error and signal. The areas used for validation of the gradient calibration are selected on the basis of gravity smoohtness, - although one area is from a more ‘ruggy’ region (Norway), for the geographical distribution, and naturally for the data availability. The gravity anomalies in the areas used have an estimated error below 5 mE (1 mE=10-12 s-2), and extend of maximally 10 degrees in latitude and 18 in longitude, corresponding to an approximate square with side lengths of 1100 km. The areas are shown below. Scale Factor Estimation Uncertainty The result of the scale factor estimation depends on several ‘configurable parameters’ such as filter type (we have tried using Butterworth, Chebyshev, Elliptic, Squarish filter with spline interpolation, - all with comparatively equal and in general good results), varying bandpass limits, varying the length of the data series, and more. All the results from these investigations are not Another factor of uncertainty is the influence of the a priori error of the gravity gradients. The plot below shows the direct connection between the gravity gradients a priori error and the scale factor error estimates. 0 100 200 300 400 500 T ra ck n o. 0.5 1 1.5 S ca le F a cto r 0 100 200 300 400 500 T ra ck n o. 0 1 2 S ca le F a cto r 0 100 200 300 400 500 T ra ck n o. 0 1 2 S ca le F a cto r 0 100 200 300 400 500 T ra ck n o. 0 1 2 S ca le F a cto r 0 0.01 0 .02 0.03 0.04 0.05 S td . d e v . o f a p rio ri e rro r o f G G (E ) 0 20 40 60 80 O u tlie rs (% ) G G C a l/V a lou tlie rs v s . a p rio ri std . d e v . X X A ustralia S candinavia C anada 0 40 80 120 160 N o o f p oints 0 0.4 0.8 1.2 S c a le F acto r S F dependency n o . o f p o in ts V xx sca le fa c to r in C a n a d ia n a re a The procedure with the use of the data in the MWB has been successfully used despite the obvious non-stationarity of the long-periodic “noise”. This ‘MWB method’ requires data to be received in time-series without gaps, or alternatively the gradient data must be split and scale factor estimation must be derived from separate series. Considering the quick degradation of the scale factor estimates when the length of the area crossing track becomes shorter, it will be examined to extend the size of the areas used. Conclusion A challenge in this comparison is the 1/f behavior of the GOCE GG errors for low frequencies. As an example, see Figure 1, where the time series of 1 day are plotted for the measured VXX and the error free VXX. Clearly a large, slowly varying error is superimposed on the true GG. The PSD of this error as well as of the true signal are plotted in Figure 2. The error shows a 1/f behaviour for low frequencies. The signal has most of its power at 1 and 2 CPR (cycles per revolution) and is above the error power for these frequencies. The error starts to dominate the signal for frequencies below 1 CPR. Figure 9: Flowchart of the processing chain. Figure 4: The Australian area with GOCE crossing tracks and measurement points Figure 3: Global map showing the selected cal/val areas Figure 10: SF estimate dependency of number of cross track points Figure 11: The amount of GG outliers as function of GG a priori error. Figure 5: Scale factor estimates from Australian region, Vxx Figure 6: Scale factor estimates from Central Scandinavian region, Vxx Figure 7: Scale factor estimates from Canadian area, Vxx Figure 8: Scale factor estimates from Norwegian area, Vxx
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Transcript of Calibration in the MBW of simulated GOCE gradients aided by ground data M. Veicherts, C. C....
Calibration in the MBW of simulated GOCE gradients aided by ground dataM. Veicherts, C. C. Tscherning, Niels Bohr Institute, University of Copenhagen, Denmark J. Bouman, SRON National Institute for Space Research, Utrecht The Netherlands
Data Processing Flowchart
Abstract. The GOCE gravity gradients will be calibrated using external gravity field data. While the GOCE gradients will have the minimal noise level within the Measurement Band-Width (MBW) from 5 to 100 mHz, they suffer from a 1/f error below the MBW. It is therefore required to band-pass filter the gradients to suppress the 1/f error on the one hand, while keeping the signal in and possibly below the MBW. The gradients are initially calibrated using a global gravity field model (GGM). Both time series of GOCE gradients and GGM derived gradients are identically filtered and scale factors for each component are determined.In order to verify this calibration result, the GGM has been enhanced using gradients computed by combining the model with ground gravity in four regions with good quality gravity data. Scale factors were determined for the gradients on each track passing through the area, and it could be concluded that the scale factors could be determined track-wise with results not significantly different from those obtained using the GGM only. Using 1 month of 1 s simulated data we have tested different procedures for extracting data in the MBW.
