KALREF—A Kalman filter and time series approach to the International Terrestrial Reference Frame realization

Abstract

The current International Terrestrial Reference Frame is based on a piecewise linear site motion model and realized by reference epoch coordinates and velocities for a global set of stations. Although linear motions due to tectonic plates and glacial isostatic adjustment dominate geodetic signals, at today's millimeter precisions, nonlinear motions due to earthquakes, volcanic activities, ice mass losses, sea level rise, hydrological changes, and other processes become significant. Monitoring these (sometimes rapid) changes desires consistent and precise realization of the terrestrial reference frame (TRF) quasi-instantaneously. Here, we use a Kalman filter and smoother approach to combine time series from four space geodetic techniques to realize an experimental TRF through weekly time series of geocentric coordinates. In addition to secular, periodic, and stochastic components for station coordinates, the Kalman filter state variables also include daily Earth orientation parameters and transformation parameters from input data frames to the combined TRF. Local tie measurements among colocated stations are used at their known or nominal epochs of observation, with comotion constraints applied to almost all colocated stations. The filter/smoother approach unifies different geodetic time series in a single geocentric frame. Fragmented and multitechnique tracking records at colocation sites are bridged together to form longer and coherent motion time series. While the time series approach to TRF reflects the reality of a changing Earth more closely than the linear approximation model, the filter/smoother is computationally powerful and flexible to facilitate incorporation of other data types and more advanced characterization of stochastic behavior of geodetic time series.

Statistically optimal estimation of degree-1 and C20 coefficients based on GRACE data and an ocean bottom pressure model

“…However, we do notice that the annual amplitude of the SLR C 10 time-series is about 1 mm larger than our estimates as well as many others. The annual phase of our C 10 coefficients is more than a month later than the SLR-and GPS-derived solutions (Rietbroek et al 2012;Cheng et al 2013b;Wu et al 2015) but close to the solution based on GRACE and altimetry data (Rietbroek et al 2016). Error estimates and the correlation coefficients are also important product of the proposed approach.…”

“…Please note that the annual amplitude A and phase φ are defined by Acos (2π (t − t 0 ) − φ), where t 0 refers to January 1 of a particular year. The solutions 'Combination approach *' and 'Combination approach **' are estimated over reduced time intervals to be more comparable with those from Wu et al (2015) and Rietbroek et al (2012). (Rietbroek et al 2016) 3 .…”

The Geodesist’s Handbook 2016

“…According to the IERS Conventions 2010 [Petit et al 2010] the ITRF origin should be considered as the mean Earth center of mass, averaged over the time span of SLR observations used and modeled as a secular (linear) function in time. It can be regarded as a crust-based TRF with the origin realized as a mean CM [Blewitt 2003;Dong et al 2003;Petit et al 2010;X. Wu et al 2015].…”

“…Taking into account today's high accuracy of the space geodetic observations, non-linear station motions caused by various geohysical phenomena (e.g., postseismic deformations, volcanic activities, atmospheric or hydrological loading effects) become significant [e.g., Bevis et al 2014;Blossfeld et al 2014;X. Wu et al 2015].…”

Tropospheric delay determination by Kalman filtering VLBI data

“…Since then, research on using a KF in VLBI analysis has been practically non-existent, except for studies by Pany et al (2007Pany et al ( , 2011, which focused solely on simulations of VLBI observations. This lack is surprising as Kalman filtering has been successfully used in geodetic Global Navigation Satellite Systems (GNSS) analysis (Schüler 2001;Webb and Zumberge 1993), gravity field studies (Kurtenbach et al 2009), and for combination of space geodetic techniques to derive Earth Orientation Parameters (EOP, Gross 2000; Gross et al 1998) or terrestrial reference frames (TRF, Wu et al 2014). Examples of Kalman filtering in GPS data processing for tropospheric investigations are studies by Jarlemark et al (1998), Emardson and Jarlemark (1999), as well as Schüler (2001).…”