Earth orientation parameters estimated from VLBI during CONT14 using a Kalman filter
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M. Karbon, B. Soja, T. Nilsson, R. Heinkelmann, J. Anderson, K. Balidakis, S. Glaser* ( ) L. Liu, C. Lu, J.A. Mora-Diaz, M. Xu, H. Schuh * Helmholz Centre Potsdam, GFZ German Research Centre for Geosciences, Potsdam Germany; Contact:
[email protected] *Technische Universität Berlin, Institute for Geodesy and Geoinformation Science, Berlin Germany Introduction: Within the project VLBI-ART we developed a Kalman filter for the GFZ version of the VLBI analysis software VieVS. This method has the advantage that it is simultaneously possible to estimate stationary parameters, e.g. station positions, and to account for the highly variable stochastic behavior of non-stationary parameters like clocks or atmospheric delays. In this paper we investigate the accuracy of the Earth orientation parameters (EOP) estimated from the continuous VLBI campaign CONT14 using a Kalman filter. For comparison we calculated daily EOP using the least squares method (LSM) and stacked the resulting normal equations to gain continuous pole coordinates and dUT1 valued with a hourly resolution. For an external validation for polar motion we used hourly GPS estimates. Data analysis: The data from the CONT14 campaign were downloaded from the IVS website in NGS-format. The group delay ambiguities of these observations are already solved and the ionospheric delays calculated. The IERS Conventions 2010 were followed, and Vienna mapping functions (VMF1) used. Least squares method (LSM) • Hourly ZWD, gradients every 360 min • Clock as hourly piece-wise linear offsets • Radio source coordinates fixed to ICRF2 • NNR, NNT conditions applied • For hourly solution only x/y Pole and dUT1, but no nutation estimated
Kalman filter (KAL) • Two solutions, one including the estimation of the celestial pole offset; for direct comparison with hourly LSM & GPS without. • Noise covariance matrix parameter from Literature or empirically determined • Forward-, backwardfiltering + smoothing • NNR, NNT conditions applied • a-priori clocks from LSM solution
The CONT14 campaign: CONT14 was a campaign of continuous VLBI sessions, observed in May 2014, from the 6th at 00:00 UT through the 20th at 24:00 UT. CONT14 represents a continuation of the series of very successful continuous VLBI campaigns that have been observed at irregular intervals since Fig. 1: The CONT14 station network 1994. The plan for the CONT14 campaign was to acquire state-of-the-art VLBI data over a time period of about two weeks to demonstrate the highest accuracy of which the current VLBI system is capable of. Seventeen globally distributed VLBI Tab. 1: Statistics of the stations in the CONT14 campaign stations participated in this campaign. Figure 1 shows the geographic distribution, and Tab. 1 gives the positions as well as a few statistical parameters like the average number of observations per day. Results: In Fig 2. the EOP determined with the various techniques show in general a good agreement, although some offsets between the techniques become evident. The daily LSM solutions is depicted at the middle of the estimation interval, i.e. 12 UT. The visible inter-technique offsets are an artifact of the different datum realization. In the upper plot of Fig 3. exemplarily the estimates for the x pole is shown. For comparison purposes the KF solution (blue) was averaged over one hour. The hourly LSM solution (green) looks noisy, as the constraints were set to 1 mas/h. However also stricter constrains do not provide a much smoother solution. All solutions show jumps at some day boundaries (@ 00UTC). Whereas for GPS the reason lies in the analysis strategy, for the VLBI solutions the origin is still unclear. Also earlier CONT campaigns show this behavior, although not that pronounced. Possible explanations reach from different settings at the correlator(s), to parameters given at integer UT (e.g. EOP, loading parameters, etc.) and of course bugs in the analysis software. This effect adds to the peaks visible at 24h in Fig. 4, and may leak also to other frequencies. [mas] LSMdaily LSM KAL GPS C04 08
Fig. 2: EOP, in black the results from the daily LSM approach, in green the hourly LSM approach, in blue the Kalman estimates, in red hourly polar motion estimates from GPS, in cyan the C04 08 time series.
Fig. 4: Spectra of the residual EOP estimates, in green the hourly LSM approach, in blue the Kalman estimates, in cyan without estimating polar offsets, in red the polar motion estimates from GPS.
LSM KAL GPS
x pole [mas] mean std 0.21 0.15 0.12 0.08 0.001 0.10
y pole [mas] mean std 0.40 0.14 0.41 0.07 0.02 0.08
dut1 [ms] mean std 0 0.01 0 0.01 -----
Fig. 3: Estimates of the x pole, LSM in green, daily LSM as asterisk, KAL in blue, and GPS in red..
High frequency EOP: To investigate the high frequency variations we calculated Fourier spectra of the time series shown in the upper plot in Fig. 3 after subtracting daily values . The spectra are plotted in Fig. 4. LSM shows strong power at the very high frequencies, one reason is that no constraints have been applied for the EOP estimation. For GPS and KAL the spectra approach 0 for very high frequencies. As expected, all solutions show significant spectral peaks in the diurnal and semi-diurnal bands, as well as several other peaks. The peaks in GPS at 24h/n are explained by the draconian period. Polar motion: Fixing the nutation leads to a huge retrograde diurnal peak visible in LSM (green) and KAL without nutation (cyan) , due to atmospheric and non-tidal ocean variations, and mitigation of the Free Core Nutation. The peaks at the diurnal band in polar motion can also be explained by e.g. polar motion excitation through non-tidal OAM and AAM, although the predicted amplitudes are much smaller (
