Identification of Suspicious Data for Robust Estimation of Stochastic Processes

  • Till SchubertEmail author
  • Jan Martin Brockmann
  • Wolf-Dieter Schuh
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 151)


Many geodetic measurements which are automatically gathered by sensors can be interpreted as a time series. For instance, measurements collected by a satellite platform along the satellite’s track can be seen as a time series along the orbit. Special treatment is required if the time series is contaminated by outliers or non-stationarities, summarized as ‘suspicious data’, stemming from sensor noise variations or changes in environment. Furthermore, the collected measurements are often – for instance due to the sensor design – correlated along the track.

We propose a general estimation procedure accounting for both, correlations and the presence of suspicious data. In the estimation scheme, we adjust an autoregressive (AR) process of a given order p to model the correlations in a residual time series, which can then be used as a very flexible and general stochastic model. The AR-process estimation is iteratively refined by screening techniques based on statistical hypothesis tests and thus robustified. We incorporate different indicators to detect suspicious data or changes in the underlying process characteristics, i.e. changes in the mean value, variance and signs of the residuals.

Here, we apply the procedure to gravity gradient observations as collected by the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission in the low orbit measurement campaign. The estimated autoregressive process is used as a stochastic model of the gravity gradients in a gradiometer-only gravity field determination following the time-wise approach. The resulting estimates are compared to the counterparts of the official EGM_TIM_RL05 processing. Additionally, with newly processed level 1B GOCE gravity gradients at hand we pursue comparison of the robust and conventional approaches for original and reprocessed data.


AR-processes Hypothesis tests Outlier detection Residual time series Stochastic modeling Time series 



We thank the anonymous reviewers for their valuable comments which helped improving the manuscript. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( for funding this project by providing computing time through the John von Neumann Institute for Computing (NIC) on the GCS Supercomputer JURECA/JUWELS at Jülich Supercomputing Centre (JSC). Some computations were performed on the cluster at the University of Bonn financed via a DFG Forschungsgroßgeräteantrag (INST 217/749-1 FUGG). This work was financially supported by the ESA GOCE HPF project (main contract No. 18308/04/NL/MM).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Till Schubert
    • 1
    Email author
  • Jan Martin Brockmann
    • 1
  • Wolf-Dieter Schuh
    • 1
  1. 1.Institute of Geodesy and GeoinformationUniversity of BonnBonnGermany

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