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On assessment of the stochastic errors of radio source position catalogues
Zinovy Malkin
Pulkovo Observatory and St. Petersburg University, St. Petersburg, Russia, malkin@gao.spb.ru

Abstract.

Assessment of the stochastic errors of the radio source position catalog Interferometry (VLBI) observations is important for estimating the quality of the catalogs and of the widely used method for estimation of the catalog stochastic errors is the 3-cotnered hat is proper accounting for correlations between the compared catalogs. In this poster, we present

ues derived from Very Long Baseline their weighting during combination. One technique. A critical point of this method a new approach to this task.

Introduction
So called "3-cornered hat" method (3CH) was originally developed for estimation of the stability of frequency standards (Gray and Allan, 1974). It was then applied for investigation of the noise level of various data, in particular, astronomical and geodetic time series and radio source position catalogs. However, despite this method is widely used, its application is not straightforward because it requires a reliable estimate of the correlation between series under investigation. Neglecting correlations often produces unacceptable results, like negative variances. In this work, we investigate some a new possibility to estimate correlations between radio source position catalogs (RSC).

Table 1. Correlations between RSC differences Corr(ij,ik) approaching correlation between i-th and j-th catalogs shown in the first column; the next 7 columns corresponds to k-th catalog.
Catalogs AUS AUS AUS AUS AUS AUS BKG BKG BKG BKG BKG GSF GSF GSF BKG GSF IAA MAO OPA USN GSF IAA MAO OPA USN IAA MAO OPA USN MAO OPA USN OPA USN USN 0.8861 0.9473 0.6918 0.8501 0.9338 0.9182 0.9553 0.9503 0.9546 0.9278 0.8597 0.9131 0.8623 0.9239 0.8373 0.9452 0.8316 0.9255 0.6505 0.8170 0.5894 0.7985 0.5863 0.7879 0.9584 0.9535 0.9499 0.9236 0.9904 0.9679 0.5391 0.5375 0.6230 0.6336 0.9463 0.9414 0.6626 0.6911 0.4284 0.5258 0.5490 0.5379 0.4369 0.4039 0.6547 0.6377 0.3558 0.4239 0.6570 0.6950 0.1595 0.2652 0.1041 0.0826 0.1708 0.0351 0.2196 0.1491 -.0876 -.0393 0.1234 0.2910 0.7408 0.6094 0.5303 0.3668 0.7943 0.6641 0.8014 0.7044 0.1123 0.0297 -.5286 -.5622 -.5239 -.4554 -.1777 -.0732 0.6601 0.7115 -.7176 -.6057 -.9694 -.9484 -.8019 -.6795 -.9470 -.9336 -.8209 -.7137 -.2426 -.1620 0.1563 0.2925 0.4145 0.6425 0.4546 0.6848 -.2146 -.2247 -.0243 -.0233 -.0305 0.0832 -.2769 0.0039 -.4356 -.3848 -.5838 -.6311 -.5805 -.4490 -.7074 -.6825 -.7059 -.5252 0.5383 0.5779 -.3158 -.0821 0.1396 0.2329 0.0242 0.1718 0.4398 0.5475 0.6252 0.5734 0.9209 0.7672 -.1868 -.2932 -.1723 -.1807 -.1934 -.2939 -.2004 -.3461 -.2059 -.2208 -.0909 0.0087 -.1408 -.1606 -.1317 -.3034 -.1595 -.0670 -.3258 -.3361 -.3114 -.3820 -.3318 -.2261 0.6182 0.6901 -.1720 -.2157 -.1929 -.1303 0.7319 0.7355 0.5439 0.5640 -.0722 0.0389 0.2891 0.4078 0.2419 0.3013 0.0391 0.1063 0.5264 0.6137 0.3826 0.6202 0.3737 0.5263 0.5047 0.6572 AUS BKG GSF 0.0259 -.0807 IAA 0.1870 0.1533 0.2932 0.3056 MAO 0.1199 0.0604 0.1493 0.1381 0.1013 0.0346 OPA 0.0057 -.1081 -.0173 -.1742 0.0414 -.0723 0.0470 0.0500 USN 0.0159 0.1137 0.0302 0.1392 0.0533 0.1498 0.0709 0.2325 0.0565 0.2801 Mean 0.0709 0.0277 0.0537 0.0231 -.0134 -.0120 -.1084 -.1016 -.1518 -.1934 -.1925 -.1211 0.6103 0.6789 0.3291 0.4222 0.1773 0.2285 0.0277 0.0754 -.1849 -.0249 0.5033 0.5618 0.2834 0.3394 0.1576 0.1544 -.0742 0.0123 0.3618 0.5086 0.2337 0.3083 0.0985 0.1396 0.6467 0.6122 0.3721 0.3409 0.6733 0.6645

3-cornered hat method
In original formulation, the 3CH method is applied to three series of measurements, which allows us to write the following system of three equations for the pair differences between the series supposing they are uncorrelated: with solution

For arbitrary number of measurement series one can use the following solution derived by Barnes (1992).

GSF IAA IAA IAA MAO

With correlations, the system to be solve consists of the equations: The key point is to obtain a reliable estimates of ij.

MAO OPA

Application to RSC
Several developments in using the 3CH for RSC made since the 1990s in the Main Astronomical Observatory (MAO) NANU, Ukraine (Molotaj et al. 1998, Bolotin & Lytvyn 2010). Several 3CH modifications method was used, all based on analysis of differences between the pairs of input RSCs and combined one. The authors discussed some shortcomings of this approach. In this presentation, we extended MAO method for using all the RSCs simultaneously. For this purpose we computed the correlations between each pair of catalogs and all others supposing that ij can be approximated by the correlation between catalog differences Corr(ij,ik). results of this computation are shown in Table 1. One can see some features of the correlations. Correlation in RA and DE are very similar, which confirms results of other authors. Discrepancies between the columns show discrepancies between corresponding catalogs confirmed by the WRMS. There is no clear dependence on the software used.

Conclusion
Proposed method of computation of the correlation between RSCs can provide a reasonable estimates of ij in a case of sufficiently large number of compared catalogs. Supplement investigations are needed, in particular, of the impact of the large-scale systematic differences between RSCs

References
J.E. Gray, D.W. Allan, Proc. 28th Annual Symposium on Frequency Control , May 1974, pp. 243-246. J.A. Barnes, The Analysis of Frequency and Time Data, Austron, Inc., May 1992. O.A. Molotaj, V.V. Tel'Nyuk-Adamchuk, Ya.S. Yatskiv. Kinematika i Fizika Nebesnykh Tel, 1998, v. 14, pp. 393-399. S.L. Bolotin, S.O. Lytvyn. Kinematika i Fizika Nebesnykh Tel, 2010, v. 26, pp. 31-42.