Range-Rate

Traitement des données de GRACE
Mesures GPS et KBR
R. Biancale (1), S. Bruinsma (1), J.-M. Lemoine (1), S. Loyer (2), F. Perosanz (1),
G. Balmino (1), F. Flechtner (3), R. Schmidt (3), Ul. Meyer (3)
(1)
(2)
(3)
CNES/GRGS, Toulouse, France
Noveltis, Ramonville Saint-Agne, France
GeoForschungsZentrum, Potsdam, Germany
Journées "Gravimétrie spatiale"
Paris, 11-12 mai 2005
GRACE
GRACE
2 satellites co-orbitant
lancement : mars 2002
orbite polaire, circulaire
altitude moyenne ~470 km
Accéléromètres (Super-STAR)
GPS : phases et pseudo-distances
KBR : mesures de phase entre les deux satellites
Î distance ambiguë
Données de niveau 1B
Î vitesse relative
fournies par JPL (5 sec)
Î accélération relative
JPL, CSR & GFZ utilisent la vitesse relative seule
⇒Étude pour utiliser les autres observables (CNES)
Principles of the GRACE gravity field mapping mission
SST observables in the high-low & low-low modes
GPS Satellites
SST-hl- n
SST-ll
Density
Anomaly
Earth
Performances prédites : erreur
cumulée sur le géoïde
… mais les performances de GRACE ne sont pas atteintes !
Sensitivity Analysis : RMS of linear perturbations
Inter-satellite range perturbations
per s. h. coefficient for periods < 1 day
starting from 10 µm (log scale in m)
Inter-satellite range-rate perturbations
per s. h. coefficient for periods < 1 day
starting from 0.1 µm/s (log scale in m/s)
Comparison of projected orbit perturbations generated by the EIGEN-GRACE02S
gravity field model in terms of range and range-rate inter-satellite perturbations,
according to each degree and order of the spherical harmonic expansion up to degree
120. It shows a much more powerful signal for range measurements, in the considered
intervals of sensitivity .
Sensitivity ratio in orbit perturbations : range vs. range-rate
Range (20 µm) / Range-Rate (0.3 µm/s )
Range (3 µm) / Range-Rate (0.3 µm/s )
%
%
The sensitivity ratio of calibrated (through noise) perturbation amplitudes of inter-satellite perturbations
is given here, per spherical harmonic coefficient, as: (range/σrange) / (range-rate/σrange-rate) in %.
It shows that, even for a 20 µm noise in range measurements, range perturbations are up to 40% more
sensitive, particularly in the sectorial band, than range-rate perturbations when assuminging a noise level
of 0.3 µm/s on the derived inter-satellite velocity.
Covariance Analysis
( analytical linear theory)
δ(l,m)
%
This figure compares errors of spherical harmonic coefficients estimated (by covariance
analysis) from K-band range measurements and from range-rate measurements between
GRACE-A and -B satellites (with white noise respectively of 20 µm and 0.3 µm/s). It
represents the ratio δ(l,m) in % such as :
δ(l,m) = { [σrange(l,m) - σrange-rate(l,m)] / σrange-rate(l,m) } x 100
It is remartkable that the wide negative sectorial band of coefficients (δ(l,m) < 0)
corresponds to coefficients for which formal errors estimated from range data are less
than those estimated from range-rate data. Away from this band, range-rate data induce
smaller errors (up to 600% for harmonics of high degree and of low order).
First conclusion :
Range and range-rate observables may be combined :
they carry different information strength vs. (l,m)
… it may even be best to also use accelerations
But :
There are discontinuities in the range Î parameterization
Each differentiation : - multiplies the signal by the frequency
- amplifies the noise
Computation of inter-satellite range-rate and acceleration
by the CNES-GRGS team from 5s sampled level-1B data
Biased range
1. Editing , Smoothing (optional)
2. Adjust & Remove 1/rev, 2/rev,…k/rev terms
Lagrange derivation operator (e.g. degree 5)
(in moving window)
Smoothing (optional)
- Restore periodic
part of velocity
3. Lagrange derivation operator
(in moving window)
Smoothing (optional)
- Restore periodic
part of acceleration
meas. rms (Level-1b) : 12 µm
in orbit processing over one
day arc (Aug. 14th, 2003)
Range rate
σ(l-1B – GRGS) = 0.1 µm/s
rms (Level-1b) : 0.24 µm/s
rms (GRGS) : 0.19 µm/s
Acceleration
σ(L-1b – GRGS) = 80 nm/s2
rms (Level-1b) : 92 nm/s2
rms (GRGS) : 34 nm/s2
Comparison of first and second derivatives of K-band range data
Parameterization of K-band data
K-band biased range, range-rate and range-acceleration data can be used concomitantly
in orbit processing and gravity field model adjustment. But empirical parameters should
be introduced to account for non stable behaviour of the K-band instrument at low
frequency. We have tried 2 strategies of parameterization:
1) a bias, a slope, once per revolution and twice per revolution periodic terms
each 90 mn;
twice per rev. sine and cosine terms
once per rev. sine and cosine terms
slope
bias
90 mn
2) a bias, a slope, even a quadratic term each 15 mn.
quadratic term
slope
bias
15 mn
In both cases, continuity constraints are applied between each consecutive interval,
except when phase breaks occur. Moreover, the same parameters are used at the
different levels of data derivation ; for example, a slope parameter in range is
interpreted as bias in range-rate, or a quadratic term in range is interpreted as bias in
range-acceleration.
K-band residuals after adjustment of biases per 15 mn
Systematic data processing …
… but : gaps in K-band data coverage !
Example in August 2003
Example of monthly solutions : August 2003
August 2003
CNES
Range-rate
August 2003
GFZ
Range-rate
Solutions sur 30 j
Août 2003
"vitesse"
Í GFZ
CNESÎ
Solutions sur 30 j
Août 2003
CNES
Í "vitesse"
"distance"Î
Solution sur 10 j
3-13 Août 2003
CNES
"vitesse"
CONCLUSIONS
1. Génération de nos propres quantités dérivées
(meilleure qualité que les données JPL)
2. Utilisation séparée/conjointe :
de la vitesse
de la distance
de l'accélération
+ GPS
(combinaison : mise au point système de pondération)
3. Solutions mensuelles : Août 2002- juillet 2004
4. Solution moyenne : champ "statique" sur cette période
5. Solutions décadaires : lorsque la couverture le permet