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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Geophysical Union (AGU)
2019-11-01
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| Series: | Earth and Space Science |
| Subjects: | |
| Online Access: | https://doi.org/10.1029/2019EA000750 |
| _version_ | 1818040546864660480 |
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| author | X. Zhou Y. Yang H. Chen W. Ouyang W. Fan |
| author_facet | X. Zhou Y. Yang H. Chen W. Ouyang W. Fan |
| author_sort | X. Zhou |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T08:16:15Z |
| format | Article |
| id | doaj.art-a740b151f65649a4a54235518c675a73 |
| institution | Directory Open Access Journal |
| issn | 2333-5084 |
| language | English |
| last_indexed | 2024-12-10T08:16:15Z |
| publishDate | 2019-11-01 |
| publisher | American Geophysical Union (AGU) |
| record_format | Article |
| series | Earth and Space Science |
| spelling | doaj.art-a740b151f65649a4a54235518c675a732022-12-22T01:56:27ZengAmerican Geophysical Union (AGU)Earth and Space Science2333-50842019-11-016112160217910.1029/2019EA000750A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity ModelsX. Zhou0Y. Yang1H. Chen2W. Ouyang3W. Fan4School of Geodesy and Geomatics Wuhan University Wuhan ChinaSchool of Geodesy and Geomatics Wuhan University Wuhan ChinaSchool of Geodesy and Geomatics Wuhan University Wuhan ChinaSchool of Geodesy and Geomatics Wuhan University Wuhan ChinaGNSS Research Center Wuhan University Wuhan ChinaAbstract 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.https://doi.org/10.1029/2019EA000750GNSS time seriesLomb‐Scargle periodogrammodified Least Square harmonics estimation |
| spellingShingle | X. Zhou Y. Yang H. Chen W. Ouyang W. Fan A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models Earth and Space Science GNSS time series Lomb‐Scargle periodogram modified Least Square harmonics estimation |
| title | A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models |
| title_full | A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models |
| title_fullStr | A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models |
| title_full_unstemmed | A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models |
| title_short | A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models |
| title_sort | modified least square harmonics estimation method and comparative analysis of established full periodicity models |
| topic | GNSS time series Lomb‐Scargle periodogram modified Least Square harmonics estimation |
| url | https://doi.org/10.1029/2019EA000750 |
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