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Farzaneh S, Sharifi M A, Parvazi K, Namazi B. Assessment of noise in time series analysis for Buoy tide observations. ijmt 2020; 13 :41-49
URL: http://ijmt.ir/article-1-688-en.html
Assessment of noise in time series analysis for Buoy tide observations
Saeed Farzaneh * 1, Mohammad Ali Sharifi1 , Kamal Parvazi1 , Bahare Namazi1
1- School of Surveying and Geomatics Engineering Faculty of Engineering University of Tehran
Abstract:   (3220 Views)
To extract valid results from time series analysis of tides observations, noise reduction is vital. This study aimed to use a precise statistical model to investigate noise types. Noise component amplitude of the proposed model was studied by Least Square Estimation (LS-VCE) through different statistical models: (1) white noise and auto-regressive noise, (2) white noise and Flicker noise, (3) white noise and random walk noise, (4) white noise and Flicker noise and random walk, and (5) auto-regressive noise and Flicker noise. Based on the values obtained for the Likelihood Function, it was concluded that the noise model that can be considered for observations of the Buoy time series includes two white and Flicker noises. In addition, tide forecasting for all stations was done by extracting important frequency calculated in two cases: (1) the first case in which matrix of observation weight matrix was considered as the unit matrix or the noise model was just a white noise (2) the case in which matrix of observation weight matrix was considered as a combination of white and Flicker noises. The results show that use of precise observation weight matrix resulted in 11 millimeter difference compared to the case in which observation with unit weight matrix was used.
Keywords: Buoy station’s time series, Least Square Estimation, Least Square -Harmonic Estimation, tides observation’s noise analysis, Maximum Likelihood Estimation.
Full-Text [PDF 949 kb]   (1106 Downloads)    
Type of Study: Research Paper | Subject: Environmental Study
Received: 2019/12/22 | Accepted: 2020/06/25
References
1. 1- Amiri-Simkooei, A. (2007). Least-squares variance component estimation: theory and GPS applications", PhD thesis, Mathematical Geodesy and Positioning, Faculty of Aerospace Engineering, Delft University of Technology, Delft, Netherlands, 2007.
2. Mousavian, R., & Hossainali, M. M. (2012). Detection of main tidal frequencies using least squares harmonic estimation method. Journal of Geodetic Science, 2(3), 224-233. [DOI:10.2478/v10156-011-0043-6]
3. Mandelbrot, B. B., & Van Ness, J. W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM review, 10(4), 422-437. [DOI:10.1137/1010093]
4. Kubik, K. (1970). The estimation of the weights of measured quantities within the method of least squares. Bulletin Géodésique (1946-1975), 95(1), 21-40. [DOI:10.1007/BF02521994]
5. Koch, K. R. (1986). Maximum likelihood estimate of variance components. Bulletin Gæodésique, 60(4), 329-338. [DOI:10.1007/BF02522340]
6. Rao, C. R. (1971). Estimation of variance and covariance components-MINQUE theory. Journal of multivariate analysis, 1(3), 257-275. [DOI:10.1016/0047-259X(71)90001-7]
7. Rao, C. R., Rao, C. R., Statistiker, M., Rao, C. R., & Rao, C. R. (1973). Linear statistical inference and its applications (Vol. 2, pp. 263-270). New York: Wiley. [DOI:10.1002/9780470316436]
8. Koch, K.R. (1978). Schätzung von varianzkomponenten. Allgemeine Vermessungs Nachrichten, 85, pp.264-269.
9. Koch, K. R. (1999). Parameter estimation and hypothesis testing in linear models. Springer Science & Business Media. [DOI:10.1007/978-3-662-03976-2]
10. Helmert, F. R. (1872). Die Ausgleichungsrechnung nach der Methode der kleinsten Quadrate: mit Anwendungen auf die Geodäsie, die Physik und die Theorie der Messinstrumente (Vol. 1). Teubner.
11. Helmert FR, Die ausgleichungsrechnung nach der methode der kleinsten quadrate. 3. AUFL., Leipzig/Berlin,1924.
12. Koch, K. R. (1987). Bayesian inference for variance components. Manuscripta geodaetica, 12(4), 309-313.
13. Teunissen, P. (2004). Towards a least-squares framework for adjusting and testing of both functional and stochastic models. Technical report, Delft University of Technology. A reprint of original 1988 report is also available in 2004, No. 26, http://www.lr.tudelft.nl/mgp. Internal research memo, Geodetic Computing Centre.
14. Amiri-Simkooei, A. R., & Tiberius, C. C. J. M. (2007). Assessing receiver noise using GPS short baseline time series. GPS solutions, 11(1), 21-35. [DOI:10.1007/s10291-006-0026-8]
15. Barnes, J. B. (2000). Real time kinematic GPS and multipath: characterisation and improved least squares modelling (Doctoral dissertation, University of Newcastle upon Tyne).
