{"id":21,"date":"2021-05-06T22:48:19","date_gmt":"2021-05-06T22:48:19","guid":{"rendered":"https:\/\/jtrfdev.jpl.nasa.gov\/?page_id=21"},"modified":"2023-10-16T20:23:36","modified_gmt":"2023-10-16T20:23:36","slug":"approach","status":"publish","type":"page","link":"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/approach\/","title":{"rendered":"Approach"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"21\" class=\"elementor elementor-21\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3bdd9ac elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3bdd9ac\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-843eec9 elementor-section-full_width elementor-section-height-min-height elementor-section-height-default elementor-section-items-middle\" data-id=\"843eec9\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3e0c1bd\" data-id=\"3e0c1bd\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b69b679 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b69b679\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-58f9c15\" data-id=\"58f9c15\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4d63834 elementor-widget elementor-widget-heading\" data-id=\"4d63834\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p class=\"elementor-heading-title elementor-size-default\">JTRF Solution<\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-28c18e7 elementor-widget elementor-widget-heading\" data-id=\"28c18e7\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Our Approach<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2afc07a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2afc07a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-e214ec5\" data-id=\"e214ec5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e0a7ff8 elementor-widget elementor-widget-heading\" data-id=\"e0a7ff8\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">A Sequential Estimation Approach<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-db41341 elementor-widget elementor-widget-text-editor\" data-id=\"db41341\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>By virtue of the sequential nature of the algorithm, JPL frames are represented through time-dependent parameters at a fixed (daily, weekly) time step, e.g. smoothed time-variable station positions, similarity transformation parameters, data assimilation residuals. JPL time-dependent parameters can be gathered and output in time series of SINEX files. The time-series representation characterizes and distinguishes JTRF from ITRF and DTRF, both adopting a parameterized representation.<\/p><p>The ultimate goal of the JPL frame products is to <strong>unify all of the space geodetic inputs into a self-consistent frame<\/strong>. Bridged together in a unified TRF, the station position and Earth rotation time series form longer and more robust space geodetic records which can be valuably used to infer highly accurate time-variable signals of the Earth deformation, its rotation, and the geocenter motion.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-742d878 elementor-widget elementor-widget-button\" data-id=\"742d878\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/doi.org\/10.1016\/j.asr.2019.11.016\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Learn More about JPL's Sequential Estimation Approach<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4448371\" data-id=\"4448371\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2cecbc2 elementor-invisible elementor-widget elementor-widget-image\" data-id=\"2cecbc2\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;slideInRight&quot;}\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-content\/uploads\/2022\/05\/tsukuba_vlbi_gnss.webp\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"JTRF2014 Plot\" data-elementor-lightbox-description=\"VLBI and GNSS Co-Observing Tsukuba\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MjA0MywidXJsIjoiaHR0cHM6XC9cL2pzZ3QuanBsLm5hc2EuZ292XC9qdHJmXC93cC1jb250ZW50XC91cGxvYWRzXC8yMDIyXC8wNVwvdHN1a3ViYV92bGJpX2duc3Mud2VicCJ9\">\n\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1000\" height=\"753\" src=\"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-content\/uploads\/2022\/05\/tsukuba_vlbi_gnss.webp\" class=\"attachment-full size-full wp-image-2043\" alt=\"Plots showing VLBI and GNSS Co-Observing Tsukuba\" srcset=\"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-content\/uploads\/2022\/05\/tsukuba_vlbi_gnss.webp 1000w, https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-content\/uploads\/2022\/05\/tsukuba_vlbi_gnss-300x226.webp 300w, https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-content\/uploads\/2022\/05\/tsukuba_vlbi_gnss-768x578.webp 768w\" sizes=\"(max-width: 1000px) 100vw, 1000px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3ef5524 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3ef5524\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-be5c3e8\" data-id=\"be5c3e8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2abd3f5 elementor-widget elementor-widget-heading\" data-id=\"2abd3f5\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Kalman