Gradient Examples
GOCEGravity
Gradients
GravityModeldata
Statevector
Attitudequaternions
FTRANS/MATLAB
Extracting theMBW part of
gradients
FTRANS/MATLAB
Extracting thenon-MBW partof gradients
PSO_EXTRACTScript of
SP3_ext,overlapper, concat
ROT_MAKESCoordinates togeodetic and
rotation matrix
FILINThinning outdata and file
merge
MERGERAdding GOCE
MBW withmodel non-MBW and
testing
GEOCOLReduction with
model data(EGM96 d/o 25)
GEOCOLGradient
prediction inGOCE
positions
SCALECalculating thescale factors
MAKE_AUX_CAL
Generateoutput
validation files
AUX_CAL_2I
TerrestrialGravity
Data
The accuracy of the SF determination naturally depends on the number of GOCE measurement points or maybe rather the ‘length’ of the crossing. In the figure below the scale factors are plotted against the number of points in the crossing and improvement is obvious as the number of points increase untill a certain point where the ‘minimum’ conditions for the estimation are fulfilled. However it is equally obvious that the quality of the scale factor estimates decrease significantly with only a small decrease of the number of points compared to the number of points in a ‘full’ crossing.
Gradient Validation Areas
Estimated Scale factors
890520000 890560000 890600000
Time (seconds)
-1400
-1360
-1320
-1280
-1240
Eu
MeasuredError free
Figure 1: Time series of "true" and measured VXX GG.
Figure 2: PSD of VXX error and signal.
The areas used for validation of the gradient calibration are selected on the basis of gravity smoohtness, - although one area is from a more ‘ruggy’ region (Norway), for the geographical distribution, and naturally for the data availability. The gravity anomalies in the areas used have an estimated error below 5 mE (1 mE=10-12 s-2), and extend of maximally 10 degrees in latitude and 18 in longitude, corresponding to an approximate square with side lengths of 1100 km. The areas are shown below.
Scale Factor Estimation Uncertainty
The result of the scale factor estimation depends on several ‘configurable parameters’ such as filter type (we have tried using Butterworth, Chebyshev, Elliptic, Squarish filter with spline interpolation, - all with comparatively equal and in general good results), varying bandpass limits, varying the length of the data series, and more. All the results from these investigations are not presented in this poster, but below the results from using the latter filter are shown.
Another factor of uncertainty is the influence of the a priori error of the gravity gradients. The plot below shows the direct connection between the gravity gradients a priori error and the scale factor error estimates.
0 100 200 300 400 500Track no.
0.5
1
1.5
Sca
le F
act
or
0 100 200 300 400 500Track no.
0
1
2
Sca
le F
act
or
0 100 200 300 400 500Track no.
0
1
2
Sca
le F
acto
r
0 100 200 300 400 500Track no.
0
1
2
Sca
le F
act
or
0 0.01 0.02 0.03 0.04 0.05S td. dev. o f a priori e rror o f G G (E )
0
20
40
60
80
Ou
tlie
rs (
%)
G G C al/Val outliers vs. a priori s td . dev. XXAustra liaScandinaviaC anada
0 40 80 120 160No of points
0
0.4
0.8
1.2
Sca
le F
acto
r
SF dependencyno. of points
Vxx scale factor in Canadian area
The procedure with the use of the data in the MWB has been successfully used despite the obvious non-stationarity of the long-periodic “noise”.This ‘MWB method’ requires data to be received in time-series without gaps, or alternatively the gradient data must be split and scale factor estimation must be derived from separate series.Considering the quick degradation of the scale factor estimates when the length of the area crossing track becomes shorter, it will be examined to extend the size of the areas used.
Conclusion
A challenge in this comparison is the 1/f behavior of the GOCE GG errors for low frequencies. As an example, see Figure 1, where the time series of 1 day are plotted for the measured VXX and the error free VXX. Clearly a large, slowly varying error is superimposed on the true GG.
The PSD of this error as well as of the true signal are plotted in Figure 2. The error shows a 1/f behaviour for low frequencies. The signal has most of its power at 1 and 2 CPR (cycles per revolution) and is above the error power for these frequencies. The error starts to dominate the signal for frequencies below 1 CPR.
Figure 9: Flowchart of the processing chain.
Figure 4: The Australian area with GOCE crossing tracks and measurement points
Figure 3: Global map showing the selected cal/val areas
Figure 10: SF estimate dependency of number of cross track points Figure 11: The amount of GG outliers as function of GG a priori error.
Figure 5: Scale factor estimates from Australian region, Vxx
Figure 6: Scale factor estimates from Central Scandinavian region, Vxx
Figure 7: Scale factor estimates from Canadian area, Vxx
Figure 8: Scale factor estimates from Norwegian area, Vxx
