A Correction Method of Height Variation Error Based on One SNR Arc Applied in GNSS–IR Sea-Level Retrieval
Sea-level monitoring is important for the safety of coastal cities and analysis of ocean and climate. Sea levels can be estimated based using the global navigation satellite system–interferometry reflectometry (GNSS–IR). The frequency in a signal-to-noise ratio (SNR) arc has been found to be related...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-12-01
|
| Series: | Remote Sensing |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2072-4292/14/1/11 |
| _version_ | 1827667762195988480 |
|---|---|
| author | Xiaolei Wang Zijin Niu Shu Chen Xiufeng He |
| author_facet | Xiaolei Wang Zijin Niu Shu Chen Xiufeng He |
| author_sort | Xiaolei Wang |
| collection | DOAJ |
| description | Sea-level monitoring is important for the safety of coastal cities and analysis of ocean and climate. Sea levels can be estimated based using the global navigation satellite system–interferometry reflectometry (GNSS–IR). The frequency in a signal-to-noise ratio (SNR) arc has been found to be related to the height between the GNSS antenna and reflecting surface, which is called reflector height (RH, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>h</mi></semantics></math></inline-formula>). The height variation of the reflecting surface causes an error, and this error is the most significant error in the GNSS–IR sea-level retrieval. The key to the correction of height variation error lies in the determination of the RH variation rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>h</mi><mo>˙</mo></mover></semantics></math></inline-formula>. The classical correction method determines <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>h</mi><mo>˙</mo></mover></semantics></math></inline-formula> based on tide analysis of a coarse RH series over a longer time period. Therefore, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>h</mi><mo>˙</mo></mover></semantics></math></inline-formula> inherits errors in coarse RH series, which contains significant bias during a storm surge, and correcting this requires data accumulation. This study proposes a correction method of height variation error based on just one SNR arc based on wavelet analysis and least-square estimation. First, using wavelet analysis, instantaneous frequencies are extracted in one SNR arc; these frequencies are then converted to RH series. Second, using least-square estimation, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>h</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>h</mi><mo>˙</mo></mover></semantics></math></inline-formula> are conjointly solved based on the RH series from wavelet analysis. Data of GNSS site HKQT located in Hong Kong, China, during a period of time that includes Typhoon Hato were used. The root-mean-square errors (RMSEs) of retrievals were 21.5 cm for L1, 9.5 cm for L2P, 9.3 cm for L2C, and 7.6 cm for L5 of GPS; 16.8 cm for L1C, 14.1 cm for L1P, 12.6 cm for L2C, and 10.7 cm for L2P of GLONASS; 15.7 cm for L1, 11.2 cm for L5, 12.2 cm for L7, and 9.6 cm for L8 of Galileo. Results showed this method can correct the height variation error based on just one SNR arc, can avoid the inheritance of errors, and can be used during periods of storm surge. |
| first_indexed | 2024-03-10T03:23:50Z |
| format | Article |
| id | doaj.art-2dfce7ffac1f49089103e72c509424fb |
| institution | Directory Open Access Journal |
| issn | 2072-4292 |
| language | English |
| last_indexed | 2024-03-10T03:23:50Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Remote Sensing |
| spelling | doaj.art-2dfce7ffac1f49089103e72c509424fb2023-11-23T12:11:44ZengMDPI AGRemote Sensing2072-42922021-12-011411110.3390/rs14010011A Correction Method of Height Variation Error Based on One SNR Arc Applied in GNSS–IR Sea-Level RetrievalXiaolei Wang0Zijin Niu1Shu Chen2Xiufeng He3School of Earth Sciences and Engineering, Hohai University, 1 Xikang Road, Nanjing 210098, ChinaSchool of Earth Sciences and Engineering, Hohai University, 1 Xikang Road, Nanjing 210098, ChinaSchool of Earth Sciences and Engineering, Hohai University, 1 Xikang Road, Nanjing 210098, ChinaSchool of Earth Sciences and Engineering, Hohai University, 1 Xikang Road, Nanjing 210098, ChinaSea-level monitoring is important for the safety of coastal cities and analysis of ocean and climate. Sea levels can be estimated based using the global navigation satellite