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1 Introduction: The GRACE Kalman Filter Approach

1 Introduction: The GRACE Kalman Filter Approach

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A. Eicker et al.



ocean variations. Since the data coverage provided by GRACE is not sufficient to

allow for a recovery of gravity field snapshots on a day-to-day basis, the introduction

of stochastic prior information from geophysical models as described in Kurtenbach

et al. (2012) has to be used to stabilize the solutions.

The Kalman filter combines this prior information and the daily GRACE observations in a joint estimation process and delivers an updated state of the gravity field for

each day. Stochastic information is introduced in terms of the process model which

formulates a prediction of the current state resulting from the state of the previous

time step. The process model is constructed from spatial and temporal covariance

matrices derived from the output of the geophysical models. The daily solutions

described by the present paper are part of the GRACE gravity field model ITGGrace2010 (Mayer-Gürr et al. 2010) and can be downloaded at http://www.igg.unibonn.de/apmg/index.php?id=itg-grace2010. For details of the method, a comparison to other constraint approaches, and some first validation results, please refer to

Kurtenbach (2011) and Kurtenbach et al. (2012). In the following, the results will be

evaluated more thoroughly by comparison to a larger number of vertical GPS station

movements.



6.2 Validation of Daily Solutions

In order to evaluate the temporal high frequency information content of the daily

GRACE models, they have to be compared to independent data sets. Mass variations

at the Earth’s surface result in geometrical deformations of the Earth’s crust which

can be measured by GPS receivers. Therefore, the global network of permanent GPS

stations provides a set of independent observations which can be used for comparing

with GRACE gravity field models. Vertical station displacements of the reprocessed

time series of the International GPS Service (IGS), see Steigenberger et al. (2006),

were compared on a daily basis to the GRACE Kalman solutions after transforming

them to vertical loading using the load Love numbers of Gegout (2005). For a detailed

description of the method for comparing GRACE and GPS, including the treatment

of the degree 1 coefficients, see Tesmer et al. (2011).

Figure 6.1 shows the time series for four exemplary GPS stations. The in-situ GPS

observations are plotted in the black curve, the GRACE time series is given by the red

curve. As a comparison vertical loading as computed from the de-aliasing product

(AOD1B RL04, blue line) used in the GRACE L1B data analysis (Flechtner 2007)

is displayed by the green line. The AOD1B RL04 product represents our knowledge

of global temporally high-frequent mass variations before the calculation of daily

GRACE solutions. The left part of each figure shows the time span 2003–2007, while

the right part presents a zoom-in on the year 2004. The top three images Fig. 6.1a–c

reveal a better agreement between the daily GRACE solutions and the independent

GPS observations than between GPS and AOD1B RL04. This implies that, here,

significant gravity field information has been recovered that is not present in the

AOD1B RL04. The three stations are located in the mid to high latitude region where



6 Comparison of Daily GRACE solutions to GPS Station Height Movements



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vertical deformation [mm]



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Fig. 6.1 Time series of observed vertical GPS station movements (black) compared to ITG-Grace

daily solutions (red) and the AOD1B RL04 dealiasing product (blue). Left complete time series.

Right zoom-in for one year. a ARTU—Arti (Russia)—λ = 58.6◦ , ϕ = 56.4◦ , b NANO—Nanoose

Bay (Canada)—λ = 235.9◦ , ϕ = 49.3◦ , c NRIL—Norilsk (Russia)—λ = 88.4◦ , ϕ = 69.4◦ ,

d GLPS—Puerto Ayora (Galapagos Islands)—λ = 269.7◦ , ϕ = −0.7◦



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(a)



−1.0



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Fig. 6.2 Quality measures for the correspondence of daily GRACE solutions with global GPS

station displacements. (a) correlation coefficient, (b) error RMS, (c) signal reduction



6 Comparison of Daily GRACE solutions to GPS Station Height Movements



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the GRACE data coverage is dense due to the orbit geometry and the high-frequent

temporal signal is strong due to large atmospheric mass variations. Figure 6.1d displays the vertical motion of a station near the equator, where the data coverage is less

dense and the mass signal exhibits a lower amplitude. The evaluation of the curves

leads us to the conclusion that at this station no significant gain in information can be

obtained from GRACE. The differences between GPS and GRACE, however, cannot

only be addressed to errors in the gravity field determination, as it is known (see for

example van Dam et al. 2007) that the quality of GPS time series is quite inhomogeneous; i.e. other signals (e.g. troposphere, station movements, antenna effects) may

be affecting the comparison.

