A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models

Abstract Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respecti...
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Autor*in:	X. Zhou [verfasserIn] Y. Yang [verfasserIn] H. Chen [verfasserIn] W. Ouyang [verfasserIn] W. Fan [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	GNSS time series Lomb‐Scargle periodogram modified Least Square harmonics estimation

Übergeordnetes Werk:	In: Earth and Space Science - American Geophysical Union (AGU), 2015, 6(2019), 11, Seite 2160-2179
Übergeordnetes Werk:	volume:6 ; year:2019 ; number:11 ; pages:2160-2179

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1029/2019EA000750

Katalog-ID:	DOAJ03290827X

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520			\|a Abstract Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. Spectrum analysis and auto‐correlation function of residuals indicates corresponding residuals are closer to white noise, indicating modified LSHE method of this paper is valid to reduce colored noise through establishing a full periodicity model.
650		4	\|a GNSS time series
650		4	\|a Lomb‐Scargle periodogram
650		4	\|a modified Least Square harmonics estimation
653		0	\|a Astronomy
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700	0		\|a Y. Yang \|e verfasserin \|4 aut
700	0		\|a H. Chen \|e verfasserin \|4 aut
700	0		\|a W. Ouyang \|e verfasserin \|4 aut
700	0		\|a W. Fan \|e verfasserin \|4 aut
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spelling	10.1029/2019EA000750 doi (DE-627)DOAJ03290827X (DE-599)DOAJa740b151f65649a4a54235518c675a73 DE-627 ger DE-627 rakwb eng QB1-991 QE1-996.5 X. Zhou verfasserin aut A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. Spectrum analysis and auto‐correlation function of residuals indicates corresponding residuals are closer to white noise, indicating modified LSHE method of this paper is valid to reduce colored noise through establishing a full periodicity model. GNSS time series Lomb‐Scargle periodogram modified Least Square harmonics estimation Astronomy Geology Y. Yang verfasserin aut H. Chen verfasserin aut W. Ouyang verfasserin aut W. Fan verfasserin aut In Earth and Space Science American Geophysical Union (AGU), 2015 6(2019), 11, Seite 2160-2179 (DE-627)816694206 (DE-600)2807271-6 23335084 nnns volume:6 year:2019 number:11 pages:2160-2179 https://doi.org/10.1029/2019EA000750 kostenfrei https://doaj.org/article/a740b151f65649a4a54235518c675a73 kostenfrei https://doi.org/10.1029/2019EA000750 kostenfrei https://doaj.org/toc/2333-5084 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2019 11 2160-2179
allfields_unstemmed	10.1029/2019EA000750 doi (DE-627)DOAJ03290827X (DE-599)DOAJa740b151f65649a4a54235518c675a73 DE-627 ger DE-627 rakwb eng QB1-991 QE1-996.5 X. Zhou verfasserin aut A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. Spectrum analysis and auto‐correlation function of residuals indicates corresponding residuals are closer to white noise, indicating modified LSHE method of this paper is valid to reduce colored noise through establishing a full periodicity model. GNSS time series Lomb‐Scargle periodogram modified Least Square harmonics estimation Astronomy Geology Y. Yang verfasserin aut H. Chen verfasserin aut W. Ouyang verfasserin aut W. Fan verfasserin aut In Earth and Space Science American Geophysical Union (AGU), 2015 6(2019), 11, Seite 2160-2179 (DE-627)816694206 (DE-600)2807271-6 23335084 nnns volume:6 year:2019 number:11 pages:2160-2179 https://doi.org/10.1029/2019EA000750 kostenfrei https://doaj.org/article/a740b151f65649a4a54235518c675a73 kostenfrei https://doi.org/10.1029/2019EA000750 kostenfrei https://doaj.org/toc/2333-5084 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2019 11 2160-2179
allfieldsGer	10.1029/2019EA000750 doi (DE-627)DOAJ03290827X (DE-599)DOAJa740b151f65649a4a54235518c675a73 DE-627 ger DE-627 rakwb eng QB1-991 QE1-996.5 X. Zhou verfasserin aut A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. Spectrum analysis and auto‐correlation function of residuals indicates corresponding residuals are closer to white noise, indicating modified LSHE method of this paper is valid to reduce colored noise through establishing a full periodicity model. GNSS time series Lomb‐Scargle periodogram modified Least Square harmonics estimation Astronomy Geology Y. Yang verfasserin aut H. Chen verfasserin aut W. Ouyang verfasserin aut W. Fan verfasserin aut In Earth and Space Science American Geophysical Union (AGU), 2015 6(2019), 11, Seite 2160-2179 (DE-627)816694206 (DE-600)2807271-6 23335084 nnns volume:6 year:2019 number:11 pages:2160-2179 https://doi.org/10.1029/2019EA000750 kostenfrei https://doaj.org/article/a740b151f65649a4a54235518c675a73 kostenfrei https://doi.org/10.1029/2019EA000750 kostenfrei https://doaj.org/toc/2333-5084 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2019 11 2160-2179
