GPS position time-series analysis based on asymptotic normality of M-estimation

Journal of Geodesy

Volumn 86, Issue 1, 2012, Pages 15-33

  Khodabandeh, A ^a   Amiri Simkooei, A R ^b,c   Sharifi, M A ^a  

^a UNIVERSITY OF TEHRAN   (Iran)

^b UNIVERSITY OF ISFAHAN   (Iran)

^c DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Asymptotic normality; GPS coordinate time series; Least squares variance component estimation (LS VCE); M estimation; Robust variance component estimation

Indexed keywords

COORDINATE; ESTIMATION METHOD; GPS; LEAST SQUARES METHOD; RANDOM WALK METHOD; TIME SERIES ANALYSIS; VARIANCE ANALYSIS;

EID: 84855202018     PISSN: 09497714     EISSN: 14321394     Source Type: Journal    
DOI: 10.1007/s00190-011-0489-4     Document Type: Article

References (54)

1. Amiri-Simkooei AR (2003) Formulation of L1 norm minimization in Gauss-Markov models. J Surv Eng 129(1): 37-43.
2. Amiri-Simkooei AR (2007) Least-squares variance component estimation: theory and GPS applications, Ph. D. thesis, Delft University of Technology, Publication on Geodesy, 64, Netherlands, Geodetic Commission, Delft.
3. Amiri-Simkooei AR, Tiberius CCJM, Teunissen PJG (2007) Assessment of noise in GPS coordinate time-series: methodology and results. J Geophys Res 112: B07413.
4. Babu GJ (1989) Strong representations for LAD estimates in linear models. Probab Theory Relat Fields 83: 547-558.
5. Bahadur RR (1966) A note on quantiles in large samples. Ann Math Stat 37: 577-580.
6. Baselga S (2007) A global optimization solution of robust estimation. J Surv Eng 133(3): 123-128.
7. Basseville M, Nikiforov IV (1993) Detection of abrupt changes: theory and application. Prentice-Hall, Englewood Cliffs, p 469.
8. Beutler G, Rothacher M, Schaer S, Springer TA, Kouba J, Neilan RE (1999) The International GPS Service (IGS): an interdisciplinary service in support of Earth sciences. Adv Space Res 23(4): 631-635.
9. Calais E (1999) Continuous GPS measurements across the Western Alps 1996-1998. Geophys J Int 138: 221-230.
10. Davis RA (1996) Gauss-Newton and M-estimation for ARMA processes with infinite variance. Stochas Process Appl 63: 75-95.
11. Ding XL, Zheng DW, Dong DN, Ma C, Chen YQ, Wang GL (2005) Seasonal and secular positional variations at eight co-located GPS and VLBI stations. J Geod 79(1-3): 71-81.
12. Dueck A, Lohr S (2005) Robust estimation of multivariate covariance components. Biometrics 61: 162-169.
13. Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman & Hall, London.
14. Erenoglu RC, Hekimoglu S (2009) An investigation into robust estimation applied to GPS networks. In: International Association of Geodesy Symposia. vol 133. Springer, Berlin, pp 639-644.
15. Gervini D, Yohai VJ (1998) Robust estimation of variance components. Can J Stat 26: 419-430.
16. Gui Q, Zhang J (1998) Robust biased estimation and its application in geodetic adjustments. J Geod 72: 430-435.
17. Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA (1986) Robust statistics: the approach based on influence functions. John Wiley & Sons, New York.
18. He X, Shao Q (1996) A general Bahadur representation of M-estimators and its application to linear regression with nonstochastic designs. Ann Stat 24(6): 2608-2630.
19. Hekimoglu S (1997) The finite sample breakdown points of conventional iterative outlier detection procedures. J Surv Eng 123(1): 15-31.
20. Huber PJ (1981) Robust statistics. John Wiley & Sons, New York.
21. Kenyeres A, Bruyninx C (2004) EPN coordinate time-series monitoring for reference frame. GPS Solut 8: 200-209.
22. Khodabandeh A, Amiri-Simkooei AR (2010) Recursive algorithm for L1 norm estimation in linear models. J Surv Eng. doi: 10. 1061/(ASCE)SU. 1943-5428. 0000031.
23. Koch KR (1996) Robuste Parameterschatzung. Allgemeine Vermessungs-Nachrichten 103: 1-18.
24. Koch KR (1999) Parameter estimation and hypothesis testing in linear models. Springer, Berlin.
25. Krarup T, Juhl J, Kubik K (1980) Götterdämmerung over least squares adjustment. Proc. 14th congress of the international society of photogrammetry, Hamburg, vol B3, pp 369-378.