Figure 6.2 shows different accuracy measures for all the compared global GPS

stations. Figure 6.2a illustrates the correlation coefficient between GRACE and GPS.

As expected, a high correlation can be found in the higher latitudes, whereas the

correlation along the equator is low. Obviously, the correlation is in particular low at

stations located on islands in the Atlantic and Pacific ocean. This can be attributed to

the fact that the ocean reacts to atmospheric mass changes by the inverse barometer

effect and therefore mass variations at island stations are particularly small, as is

also the case for the station GLPS in Fig. 6.1d. As second quality measure, Fig. 6.2

displays the error RMS between the GPS and GRACE time series for each station,

i.e. representing the mean squared differences between the two time series. Again

it can be observed that the errors are smaller in higher latitudes with values around

4–6 mm, whereas in the lower latitudes values up to 12 mm can be reached. As the

correlation coefficient is only sensitive to phase shifts and the error RMS depends

strongly on the magnitude of the signal, a third quality measure is introduced in

Fig. 6.2c. The signal reduction represents the percentage of the signal of each at the

stations that can be explained by the GRACE observations. It can be interpreted as

the ratio between error RMS and signal RMS. Again the conclusion is confirmed that

especially in the higher latitude regions a large part of the temporally high-frequent

gravity field signal can be explained by the daily GRACE solutions.



6.3 Conclusions and Outlook

We note that the gravity field variations observed independently by GRACE and

GPS show a good agreement for a large part of the global IGS stations. This allows

the conclusion that the GRACE Kalman filter approach is able to recover temporally high-frequent gravity field variations. These variations can be considered as

an improved de-aliasing product. The improvement can be attributed to two effects

which cannot easily be separated: First of all the daily GRACE solutions represent,

beside the atmospheric and oceanic variations contained in the AOD1B RL04 product, also high-frequent hydrological mass changes. Furthermore, they also account

for model errors in the atmosphere and ocean models, as was independently proven

by Bonin and Chambers (2011).



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Acknowledgments The financial support of the German Federal Ministry of Education and

Research (BMBF) in the frame of LOTSE-CHAMP/GRACE project is gratefully acknowledged.



References

Bettadpur S (2007) UTCSR Level-2 processing standards document for level-2 product release

0004. CSR Publ. GR-03-03

Bonin JA, Chambers DP (2011) Evaluation of high-frequency oceanographic signal in GRACE

data: implications for de-aliasing. Geophys Res Lett 38(L17608)

Bruinsma S, Lemoine J-M, Biancale R, Valés N (2010) CNES/GRGS 10-day gravity field models

(release 2) and their evaluation. Adv Space Res 45(4):587–601. http://www.sciencedirect.com/

science/article/B6V3S-4XHM1CC-1/% 2/8394fd9d92b0bb8c99df396bb61ad0d7

Flechtner F (2007) AOD1B product description document for product releases 01 to 04. Technical

Report, Geoforschungszentrum, Potsdam. http://dx.doi.org/10.1016/j.asr.2009.10.012

Flechtner F, Dahle C, Neumayer K-H, Koenig R, Foerste C (2010) The release 04 CHAMP

and GRACE EIGEN gravity field models. In: Flechtner F, Gruber T, Guentner A, Mandea M,

Rothacher M, Wickert J (eds) Satellite geodesy and Earth system science G observation of the

Earth from Space. Springer, Berlin

Gegout P (2005) Load love numbers. http://gemini.gsfc.nasa.gov/aplo/Load_Love2_CM.dat

Kurtenbach E (2011) Entwicklung eines Kalman-Filters zur Bestimmung kurzzeitiger Variationen

des Erdschwerefeldes aus Daten der Satellitenmission GRACE. Ph.D. thesis, University of Bonn

