{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T03:37:04Z","timestamp":1768793824356,"version":"3.49.0"},"reference-count":40,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T00:00:00Z","timestamp":1550188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Bo Zhong","award":["41474019"],"award-info":[{"award-number":["41474019"]}]},{"name":"Hao Zhou","award":["41704012"],"award-info":[{"award-number":["41704012"]}]},{"name":"Qiong Li","award":["41504014"],"award-info":[{"award-number":["41504014"]}]},{"name":"Yihao Wu","award":["No.17-01-09"],"award-info":[{"award-number":["No.17-01-09"]}]},{"name":"Yihao Wu","award":["No.SKLGED 2018-1-2-E"],"award-info":[{"award-number":["No.SKLGED 2018-1-2-E"]}]},{"name":"Lilu Cui","award":["No.16-01-04"],"award-info":[{"award-number":["No.16-01-04"]}]},{"name":"Chaolong Yao","award":["No.17-01-08"],"award-info":[{"award-number":["No.17-01-08"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Monthly gravitational field solutions as spherical harmonic coefficients produced by the GRACE satellite mission require post-processing to reduce the effects of shortwave-length noises and north\u2013south stripe errors. However, the spatial smoothing and de-striping filter commonly used in the post-processing step will either reduce spatial resolution or remove short-wavelength features of geophysical signals, mainly at high latitudes. Here, by using prior covariance information that reflects the spatial and temporal features of the geophysical signals and the correlated errors derived from the synthetic model, together with the covariance matrix of the formal errors for the monthly gravity spherical harmonic coefficients, we apply the Kalman filter to separate the geophysical signal from GRACE Level-2 data and simultaneously to estimate the correlated errors. By increasing the number of observations, the iterative process is applied to update the state vector and covariance in the Kalman filter because the prior information is not accurate. Due to the inevitable truncation error, multiple gridded-gain factors method considering different temporal frequencies has been developed to recover the geophysical signal. The results show that the Kalman filter can reduce the high-frequency noises and correlated errors remarkably. When compared with the commonly used filter, no spatial filter (such as Gaussian filter) is used in the Kalman filter. Therefore, the estimated signal preserves its natural resolution, and more detailed information is retained. It shows good consistency when compared with mascon solutions in both secular trend and annual amplitude.<\/jats:p>","DOI":"10.3390\/rs11040393","type":"journal-article","created":{"date-parts":[[2019,2,17]],"date-time":"2019-02-17T22:11:50Z","timestamp":1550441510000},"page":"393","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Separation and Recovery of Geophysical Signals Based on the Kalman Filter with GRACE Gravity Data"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6037-9871","authenticated-orcid":false,"given":"Xiaolong","family":"Wang","sequence":"first","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhicai","family":"Luo","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute of Geophysics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"},{"name":"Collaborative Innovation Center of Geospatial Technology, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Zhong","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yihao","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Earth Sciences and Engineering, Hohai University, Nanjing 210098, China"},{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengkai","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0169-9015","authenticated-orcid":false,"given":"Hao","family":"Zhou","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute of Geophysics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiong","family":"Li","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute of Geophysics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"L09607","DOI":"10.1029\/2004GL019920","article-title":"The gravity recovery and climate experiment: Mission overview and early results","volume":"31","author":"Tapley","year":"2004","journal-title":"Geophys. Res. Lett."},{"key":"ref_2","first-page":"B01403","article-title":"Global mass flux solutions from GRACE: A comparison of parameter estimation strategies\u2014Mass concentrations versus Stokes coefficients","volume":"115","author":"Rowlands","year":"2010","journal-title":"J. Geophys. