Assessment of Reference Frame Stability trough offset detection in GPS coordinate time seriesDragan Blagojević 1), Goran Todorović 2), Violeta Vasilić 1)

1) Department of Geodesy and Geoinformatics, Faculty of Civil Engineering, Belgrade, Serbia

2) Department of Mathematics, Phisycs and Descriptive Geometry, Faculty of Civil Engineering, Belgrade, Serbia

Belgrade University Faculty of Civil Engineering

Introduction

Investigation of irregularities in GNSS coordinate time series, like offsets and discontinuities, represents the key task for ITRF in order to fulfill scientific demands of being accurate, reliable and internally consistent. This kind of analysis is also important because it contributes to understanding of Reference Frame stability and enables deeper insight into local, regional and global geodynamical processes.

At the end of 2005, the network of 32 permanent GNSS stations called AGROS was established in Republic of Serbia (figure 1). TRIMBLE and LEICA equipment and network software were employed in order to realize national reference system and support various positioning and surveying tasks. Coordinate time series from this network were used for frame stability analysis, because any interruption, environmental or equipment configuration change may introduce coordinate offsets or outliers.

For this purpose, ITRF 2005 station coordinates from GPS week 1509 to 1631 were determined. BERNESE software ver.5.0 and standard procedure were used for weekly solutions [3] with EPN and IGS stations coordinates and velocities for datum definition. Figure 1. Serbian network of permanent stations

References

[1] Altamimi Z., and al., ITRF2005: A new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters, J. Geophys. Res., Vol. 112, 2007.[2] Altamimi Z., Station Positioning and the ITRF, Institut Geographique National, ENSG/LAREG, France, 2008.[3] Dach R., and al. Bernese GPS Software Version 5.0. Astronomical Institute, University of Bern, 2007.[4] Kenyeres A., Bruyninx C., EPN coordinate time series monitoring for reference frame maintenance, GPS Solutions 8, 200-209, 2004.

General Assembly 2012Vienna | Austria | 22 – 27 April 2012

European Geosciences Union

Coordinate time series and influences

It is now common practice to use coordinate time series as input for terrestrial reference frame definition [1], [2]. Reasons for that include among others: monitoring of non-linear station motions and all kind of discontinuities, rigorously and consistently including EOPs in the combination of space techniques, examining the temporal behavior of the frame physical parameters, and assessing space geodesy positioning performance.

However, any change in station components can affect the characteristics of time series, because it appears as offset, discontinuity or outlier, and as such seriously degrades the quality of estimated parameters. Numerous effects can cause this change, but the most important are [4]:

• Equipment change, especially antenna replacement which predominantly affect height component.• Antenna malfunctioning because of internal electronics failure, becoming unable to track satellites within a specific azimuth and elevation range.• Residual annual periodicities which indicate monumentation weakness, environmental and unmodeled effects, visible very often in horizontal as well as in vertical component.• Tectonic activities such as earthquaqes and post-seismic relaxation, resulting in sudden changes and non-linear behavior of coordinate time series.• Processing strategy changes (new antenna PCV model, different elevation angle, mapping function, number of unknown parameters, method for datum definition).

Figure 2. a) Regression line, b) residuals

Figure 3. a) Heaviside fit function, b) first derivative

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b)

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Offset detection in coordinate time series

Methodology for offset detection is illustrated in figures 2 and 3 with the example of northing component of station BAJI. Visible change in time series is due to change of datum definition method during processing.

The steps required are as follows:

• Fitting the straight line (least squares linear trend) trough raw coordinate series data (figure 2 a)),• Calculation of data residuals with respect to regression line (figure 2 b)),• Preliminary detection of offset location using first derivative data in the form of first differences applied to residuals from previous step (figure 3 b)),• Final detection of offset location and offset magnitude in residual data, using Heaviside fit function (figure 3 a)) in the form:

H(t) = a1h(t) + a2h(t – t1) + a3h(t – t2)

where an, tn denote fitting parameters describing magnitude and position of offsets, and h(t) denotes Heaviside unit step function defined as 0 for t < 0, and 1 for t >=0.

Conclusion

Coordinate time series in AGROS network of permanent GNSS stations were analysed focusing on detection and estimation of offset parameters. Although many factors influencing AGROS station coordinate components are present, we have illustrated the situation where changed processing strategy (datum definition method) has dominantly affected consinstancy of time series.

Generaly, offset detection is less demanding task because application of simple method like first differences can be very effective. However, this is not the case with estimation of offset magnitude if reliability represents the most important request. Our initial experience shows that Heaviside function can be promising fit function for the purpose of offset magnitude estimation.

Finaly, irrespective of the method used, it is very important to interpret the estimated offset parameters in order to properly assess the national reference frame stability and reliably separate significant geodynamical signals.