system–interferometry reflectometry (GNSS–IR). The frequency in a signal-to-noise ratio (SNR) arc has been found to be related to the height between the GNSS antenna and reflecting surface, which is called reflector height (RH, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>h</mi></semantics></math></inline-formula>). The height variation of the reflecting surface causes an error, and this error is the most significant error in the GNSS–IR sea-level retrieval. The key to the correction of height variation error lies in the determination of the RH variation rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>h</mi><mo>˙</mo></mover></semantics></math></inline-formula>. The classical correction method determines <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>h</mi><mo>˙</mo></mover></semantics></math></inline-formula> based on tide analysis of a coarse RH series over a longer time period. Therefore, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>h</mi><mo>˙</mo></mover></semantics></math></inline-formula> inherits errors in coarse RH series, which contains significant bias during a storm surge, and correcting this requires data accumulation. This study proposes a correction method of height variation error based on just one SNR arc based on wavelet analysis and least-square estimation. First, using wavelet analysis, instantaneous frequencies are extracted in one SNR arc; these frequencies are then converted to RH series. Second, using least-square estimation, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>h</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>h</mi><mo>˙</mo></mover></semantics></math></inline-formula> are conjointly solved based on the RH series from wavelet analysis. Data of GNSS site HKQT located in Hong Kong, China, during a period of time that includes Typhoon Hato were used. The root-mean-square errors (RMSEs) of retrievals were 21.5 cm for L1, 9.5 cm for L2P, 9.3 cm for L2C, and 7.6 cm for L5 of GPS; 16.8 cm for L1C, 14.1 cm for L1P, 12.6 cm for L2C, and 10.7 cm for L2P of GLONASS; 15.7 cm for L1, 11.2 cm for L5, 12.2 cm for L7, and 9.6 cm for L8 of Galileo. Results showed this method can correct the height variation error based on just one SNR arc, can avoid the inheritance of errors, and can be used during periods of storm surge.https://www.mdpi.com/2072-4292/14/1/11GNSS–interferometry reflectometrysea levelretrieval methodwavelet analysisleast-square estimation |
| spellingShingle | Xiaolei Wang Zijin Niu Shu Chen Xiufeng He A Correction Method of Height Variation Error Based on One SNR Arc Applied in GNSS–IR Sea-Level Retrieval Remote Sensing GNSS–interferometry reflectometry sea level retrieval method wavelet analysis least-square estimation |
| title | A Correction Method of Height Variation Error Based on One SNR Arc Applied in GNSS–IR Sea-Level Retrieval |
| title_full | A Correction Method of Height Variation Error Based on One SNR Arc Applied in GNSS–IR Sea-Level Retrieval |
| title_fullStr | A Correction Method of Height Variation Error Based on One SNR Arc Applied in GNSS–IR Sea-Level Retrieval |
| title_full_unstemmed | A Correction Method of Height Variation Error Based on One SNR Arc Applied in GNSS–IR Sea-Level Retrieval |
| title_short | A Correction Method of Height Variation Error Based on One SNR Arc Applied in GNSS–IR Sea-Level Retrieval |
| title_sort | correction method of height variation error based on one snr arc applied in gnss ir sea level retrieval |
| topic | GNSS–interferometry reflectometry sea level retrieval method wavelet analysis least-square estimation |
| url | https://www.mdpi.com/2072-4292/14/1/11 |
| work_keys_str_mv | AT xiaoleiwang acorrectionmethodofheightvariationerrorbasedononesnrarcappliedingnssirsealevelretrieval AT zijinniu acorrectionmethodofheightvariationerrorbasedononesnrarcappliedingnssirsealevelretrieval AT shuchen acorrectionmethodofheightvariationerrorbasedononesnrarcappliedingnssirsealevelretrieval AT xiufenghe acorrectionmethodofheightvariationerrorbasedononesnrarcappliedingnssirsealevelretrieval AT xiaoleiwang correctionmethodofheightvariationerrorbasedononesnrarcappliedingnssirsealevelretrieval AT zijinniu correctionmethodofheightvariationerrorbasedononesnrarcappliedingnssirsealevelretrieval AT shuchen correctionmethodofheightvariationerrorbasedononesnrarcappliedingnssirsealevelretrieval AT xiufenghe correctionmethodofheightvariationerrorbasedononesnrarcappliedingnssirsealevelretrieval |