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"613","DOI":"10.3189\/2013JoG12J147","article-title":"Antarctica, Greenland and Gulf of Alaska land-ice evolution from an iterated GRACE global mascon solution","volume":"59","author":"Luthcke","year":"2013","journal-title":"J. Glaciol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2648","DOI":"10.1002\/2014JB011547","article-title":"Improved methods for observing Earth\u2019s time variable mass distribution with GRACE using spherical cap mascons","volume":"120","author":"Watkins","year":"2015","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"30205","DOI":"10.1029\/98JB02844","article-title":"Time variability of the Earth\u2019s gravity field: Hydrological and oceanic effects and their possible detection using GRACE","volume":"103","author":"Wahr","year":"1998","journal-title":"J. Geophys. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"10252","DOI":"10.1029\/2018JB015556","article-title":"Impact of different kinematic empirical parameters processing strategies on temporal gravity field model determination","volume":"123","author":"Zhou","year":"2018","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_7","unstructured":"Jekeli, C. (1981). Alternative Methods to Smooth the Earth\u2019s Gravity Field, School of Earth Science, The Ohio State University. Scientific Report 327."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1111\/j.1365-246X.2005.02756.x","article-title":"Non-isotropic filtering of GRACE temporal gravity for geophysical signal enhancement","volume":"163","author":"Han","year":"2005","journal-title":"Geophys. J. Int."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"L17311","DOI":"10.1029\/2009GL039459","article-title":"An effective filtering for GRACE time-variable gravity: Fan filter","volume":"36","author":"Zhang","year":"2009","journal-title":"Geophys. Res. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/s00190-006-0104-2","article-title":"Attenuation effect on seasonal basin-scale water storage changes from GRACE time-variable gravity","volume":"81","author":"Chen","year":"2007","journal-title":"J. Geod."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"L20504","DOI":"10.1029\/2004GL020873","article-title":"Basin scale estimates of evapotranspiration using GRACE and other observations","volume":"31","author":"Rodell","year":"2004","journal-title":"Geophys. Res. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"L16401","DOI":"10.1029\/2007GL030733","article-title":"Multi-sensor analysis of water storage variations of the Caspian Sea","volume":"34","author":"Swenson","year":"2007","journal-title":"Geophys. Res. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.5194\/hess-11-1227-2007","article-title":"The bias in GRACE estimates of continental water storage variations","volume":"11","author":"Klees","year":"2007","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"W04531","DOI":"10.1029\/2011WR011453","article-title":"Accuracy of scaled GRACE terrestrial water storage estimates","volume":"48","author":"Landerer","year":"2012","journal-title":"Water Resour. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2574","DOI":"10.1002\/2014WR016853","article-title":"Global analysis of approaches for deriving total water storage changes from GRACE satellites","volume":"51","author":"Long","year":"2015","journal-title":"Water Resour. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"L08402","DOI":"10.1029\/2005GL025285","article-title":"Post-processing removal of correlated errors in GRACE data","volume":"33","author":"Swenson","year":"2006","journal-title":"Geophys. Res. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1007\/s00190-009-0327-0","article-title":"On the postprocessing removal of correlated errors in GRACE temporal gravity field solutions","volume":"83","author":"Duan","year":"2009","journal-title":"J. Geod."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"L17603","DOI":"10.1029\/2006GL027296","article-title":"Evaluation of new GRACE time-variable gravity data over the ocean","volume":"33","author":"Chambers","year":"2006","journal-title":"Geophys. Res. Lett."},{"key":"ref_19","first-page":"C03010","article-title":"Observing seasonal steric sea level variations with GRACE and satellite altimetry","volume":"111","author":"Chambers","year":"2006","journal-title":"J. Geophys. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"L13302","DOI":"10.1029\/2007GL030356","article-title":"GRACE detects coseismic and postseismic deformation from the Sumatra-Andaman earthquake","volume":"34","author":"Chen","year":"2007","journal-title":"Geophys. Res. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1007\/s11430-011-4275-1","article-title":"Trend of mass change in the Antarctic ice sheet recovered from the GRACE temporal gravity field","volume":"55","author":"Luo","year":"2012","journal-title":"Sci. China Earth Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.epsl.2007.10.057","article-title":"Antarctic regional ice loss rates from GRACE","volume":"266","author":"Chen","year":"2008","journal-title":"Earth Planet. Sci. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1007\/s10040-015-1362-y","article-title":"A quantitative approach for hydrological drought characterization in southwestern China using GRACE","volume":"24","author":"Chao","year":"2016","journal-title":"Hydrogeol. J."},{"key":"ref_24","first-page":"B06408","article-title":"Optimized smoothing of Gravity Recovery and Climate Experiment (GRACE) time-variable gravity observations","volume":"111","author":"Chen","year":"2006","journal-title":"J. Geophys. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"L23711","DOI":"10.1029\/2007GL032098","article-title":"Improved accuracy of GRACE gravity solutions through empirical orthogonal function filtering of spherical harmonics","volume":"34","author":"Wouters","year":"2007","journal-title":"Geophys. Res. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.rse.2017.01.011","article-title":"Estimation of Amazon River discharge based on EOF analysis of GRACE gravity data","volume":"191","author":"Eom","year":"2017","journal-title":"Remote Sens. Environ."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1109\/LGRS.2009.2037837","article-title":"Denoising Satellite Gravity Signals by Independent Component Analysis","volume":"7","author":"Frappart","year":"2010","journal-title":"IEEE Geosci. Rem. Sens. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.jog.2012.02.006","article-title":"Improved daily GRACE gravity field solutions using a Kalman smoother","volume":"59","author":"Kurtenbach","year":"2012","journal-title":"J. Geodyn."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2915","DOI":"10.1002\/2015JB012650","article-title":"Stochastic filtering for determining gravity variations for decade-long time series of GRACE gravity","volume":"121","author":"Wang","year":"2016","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_30","unstructured":"Bettadpur, S., and The CSR Level-2 Team (2012, January 3\u20137). Assessment of GRACE mission performance and the RL05 gravity fields. Presented at the 2012 Fall Meeting, AGU, San Francisco, CA, USA."},{"key":"ref_31","unstructured":"Dahle, C. (2013). GFZ GRACE Level-2 Processing Standards Document for Level-2 Product Release 0005, Deutsches GeoForschungsZentrum GFZ."},{"key":"ref_32","unstructured":"Watkins, M.M., and Yuan, D.N. (2012). JPL Level-2 Processing Standards Document for Level-2 Product Release 05, GRACE Document."},{"key":"ref_33","unstructured":"Mayer-G\u00fcrr, T., Zehentner, N., Klinger, B., and Kvas, A. (October, January 29). ITSG-Grace2014: A new GRACE gravity field release computed in Graz. Proceedings of the GRACE Science Team Meeting, Potsdam, Germany."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3822","DOI":"10.1175\/JCLI4206.1","article-title":"Mechanisms Controlling the Interannual Variation of Mixed Layer Temperature Averaged over the Ni\u00f1o-3 Region","volume":"20","author":"Kim","year":"2007","journal-title":"J. Clim."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1093\/gji\/ggs030","article-title":"Computations of the viscoelastic response of a 3-D compressible Earth to surface loading: An application to Glacial Isostatic Adjustment in Antarctica and Canada","volume":"192","author":"Geruo","year":"2013","journal-title":"Geophys. J. Int."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1007\/BF02585615","article-title":"Estimation and application of degree variances of gravity","volume":"14","author":"Pellinen","year":"1970","journal-title":"Stud. Geophys. Geod."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Cheng, M., and Tapley, B.D. (2004). Variations in the Earth\u2019s oblateness during the past 28 years. J. Geophys. Res., 109.","DOI":"10.1029\/2004JB003028"},{"key":"ref_38","first-page":"113","article-title":"Estimating geocenter variations from a combination of GRACE and ocean model output","volume":"113","author":"Swenson","year":"2008","journal-title":"J. Geophys. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1038\/s41558-017-0029-1","article-title":"Changes in Greenland\u2019s peripheral glaciers linked to the North Atlantic Oscillation","volume":"8","author":"Aagaard","year":"2018","journal-title":"Nat. Clim. Chang."},{"key":"ref_40","first-page":"B03404","article-title":"A comparison of annual vertical crustal displacements from GPS and Gravity recovery and climate experiment (GRACE) over Europe","volume":"112","author":"Wahr","year":"2007","journal-title":"J. Geophys. Res."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/4\/393\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:32:21Z","timestamp":1760185941000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/4\/393"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,15]]},"references-count":40,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["rs11040393"],"URL":"https:\/\/doi.org\/10.3390\/rs11040393","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,15]]}}}