Kurtenbach E, Eicker A, Mayer-Gürr T, Holschneider M, Hayn M, Fuhrmann M, Kusche J (2012)

Improved daily GRACE gravity field solutions using a Kalman smoother. J Geodyn 59–60:39–48

Mayer-Gürr T, Kurtenbach E, Eicker A (2010) ITG-Grace2010 gravity field model. http://www.

igg.uni-bonn.de/apmg/index.php?id=itg-grace2010

Steigenberger P, Rothacher M, Dietrich R, Fritsche M, Rulke A, Vey S (2006) Reprocessing of a

global GPS network. J Geophys Res 111:B05402

Tesmer V, Steigenberger P, van Dam T, Mayer-Gürr T (2011) Vertical deformations from homogeneously processed GRACE and global GPS long-term series. J Geodesy 85:291–310

van Dam T, Wahr J, Lavallée D (2007) A comparison of annual vertical crustal displacements

from GPS and Gravity recovery and climate experiment (GRACE) over Europe. J Geophys Res

112:B03404

Watkins M, Yuan D-N (2007) JPL level-2 processing standards document for level-2 product release

04. ftp://podaac.jpl.nasa.gov/pub/grace/doc/



Chapter 7



Identification and Reduction of Satellite-Induced

Signals in GRACE Accelerometer Data

Nadja Peterseim, Anja Schlicht, Jakob Flury and Christoph Dahle



Abstract Although the GRACE satellite mission has achieved outstanding results in

the ten years since it has been launched, signals within accelerometer data remain nonunderstood. We analyzed 10 Hz Level 1a Accelerometer data (ACC1A) and could

link signals to switch events due to magnetic torquers and heaters, and also were able

to find a systematic for so called “twangs”. Those signals could be either empirically

or physically modelled. With those signals time-series consisting of spikes only

could be computed, with which a possible impact onto the gravity field could be

determined. It showed that especially the radial component could have an impact. In

order to investigate the impact onto the gravity field sufficiently we subtracted the

modelled signals from ACC1A, downsampled that data to 1 Hz in order to obtain

ACC1B data format and derived a gravity field with the use of our ACC1B dataset.

The results appear to have a little, but visible effect of up to 2 cm equivalent water

height onto the gravity field determined by GRACE.



N. Peterseim (B)

Institut für astronomische und physikalische Geodäsie, Technische Universität München,

Munich, Germany

e-mail: Nadja.Peterseim@bv.tu-muenchen.de

A. Schlicht

Forschungseinrichtung für Satellitengeodäsie, Technische Universität München,

Munich, Germany

J. Flury

Institut für Erdmessung, QUEST, Leibniz Universität Hannover, Hannover, Germany

C. Dahle

Helmholtz-Zentrum Potsdam, Deutsches GeoForschungsZentrum (GFZ), Potsdam, Germany



F. Flechtner et al. (eds.), Observation of the System Earth from Space - CHAMP, GRACE,

GOCE and Future Missions, Advanced Technologies in Earth Sciences,

DOI: 10.1007/978-3-642-32135-1_7, © Springer-Verlag Berlin Heidelberg 2014



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7.1 Introduction

The GRACE satellite mission is in orbit since March 2002 and is since then collecting

valuable information about the Earth gravity field. In the past ten year the results

within the temporal as well as spatial gravity field are outstanding and remarkable.

GRACE determines the Earth gravity field by measuring the inter-satellite ranges,

which is carried out by the onboard K-Band Ranging System (KBR). This system

detects the range with micrometer accuracy (Kim and Lee 2009).

In order to retrieve the gravitational part only, the non-gravitational forces, such

as atmospheric drag or solar radiation pressure, must be well known. For this purpose

both GRACE satellites are equipped with a SuperSTAR accelerometer manufactured

by ONERA in France. The accelerometer is located in the center of mass (CoM)

√ of

the satellite and has in the case of SuperSTAR an accuracy of 10−10 m/s2 / H z

(Rodrigues et al. 2003; Flury et al. 2008).