26. Krarup T, Kubik K (1983) The danish method: experience and Philosophy. DGK Reihe A. Heft 98: 131-134.
27. Langbein J (2008) Noise in GPS displacement measurements from Southern California and Southern Nevada. J Geophys Res 113(B5): B05405.
28. Magnus JR (1988) Linear structures. London School of Economics and Political Science. Charles Griffin & Company LTD, London, Oxford University Press, New York.
29. Mao A, Harrison CGA, Dixon TH (1999) Noise in GPS coordinate time-series. J Geophys Res 104(B2): 2797-2816.
30. Maronna RA, Martin RD, Yohai VJ (2006) Robust statistics: theory and methods. Wiley series in probability and statistics, England.
31. Martin RD (1981) Robust methods for time-series. In: Findley DF (eds) Applied time-series analysis II. Academic Press, New York, pp 683-759.
32. Martin RD, Yohai VJ (1986) Influence functionals for time-series. Ann Stat 14: 781-818.
33. Martin RD, Yohai VJ (1991) Bias robust estimation of autoregression parameters. In: Stahel W, Weisberg S (eds) Directions in robust statistics and diagnostics Part I, IMA Volumes in Mathematics and its Applications, vol 30. Springer, Berlin.
34. Peng JH (2005) The asymptotic variance-covariance matrix, Baarda testing and the reliability of L1 norm estimates. J Geod 78: 668-682.
35. Peng JH (2009) Jointly robust estimation of unknown parameters and variance components based on expectation- maximization algorithm. J Surv Eng 135(1): 1-9.
36. Perfetti N (2006) Detection of station coordinate discontinuities within the Italian GPS Fiducial Network. J Geod 80(7): 381-396.
37. Pope AJ (1976) The statistics of residuals and the detection of outliers. NOAA technical report NOS65 NGS1, US Department of commerce, National Geodetic Survey, Rockville, Maryland.
38. Ray J, Altamimi Z, Collilieux X, van Dam T (2008) Anomalous harmonics in the spectra of GPS position estimates. GPS Solut 12: 55-64.
39. Rousseuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New York.
40. Shao J (2003) Mathematical Statistics, 2nd edn. Springer, New York.
41. Teunissen PJG (1988) Towards a least-squares framework for adjusting and testing of both functional and stochastic model. Internal research memo, Geodetic Computing Centre, Delft.
42. Teunissen PJG (2000) Testing theory: an introduction. Delft University press, Series on mathematical Geodesy and positioning, The Netherlands.
43. Teunissen PJG, Simons DG, Tiberius CCJM (2005) Probability and observation theory. In: Lecture notes AE2-E01, Delft University of technology, Delft, The Netherlands.
44. Teunissen PJG, Amiri-Simkooei AR (2008) Least-squares variance component estimation. J Geod 82(2): 65-82.
45. Vanicek P (1969) Approximate spectral analysis by least-squares fit. Astrophys Space Sci 4: 387-391.
46. Williams SDP (2003a) The effect of coloured noise on the uncertainties of rates estimated from geodetic time-series. J Geod 76: 483-494.
47. Williams SDP (2003b) Offsets in global positioning system time-series. J Geophys Res 108(B6): 2310.
48. Williams SDP, Bock Y, Fang P, Jamason P, Nikolaidis RM, Prawirodirdjo L, Miller M, Johnson DJ (2004) Error analysis of continuous GPS position time-series. J Geophys Res 109: B03412.
49. Yang Y (1994) Robust estimation for dependent observations. Manuscr Geod 19: 10-17.
50. Yang Y (1999) Robust estimation of geodetic datum transformation. J Geod 73: 268-274.
51. Yang Y, Song L, Xu T (2001) robust estimator for the adjustment of correlated GPS networks. In: Carosio A, Kutterer H (eds) First International Symposium on Robust Statistics and Fuzzy Techniques in Geodesy and GIS, vol 295, pp 199-207.
52. Yang Y, Xu TH, Song LJ (2005) Robust estimation of variance components with application in global positioning system network adjustment. J Surv Eng 131(4): 107-112.
53. Zhang J, Bock Y, Johnson H, Fang P, Williams S, Genrich J, Wdowinski S, Behr J (1997) Southern California permanent GPS geodetic array: error analysis of daily position estimates and site velocitties. J Geophys Res 102: 18035-18055.
54. Zumberge JF, Heflin MB, Jefferson DC, Watkins MM, Webb FH (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res 102: 5005-5017.