Filter<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-42a4bfa elementor-widget elementor-widget-text-editor\" data-id=\"42a4bfa\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Kalman filtering is one of the elective approaches in recursive optimal state estimation. Widely applied to a variety of disciplines and applications ranging from:<\/p><ul><li>oceanography,<\/li><li>global sea level rise,<\/li><li>precise satellite orbit determination,<\/li><li>GPS positioning,<\/li><li>VLBI data analyses,<\/li><li>Earth rotation,<\/li><li>combination of loosely constrained positions inferred from SG and terrestrial geodesy,<\/li><li>and studies of correlations of the radial component of position time series at SG co-located sites<\/li><\/ul><p>Kalman filtering allows for optimal state estimation of a dynamical system by assimilating noisy observations when an adequate stochastic description of the system is supplied. During the data assimilation, Kalman filtering sequentially modifies the set of variables describing the state of a dynamical system by minimizing misfits between what is observed and to what the model physics predicts.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d1dea70 elementor-widget elementor-widget-button\" data-id=\"d1dea70\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/ipnpr.jpl.nasa.gov\/progress_report\/42-233\/42-233A.pdf\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Learn More about Kalman Filters<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-8db13dc\" data-id=\"8db13dc\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-efb89ef elementor-invisible elementor-widget elementor-widget-image\" data-id=\"efb89ef\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;slideInRight&quot;}\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-content\/uploads\/2022\/05\/kalman_rts.webp\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"Kalman Filter and RTS Smoother\" data-elementor-lightbox-description=\"Plot demonstrating Kalman Filter and RTS Smoother\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MjA0MiwidXJsIjoiaHR0cHM6XC9cL2pzZ3QuanBsLm5hc2EuZ292XC9qdHJmXC93cC1jb250ZW50XC91cGxvYWRzXC8yMDIyXC8wNVwva2FsbWFuX3J0cy53ZWJwIn0%3D\">\n\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1000\" height=\"709\" src=\"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-content\/uploads\/2022\/05\/kalman_rts.webp\" class=\"attachment-large size-large wp-image-2042\" alt=\"Plot demonstrating Kalman Filter and RTS Smoother\" srcset=\"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-content\/uploads\/2022\/05\/kalman_rts.webp 1000w, https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-content\/uploads\/2022\/05\/kalman_rts-300x213.webp 300w, https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-content\/uploads\/2022\/05\/kalman_rts-768x545.webp 768w\" sizes=\"(max-width: 1000px) 100vw, 1000px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-038387b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"038387b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-b65aa98\" data-id=\"b65aa98\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a840ee3 elementor-widget elementor-widget-heading\" data-id=\"a840ee3\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Rauch-Tung-Striebel (RTS) Smoother\u200b<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8ea4b92 elementor-widget elementor-widget-text-editor\" data-id=\"8ea4b92\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The fixed-interval RTS smoother is executed backward in time, thus ensuring optimal state estimate based on all the measurements acquired over the entire data assimilation time span. Algebraical details on the algorithm implementation can be found in\u00a0<i>Wu et al.<\/i>\u00a0[<a id=\"jgrb52273-bib-0078R\" class=\"bibLink tab-link\" href=\"#references\" data-tab=\"pane-pcw-references\">2015<\/a>], whereas for an in-depth coverage of the subject, the interested reader is addressed to, e.g.,\u00a0<i>Gelb<\/i>\u00a0[<a id=\"jgrb52273-bib-0035R\" class=\"bibLink tab-link\" href=\"#references\" data-tab=\"pane-pcw-references\">1974<\/a>] and\u00a0<i>Simon<\/i>\u00a0[<a id=\"jgrb52273-bib-0066R\" class=\"bibLink tab-link\" href=\"#references\" data-tab=\"pane-pcw-references\">2006<\/a>].<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-53436ae\" data-id=\"53436ae\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a5a33ea elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a5a33ea\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-114b69d\" data-id=\"114b69d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bb63e81 elementor-widget elementor-widget-menu-anchor\" data-id=\"bb63e81\" data-element_type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-menu-anchor\" id=\"references\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3611f85 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3611f85\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-55f633e\" data-id=\"55f633e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1e2bb4f elementor-widget elementor-widget-heading\" data-id=\"1e2bb4f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">References<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-25b6b6d elementor-widget elementor-widget-text-editor\" data-id=\"25b6b6d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span class=\"author\">Abbondanza, C.