However, there are very few investigations and studies available concerning the

quality of the accelerometer data. Furthermore, it is rather difficult to make an actual

distinction between accelerometer sensor error and effects from the onboard environment onto the accelerometer. The determined gravity field could be an indicator of the

quality of the accelerometer, but is rather unspecific and can only reveal the quality

to a certain extend. Also, the predicted performance for the gravity field carried out

by simulations prior to mission launch has not yet been achieved (Förste et al. 2008).

The 10 Hz Level 1a accelerometer data (ACC1A) of GRACE offers an opportunity

to identify sensor errors and impacts by other onboard instruments. These signals

often have a very high frequency and are therefore hard to be observed and analyzed

in the 1 Hz Level 1b accelerometer data (ACC1B).

In our study, we focused on the ACC1A data of 2008 and investigated effects onto

the accelerometer data due to the onboard heaters as well as magnetic torquers and

also analyzed the phenomenon referred to as “twangs”.



7.2 Magnetic Torquer Spikes

One of the signals investigated are due to changes in the electric current in the

magnetic torquers which are used for maintenance of the attitude. The magnetic

torquer system is part of the Attitude and Orbit Control System (AOCS) and is used

for attitude maintenance of the spacecraft. It consists of a set of three rods consisting

of a nickel-alloy core wrapped by a coil, forming an electro magnet. By applying an

electric current to a magneto torquer rod a magnetic dipole is evoked, which will in

combination with the Earth magnetic field enforce a torque upon the spacecraft. The

needed torque for attitude maintenance is determined by the AOCS under detection of

the Earth magnetic field as well as the divergence of the mandatory attitude derived by

the onboard star sensor system. By combining the three magnetic dipoles evoked by

the three torque rods and the Earth magnetic field the needed torque can be enforced.



7 Identification and Reduction of Satellite-Induced Signals



55



Fig. 7.1 Spike due to a current change in Magnetic Torquer in the along Track accelerometer

component. Red dots plot the superimposed 10 Hz accelerometer data (ACC1A), the blue solid line

the mean of the superimposed ACC1A data at the given time



The electric current used for the magneto torquers may range from 0 to 120 mA,

whereas the current is able to flow both ways in order to provide the magnetic dipole

with the direction needed. A signal in 10 Hz Level 1a accelerometer (ACC1A) data

can be detected each time the magnitude of the electric current is changed in one of the

torque rods. Accelerometer data for both GRACE satellites show the same behavior

for the same current steps due to the same torque rods and hence we will describe

this phenomenon as one. This signal usually consists of 2 peaks with a period of less

than one second. The orientation of the peaks is strictly correlated to an increasing or

decreasing electric current (cf. Fig. 7.1). When a stronger current is applied, a downup pattern can be detected, whereas an up-down pattern is observable for a decreasing

electric current. The amplitude of the signal is depending on the magnitude of the

current step and can be as high as 20 nm/s2 (Peterseim et al. 2012; Peterseim 2010).

However, the behavior of the amplitude is not linear to the magnitude of the current

change, but rather exponential (cf. Fig. 7.2).

Due to the availability of the MAG1B data product, where the current of the

magentic torquer is being saved, it is easy to superimpose accelerometer data due to

a certain magnitude of current change. In fact, for one single spike the 10 Hz would

not resolve the spike clearly enough, but if a sufficient number of samples can be

superimposed the spike is resolved quite clearly (cf. Fig. 7.1). This allows us to build

mean models for a spike which we can use afterwards for a signal reduction due to

Magneto Torquers. Upon that mean model, a time-series consisting of spikes due to



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Fig. 7.2 Amplitudes of spikes in along track accelerometer data due to electric current changes in

along track magnetic torquer rod with an initial current of 0 mA



current changes can be computed. For this, the period and the starting point of the

spike are known and we alter the amplitude of the spike with respect to the magnitude

of the current change.

Being able to model any given spike due to current changes in Magneto Torquers

allows us to compute time-series consisting of these spikes only, which can furthermore be used to reduced torquer induces spikes in Level 1a accelerometer data. This

is one step to improve the existing accelerometer data products as the current changes

are not expected to enforce an actual acceleration upon the spacecraft.



