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4 th IVS General Meeting January 9-13, 2006 in Concepcion, Chile

4 th IVS General Meeting January 9-13, 2006 in Concepcion, Chile. [01]. First steps to investigate long-term stability of radio sources in VLBI analysis. Gerald Engelhardt, Volkmar Thorandt Bundesamt für Kartographie und Geodäsie (BKG) Karl-Rothe-Strasse 10-14, D-04105 Leipzig, Germany.

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4 th IVS General Meeting January 9-13, 2006 in Concepcion, Chile

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  1. 4th IVS General Meeting January 9-13, 2006 in Concepcion, Chile [01] First steps to investigate long-term stability of radio sources in VLBI analysis Gerald Engelhardt, Volkmar Thorandt Bundesamt für Kartographie und Geodäsie (BKG) Karl-Rothe-Strasse 10-14, D-04105 Leipzig, Germany

  2. Contents [02] • General information • Computation of time series for radio source positions • Estimation of the weighted mean for each radio source coordinate component based on these time series • Outlier detection • Test for normal distribution to uncover systematic errors • Comparison with radio source stability criterion by M. FEISSEL-VERNIER and source structure index by P. CHARLOT • Conclusions and outlook

  3. General information [03] • Presently global complete geodetic VLBI solutions with more than 20 years of data are possible • Stable compact radio sources can be modeled with only one source position for the whole length of time • Unstable radio sources known by e.g. high-level source structure complexity are not suitable for this – modeling error • Question: Which radio sources are stable? Support: - list of the ICRF defining sources - list of stable compact radio sources by M. FEISSEL-VERNIER - list of structure indices of radio sources by P. CHARLOT • Estimation and analyzing of time series for radio source positions are one possibility to answer the question

  4. Time series for radio source positions (1) [04] • Basis: global complete VLBI solution with 24 hours VLBI sessions from January 1984 to February 2005 • Main parameter types are global station coordinates and velocities, 199 stable radio source positions(detected by M. FEISSEL-VERNIER) - Minimal constraints for the datum definition are applied to get: • > Zero net rotation and zero net translation for 26 selected • station positions and velocities with respect to VTRF2003 • > Zero net rotation for 199 stable sources (detected by M. FEISSEL-VERNIER) with respect to ICRF • - Axis offsets recommended by IVS Analysis Coordinator • Estimation of local radio source positions in each session for generating the time series – basis solution 1

  5. Time series for radio source positions (2) [05] • Problem: basis solution 1 with no time series for 199 stable radio sources • Reduce set of stable radio sources for the datum definition by one source • Separate solution with no other changes referring to basis solution 1 for estimation of local source positions for this selected stable radio source • Advantage: nearly no change in datum definition for generating of time series for all radio source positions • Disadvantage: separate calculation for each stable radio source • Result: time series for all radio sources

  6. Weighted mean for each radio source [06] • Assumption: all radio sources are stable • Use the time series with locally determined source positions (L) and their standard deviations (s) to estimate a weighted mean (x) for each radio source component • Definition of the weights: pi = 1 / (si)**2 for i = 1,2, …, n and n = number of values in the time series of the source component • Weighted mean: x = [pL] / [p] • Residuals: vi = x – Li • Result: Weighted mean and residuals for all radio sources in both components (right ascension and declination)

  7. Outlier detection [07] • Purpose: increase the reliability of the used data • Basis: outlier test by GRUBBS (e.g. in HELMUT WOLF (1975), Ausgleichungsrechnung), test of the maximum residual vmax • Test statistic: g = |v|max / SQRT ( [vv] / n) • Confidence level gs from a table with the number of data points and the significance level of 1 percent • Decision rule: g < gs or g = gs no outlier detected, no action necessary • Decision rule: g > gs outlier detected, corresponding data point not used for new estimation of the weighted mean

  8. Test for normal distribution (1) [08] • Starting point: based on time series of radio source positions residuals to the weighted mean of a radio source component can be tested for normal distribution (at least 25 sessions) • Purpose: uncovering of systematic errors • Basis: smooth test between the empirically determined distribution and the theoretical normal distribution (e.g. in G. REISSMANN (1978), Die Ausgleichungsrechnung) • Parameters of the normal distribution: mean value and variance, computed from the sample (residuals) vmean = [ v ] / n and s2=[(v-vmean)2]/n-1 • Test statistic: r: number of classes (r=10), class width = s/2 m: current number of classes hm: empirical absolute frequency of class m pm: theoretical probability of class m

  9. Test for normal distribution (2) [09] • Confidence level from a table of the chi-square distribution with the significance level of 1 percent • Decision rule: < distribution of the sample (residuals) in no contradiction with assumption that it comes from a normal population - systematic errors could not be proven • Decision rule: > distribution of the sample (residuals) in contradiction with assumption that it comes from a normal population - systematic errors could be proven, e.g. instabilities of radio source components exist

  10. First results and comparisons [10] • 938 radio sources with position time series available • 223 radio sources investigated with at least 25 sessions • Normal distribution not rejected ( < ) for 121 radio sources in both components (DEC, RA) and 62 in only one component 121 = 37 “defining” + 49 “candidate” + 29 “other” + 6 “new” • Stability criterion by M. FEISSEL-VERNIER 1 and 2 for 61 radio sources, 3 and 4 for 51 sources, 9 sources not determined • Source structure index for X band (level of position disturbance) by P. CHARLOT 1 and 2 for 56 radio sources, 3 for 29 sources, 4 for 8 sources, 28 sources not determined

  11. Time series of radio source 0215+015 (DEC) [11]

  12. Time series of radio source 0215+015 (RA) [12]

  13. Histogram and normal curve of source 0212+015 [13]

  14. Time series of radio source 1739+522 (DEC) [14]

  15. Time series of radio source 1739+522 (RA) [15]

  16. Histogram and normal curve of source 1739+522 [16]

  17. Stability criteria for 183 radio sources [17]

  18. Stability criteria for 183 radio sources [18]

  19. Stability criteria for 183 radio sources [19]

  20. Stability criteria for 183 radio sources [20]

  21. Stability criteria for 183 radio sources [21]

  22. Stability criteria for 183 radio sources [22]

  23. Stability criteria for 183 radio sources [23]

  24. Conclusions and outlook [24] • Generating and statistical analyzing of time series for radio source positions are useful to get more information about long-term stability of radio sources • After successful test for normal distribution of residuals to the weighted mean of both radio source components also inspection of WRMS, rate estimation, distribution of the data points (sessions) in the time scale necessary to answer question for stable source • Development of a procedure to check the stability of the axes of the CRF materialized by a set of selected radio sources • Handling of unstable sources

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