Identification of Suspicious Data for Robust Estimation of Stochastic Processes
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 trea
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Abstract
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. Keywords
AR-processes Hypothesis tests Outlier detection Residual time series Stochastic modeling Time series
T. Schubert () · J. M. Brockmann · W.-D. Schuh Institute of Geodesy and Geoinformation, University of Bonn, Bonn, Germany e-mail: [email protected]; [email protected]; [email protected]
Electronic Supplementary Material The online version of this chapter (https://doi.org/10.1007/1345_2019_80) contains supplementary material, which is available to authorized users.
International Association of Geodesy Symposia, https://doi.org/10.1007/1345_2019_80, © Springer Nature Switzerland AG 2019
T. Schubert et al.
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Introduction and Related Work
Modern sensors deliver a big treasure of measurements to determine process parameters of the Earth system. A prerequisite for a consistent model, which does not only describe the signal information but also its uncertainties in agreement with the data characteristics, is a clean and accurate modeling. Data adaptive strategies are necessary to adopt peculiarities of the measurement series. Robust estimation techniques, introduced in 1760 by R. Boˆskovi´c, and data snooping (Baarda 1968) have a long tradition
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