7.3 Heater Spikes

Similar to the spikes induced by Magneto Torquers the onboard heaters evoke a

spike in the 10 Hz accelerometer data as well. Heaters onboard of GRACE are used

to maintain a certain temperature needed by a variety of payloads that may only

function properly in a given temperature range. Therefore, each GRACE satellite is

equipped with 64 heater circuits consisting of at least one or more heaters that control

one or more spacecraft payloads.

A spike in accelerometer data occurs each time a heater is being activated or

deactivated. Due to the larger amount of heater onboard of the satellites, this can

lead up to 120,000 of such switch events per day (Flury et al. 2008).

Activation and Deactivation of the heaters are stored in the THHC data, which

is indeed not an official Level 1B data product. By that data we were able to refer-



7 Identification and Reduction of Satellite-Induced Signals



57



Fig. 7.3 Spike in ACC1A data due to deactivation of THHA0113 heater circuit. The small colored

dots display the superimposed accelerometer data



ence and superimpose accelerometer data due to switch events of single heaters and

determine the period and amplitudes of the spikes evoked by these events. We found,

that the same heater would evoke always the same peak as in period and amplitude,

except for a small variance in the amplitude which is due to the battery voltage at

the time the given event took place.

Considering that battery voltage, which is like the heater data no official product

but yet available, amplitudes and periods can be predicted very accurately.

With the same approach used for modeling the spikes due to current changes in

the Magneto Torquer we were able to derive mean models for each switch event

of the heater by building the mean spike of the superimposed accelerometer data

(cf. Fig. 7.3).

Also here, time-series of spikes could be computed which can be used for reduction

of heater induced spikes.



7.4 Twangs

The biggest spikes that can be found in GRACE accelerometer data are so called

“twangs”. The name originates in its shape, a major spike often followed by an oscillating decay. Twangs cannot be linked to any onboard instrument and the mechanisms

causing a twang are up to date not clearly resolved. Twangs can be easiest identified

in the radial component of the accelerometer data, where they can have an amplitude

of up to 50 µm/s2 .

Twangs can easiest be spotted by eliminating all other described effects as well as

avoiding any data that may have be impacted by the thruster activations. By means

of cross-correlation of reconstructed signal to 100 Hz, twangs can be superimposed

with respect to the highest correlation coefficient analogue to the approach used

for magneto torquers and heater switch events. In order to determine the highest

correlation coefficient more accurate than 10 Hz would actually allow it is feasible



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Fig. 7.4 ‘Negative’ Twang, where first peak is negative. The blue dots display superimposed

ACC1A data found by means of cross-correlation, the colored solid line constitutes the physical

model, whereas red is the derivative of the Gaussian curve including an anisotropic scaling factor,

green a double damped oscillation and cyan a third degree polynomial connecting these two



to resample the accelerometer data up to 100 Hz by means of a reconstruction filter,

such as a Sinc, Lanczos or Gaussian filter. Figure 7.4 displays that superimposed

twangs appear to have the same period and similar behavior, independent from the

selected cross-correlation factor. This allows us basically to divide into to types of

twangs, namely a positive and a negative oriented twang.

With this knowledge a physical model can be build, that consists of the derivative

of the Gaussian bell for the first two peaks, whereas the amplitude as well as the

anisotropy need to be considered with a factor, and a double damped oscillation for

the oscillating decay, as one damping factor alone could not describe the oscillation

in many cases (cf. Fig. 7.4).

This physical model can be fit to any twang in accelerometer data using the

Least Square Adjustment method, considering keeping strongly correlated parameters apart from each other in order to avoid ambiguities. Using this approach, approximately 95 % of all twangs can be modeled sufficiently. By subtracting the adjusted

model from the real accelerometer we expect to reduce the twang from data but keep

the subjacent signal as untouched as possible (cf Fig. 7.5).

Also, the modeled twangs can be stored in time series consisting merely of the

twangs, which will become feasible in investigating the possible influence of twangs

onto the Earth gravity field determined by the GRACE mission.



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