allfieldsSound	10.1029/2019EA000750 doi (DE-627)DOAJ03290827X (DE-599)DOAJa740b151f65649a4a54235518c675a73 DE-627 ger DE-627 rakwb eng QB1-991 QE1-996.5 X. Zhou verfasserin aut A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. Spectrum analysis and auto‐correlation function of residuals indicates corresponding residuals are closer to white noise, indicating modified LSHE method of this paper is valid to reduce colored noise through establishing a full periodicity model. GNSS time series Lomb‐Scargle periodogram modified Least Square harmonics estimation Astronomy Geology Y. Yang verfasserin aut H. Chen verfasserin aut W. Ouyang verfasserin aut W. Fan verfasserin aut In Earth and Space Science American Geophysical Union (AGU), 2015 6(2019), 11, Seite 2160-2179 (DE-627)816694206 (DE-600)2807271-6 23335084 nnns volume:6 year:2019 number:11 pages:2160-2179 https://doi.org/10.1029/2019EA000750 kostenfrei https://doaj.org/article/a740b151f65649a4a54235518c675a73 kostenfrei https://doi.org/10.1029/2019EA000750 kostenfrei https://doaj.org/toc/2333-5084 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2019 11 2160-2179
language	English
source	In Earth and Space Science 6(2019), 11, Seite 2160-2179 volume:6 year:2019 number:11 pages:2160-2179
sourceStr	In Earth and Space Science 6(2019), 11, Seite 2160-2179 volume:6 year:2019 number:11 pages:2160-2179
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	GNSS time series Lomb‐Scargle periodogram modified Least Square harmonics estimation Astronomy Geology
isfreeaccess_bool	true
container_title	Earth and Space Science
authorswithroles_txt_mv	X. Zhou @@aut@@ Y. Yang @@aut@@ H. Chen @@aut@@ W. Ouyang @@aut@@ W. Fan @@aut@@
publishDateDaySort_date	2019-01-01T00:00:00Z
hierarchy_top_id	816694206
id	DOAJ03290827X
language_de	englisch
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Zhou</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="2"><subfield code="a">A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. 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callnumber-first	Q - Science
author	X. Zhou
spellingShingle	X. Zhou misc QB1-991 misc QE1-996.5 misc GNSS time series misc Lomb‐Scargle periodogram misc modified Least Square harmonics estimation misc Astronomy misc Geology A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models
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topic_title	QB1-991 QE1-996.5 A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models GNSS time series Lomb‐Scargle periodogram modified Least Square harmonics estimation
topic	misc QB1-991 misc QE1-996.5 misc GNSS time series misc Lomb‐Scargle periodogram misc modified Least Square harmonics estimation misc Astronomy misc Geology
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title	A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models
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title_full	A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models
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title_sort	modified least square harmonics estimation method and comparative analysis of established full periodicity models
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title_auth	A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models
abstract	Abstract Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. Spectrum analysis and auto‐correlation function of residuals indicates corresponding residuals are closer to white noise, indicating modified LSHE method of this paper is valid to reduce colored noise through establishing a full periodicity model.
abstractGer	Abstract Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. Spectrum analysis and auto‐correlation function of residuals indicates corresponding residuals are closer to white noise, indicating modified LSHE method of this paper is valid to reduce colored noise through establishing a full periodicity model.
abstract_unstemmed	Abstract Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. Spectrum analysis and auto‐correlation function of residuals indicates corresponding residuals are closer to white noise, indicating modified LSHE method of this paper is valid to reduce colored noise through establishing a full periodicity model.
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title_short	A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models
url	https://doi.org/10.1029/2019EA000750 https://doaj.org/article/a740b151f65649a4a54235518c675a73 https://doaj.org/toc/2333-5084
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Zhou</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="2"><subfield code="a">A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. Spectrum analysis and auto‐correlation function of residuals indicates corresponding residuals are closer to white noise, indicating modified LSHE method of this paper is valid to reduce colored noise through establishing a full periodicity model.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">GNSS time series</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lomb‐Scargle periodogram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">modified Least Square harmonics estimation</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Astronomy</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Geology</subfield></datafield><datafield tag="700" ind1="0" ind2=" "><subfield code="a">Y. Yang</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="0" ind2=" "><subfield code="a">H. 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A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models

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