<\/span>, <span class=\"author\">T. M. Chin<\/span>,<span class=\"author\"> R. S. Gross<\/span><span class=\"author\">, M. B. Heflin<\/span>, <span class=\"author\">J. W. <\/span><span class=\"author\">Parker,<\/span> <span class=\"author\">B. S <\/span><span class=\"author\">Soja,<\/span> <span class=\"author\">T. <\/span><span class=\"author\">van Dam, <\/span>and <span class=\"author\">X. Wu<\/span>\u00a0(<span class=\"pubYear\">2017<\/span>),\u00a0<span class=\"articleTitle\">JTRF2014, the JPL Kalman filter, and smoother realization of the International Terrestrial Reference System<\/span>,\u00a0<i>J. Geophys. Res. Solid Earth<\/i>,\u00a0<i>122<\/i>,\u00a0<span class=\"pageFirst\">8474<\/span>\u2013\u00a0<span class=\"pageLast\">8510<\/span>, doi:<a class=\"accessionId\" title=\"Link to external resource: 10.1002\/2017JB014360\" href=\"https:\/\/doi.org\/10.1002\/2017JB014360\" target=\"_blank\" rel=\"noopener\">10.1002\/2017JB014360<\/a>.<\/p><p>Abbondanza, C., T. M. Chin, R. S. Gross, M. B. Heflin, J. W. Parker, B. S. Soja, and X. Wu (2020), A sequential estimation approach to terrestrial reference frame determination, <em>Adv. Space Res.<\/em>,\u00a0<em>65<\/em>(4),\u00a0<span class=\"pageFirst\">1235<\/span>\u2013\u00a0<span class=\"pageLast\">1249<\/span>, doi:<a href=\"https:\/\/doi.org\/10.1016\/j.asr.2019.11.016\">10.1016\/j.asr.2019.11.016<\/a>.<\/p><p><span class=\"author\">Chin, T. M.<\/span> (<span class=\"pubYear\">2023<\/span>), <span class=\"articleTitle\">Square-Root formulas for Kalman filter, information filter, and RTS smoother: Links via boomerang prediction residual<\/span>, <i>Interplanetary Network Progress Report<\/i>, <i>42-233<\/i>, <span class=\"pageFirst\">1<\/span>\u2013<span class=\"pageLast\">23<\/span>, <a href=\"https:\/\/ipnpr.jpl.nasa.gov\/progress_report\/42-233\/42-233A.pdf\">https:\/\/ipnpr.jpl.nasa.gov\/progress_report\/42-233\/42-233A.pdf<\/a>.<\/p><p><span class=\"author\">Gelb, A<\/span>\u00a0(<span class=\"pubYear\">1974<\/span>),\u00a0<span class=\"bookTitle\">Applied Optimal Estimation<\/span>, MIT Press,\u00a0<span class=\"publisherLocation\">Cambridge, Mass.<\/span><\/p><p><span class=\"author\">Simon, D.<\/span>\u00a0(<span class=\"pubYear\">2006<\/span>),\u00a0<span class=\"bookTitle\">Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches<\/span>, Wiley,\u00a0<span class=\"publisherLocation\">Hoboken, N. J.<\/span><\/p><p><span class=\"author\">Wu, X.<\/span>,\u00a0<span class=\"author\">C. Abbondanza<\/span>,\u00a0<span class=\"author\">Z. Altamimi<\/span>,\u00a0<span class=\"author\">T. M. Chin<\/span>,\u00a0<span class=\"author\">X. Collilieux<\/span>,\u00a0<span class=\"author\">R. S. Gross<\/span>,\u00a0<span class=\"author\">M. B. Heflin<\/span>,\u00a0<span class=\"author\">Y. Jiang<\/span>, and\u00a0<span class=\"author\">J. W. Parker<\/span>\u00a0(<span class=\"pubYear\">2015<\/span>),\u00a0<span class=\"articleTitle\">KALREF\u2014A Kalman filter and time series approach to the International Terrestrial Reference Frame realization<\/span>,\u00a0<i>J. Geophys. Res. Solid Earth<\/i>,\u00a0<i>120<\/i>,\u00a0<span class=\"pageFirst\">3775<\/span>\u2013<span class=\"pageLast\">3802<\/span>, doi:<a class=\"accessionId\" title=\"Link to external resource: 10.1002\/2014JB011622\" href=\"https:\/\/doi.org\/10.1002\/2014JB011622\" target=\"_blank\" rel=\"noopener\">10.1002\/2014JB011622<\/a>.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-f14feb9\" data-id=\"f14feb9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>JTRF Solution Our Approach A Sequential Estimation Approach By virtue of the sequential nature of the algorithm, JPL frames are represented through time-dependent parameters at a fixed (daily, weekly) time step, e.g. smoothed time-variable station positions, similarity transformation parameters, data assimilation residuals. JPL time-dependent parameters can be gathered and output in time series of SINEX &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/approach\/\"> <span class=\"screen-reader-text\">Approach<\/span> Read More \u00bb<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"no-sidebar","site-content-layout":"page-builder","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"disabled","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"_links":{"self":[{"href":"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-json\/wp\/v2\/pages\/21"}],"collection":[{"href":"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-json\/wp\/v2\/comments?post=21"}],"version-history":[{"count":96,"href":"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-json\/wp\/v2\/pages\/21\/revisions"}],"predecessor-version":[{"id":3817,"href":"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-json\/wp\/v2\/pages\/21\/revisions\/3817"}],"wp:attachment":[{"href":"https:\/\/www.jpl.nasa.gov\/site\/jsgt\/jtrf\/wp-json\/wp\/v2\/media?parent=21"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}