16. Bischoff, W., Heck, B., Howind, J., & Teusch, A. (2005). A procedure for testing the assumption of homoscedasticity in least squares residuals: a case study of GPS carrier-phase observations. Journal of Geodesy, 78(7-8), 397-404. [DOI:10.1007/s00190-004-0390-5]
17. Bischoff, W., Heck, B., Howind, J., & Teusch, A. (2006). A procedure for estimating the variance function of linear models and for checking the appropriateness of estimated variances: a case study of GPS carrier-phase observations. Journal of Geodesy, 79(12), 694-704. [DOI:10.1007/s00190-006-0024-1]
18. Bona, P. (2000). Precision, cross correlation, and time correlation of GPS phase and code observations. GPS solutions, 4(2), 3-13. [DOI:10.1007/PL00012839]
19. Chen, Y. Q. (1990). Assessments of observations using minimum norm quadratic unbiased estimation (MINQUE). CISM J. ACSGC, 44, 36-49. [DOI:10.1139/geomat-1990-0004]
20. Fotopoulos, G. (2005). Calibration of geoid error models via a combined adjustment of ellipsoidal, orthometric and gravimetric geoid height data. Journal of Geodesy, 79(1-3), 111-123. [DOI:10.1007/s00190-005-0449-y]
21. Kusche, J. (2003). A Monte-Carlo technique for weight estimation in satellite geodesy. Journal of Geodesy, 76(11-12), 641-652. [DOI:10.1007/s00190-002-0302-5]
22. Kusche, J. (2003). Noise variance estimation and optimal weight determination for GOCE gravity recovery. Advances in Geosciences, 1, 81-85. [DOI:10.5194/adgeo-1-81-2003]
23. Satirapod, C., Wang, J., & Rizos, C. (2002). A simplified MINQUE procedure for the estimation of variance-covariance components of GPS observables. Survey Review, 36(286), 582-590. [DOI:10.1179/sre.2002.36.286.582]
24. Schön, S., & Brunner, F. K. (2008). Atmospheric turbulence theory applied to GPS carrier-phase data. Journal of Geodesy, 82(1), 47-57. [DOI:10.1007/s00190-007-0156-y]
25. Schön, S., & Brunner, F. K. (2008). A proposal for modelling physical correlations of GPS phase observations. Journal of Geodesy, 82(10), 601-612. [DOI:10.1007/s00190-008-0211-3]
26. Teunissen, P. J., Jonkman, N. F., & Tiberius, C. C. J. M. (1998). Weighting GPS dual frequency observations: bearing the cross of cross-correlation. GPS Solutions, 2(2), 28-37. [DOI:10.1007/PL00000033]
27. Tiberius, C. C. J. M., & Kenselaar, F. (2000). Estimation of the stochastic model for GPS code and phase observables. Survey Review, 35(277), 441-454. [DOI:10.1179/sre.2000.35.277.441]
28. Wang, J., Stewart, M. P., & Tsakiri, M. (1998). Stochastic modeling for static GPS baseline data processing. Journal of Surveying Engineering, 124(4), 171-181. [DOI:10.1061/(ASCE)0733-9453(1998)124:4(171)]
29. Xu, P., Shen, Y., Fukuda, Y., & Liu, Y. (2006). Variance component estimation in linear inverse ill-posed models. Journal of Geodesy, 80(2), 69-81. [DOI:10.1007/s00190-006-0032-1]
30. Xu, P., Liu, Y., Shen, Y. and Fukuda, Y.(2007). Estimability analysis of variance and covariance components. Journal of Geodesy, 81(9), pp.593-602. [DOI:10.1007/s00190-006-0122-0]
31. Williams, S.D., Bock, Y., Fang, P., Jamason, P., Nikolaidis, R.M., Prawirodirdjo, L., Miller, M. and Johnson, D.J.(2004). Error analysis of continuous GPS position time series. Journal of Geophysical Research: Solid Earth, 109(B3). [DOI:10.1029/2003JB002741]
32. Amiri-Simkooei, A. R. (2009). Noise in multivariate GPS position time-series. Journal of Geodesy, 83(2), 175-187. [DOI:10.1007/s00190-008-0251-8]
33. Amiri‐Simkooei, A. R., Tiberius, C. C. J. M., & Teunissen, S. P. (2007). Assessment of noise in GPS coordinate time series: methodology and results. Journal of Geophysical Research: Solid Earth, 112(B7). [DOI:10.1029/2006JB004913]
34. 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. Journal of Geophysical Research, 102: 18035-18055. [DOI:10.1029/97JB01380]
35. Johnson HO, Wyatt FK (1994). Geodetic network design for fault-mechanics studies. Manuscripta Geodaetica, 19: 309-323.
36. Mao A, Harrison CGA, Dixon TH (1999). Noise in GPS coordinate time series. Journal of Geophysical Research, 104(B2): 2797-2816. [DOI:10.1029/1998JB900033]
37. Boashash, B. and Putland, G., 2003, Polynomial Wigner-Ville Distributions and Design of High-Resolution Quadratic TFDs with Separable Kernals. In TIme-Frequency Signal Analysis and Processing: A Comprehensive Reference (pp. 3-27), Elsevier Ltd.
38. Wu, Z., Huang, N.E. and Chen, X., 2009, The multi-dimensional ensemble empirical mode decomposition method. Advances in Adaptive Data Analysis, 1(03), 339-372. [DOI:10.1142/S1793536909000187]
39. Rubin, D. B., 2002, Statistical Analysis with Missing Data. ISBN: 978-0-471-18386-0.
40. Papa, F., Legrésy, B. and Rémy, F., 2003, Use of the Topex-Poseidon dualfrequencyradar altimeter over land surfaces. Remote sensing of Environment, 87(2-3), 136-147. [DOI:10.1016/S0034-4257(03)00136-6]
41. [41] Tomczak, M. (2000). Lecture Notes in Oceanography. Flinders University, Adelaide, Australia School of Chemistry, Physics & Earth Sciences.
42. [42] Fitzpatrick, R. (2010). Newtonian dynamics. Austin, Tex: The University of Texas, 2011 [2012-5-14]: 201-217. http://farside. ph. utexas, edu/teaching/336k/Newton.
43. [43] Pirooznia, M., Raoofian Naeeni, M. and Amerian, Y., 2019. A Comparative Study Between Least Square and Total Least Square Methods for Time-Series Analysis and Quality Control of Sea Level Observations. Marine Geodesy, 42(2), pp.104-129. [DOI:10.1080/01490419.2018.1553806]
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