Three-Corner Hat for the assessment of the uncertainty of non-linear residuals of space-geodetic time series in the context of terrestrial reference frame analysis

A Kalman filter and time series approach to the International Terrestrial Reference Frame (ITRF) realization (KALREF) has been developed and used in JPL. KALREF combines weekly or daily SLR, VLBI, GNSS and DORIS data and realizes a terrestrial reference frame in the form of time-variable geocentric station coordinate time series. The origin is defined at nearly instantaneous Center-of-Mass of the Earth system (CM) sensed by weekly SLR data and the scale is implicitly defined by the weighted averages of those of weekly SLR and daily VLBI data. The standard KALREF formulation describes the state vector in terms of time variable station coordinates and other constant parameters. Such a formulation is fine for station positions and their uncertainties or covariance matrices at individual epochs. However, coordinate errors are strongly correlated over time given KALREF&#8217;s unique nature of combining different technique data with various frame strengths through local tie measurements and co-motion constraints and its use of random walk processes. For long time series and large space geodetic networks in the ITRF, KALREF cannot keep track of such correlations over time. If they are ignored when forming geocentric displacements for geophysical inverse or network shift geocenter motion studies, the covariance matrices of coordinate differences cannot adequately represent those of displacements. Consequently, significant non-uniqueness and inaccuracies would occur in the results of studies using such matrices. To overcome this difficulty, an advanced KALREF formulation is implemented that features explicit displacement parameters in the state vector that would allow the Kalman filter and smoother to compute and return covariance matrices of displacements. The use of displacement covariance matrices reduces the impact of time correlated errors and completely solves the non-uniqueness problem. However, errors in the displacements are still correlated in time. Further calibrations are needed to accurately assess covariance matrices of derivative quantities such as averages, velocities and accelerations during various time periods. We will present KALREF results of the new formulation and their use along with newly reprocessed RL06 GRACE gravity data in a new unified inversion for geocenter motion.

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

Journal of Geophysical Research Solid Earth ◽

10.1002/2014jb011622 ◽

2015 ◽

Vol 120 (5) ◽

pp. 3775-3802 ◽

Cited By ~ 24

Author(s):

Xiaoping Wu ◽

Claudio Abbondanza ◽

Zuheir Altamimi ◽

T. Mike Chin ◽

Xavier Collilieux ◽

...

Keyword(s):

Time Series ◽

Kalman Filter ◽

Reference Frame ◽

Terrestrial Reference Frame ◽

International Terrestrial Reference Frame ◽

Time Series Approach

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ITRF2005: A new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters

Journal of Geophysical Research Atmospheres ◽

10.1029/2007jb004949 ◽

2007 ◽

Vol 112 (B9) ◽

Cited By ~ 612

Author(s):

Z. Altamimi ◽

X. Collilieux ◽

J. Legrand ◽

B. Garayt ◽

C. Boucher

Keyword(s):

Time Series ◽

Reference Frame ◽

Terrestrial Reference Frame ◽

Earth Orientation Parameters ◽

Earth Orientation ◽

International Terrestrial Reference Frame ◽

Orientation Parameters

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Combined IVS contribution to the ITRF2020

10.5194/egusphere-egu21-10678 ◽

2021 ◽

Author(s):

Hendrik Hellmers ◽

Sabine Bachmann ◽

Daniela Thaller ◽

Mathis Bloßfeld ◽

Manuela Seitz

Keyword(s):

Time Series ◽

Reference Frame ◽

Terrestrial Reference Frame ◽

Station Coordinates ◽

Space Geodetic Techniques ◽

International Vlbi Service ◽

Combined Solution ◽

Individual Contributions ◽

The Individual ◽

External Time

The ITRF2020 will be the next official solution of the International Terrestrial Reference Frame and the successor of the currently used frame, i.e., ITRF2014. Based on an inter-technique combination of all four space geodetic techniques VLBI, GNSS, SLR and DORIS, contributions from different international institutions lead to the global ITRF2020 solution. In this context, the IVS Combination Centre operated by the Federal Agency for Cartography and Geodesy (BKG, Germany) in close cooperation with the Deutsches Geod&#228;tisches Forschungsinstitut (DGFI-TUM, Germany) generates the final contribution of the International VLBI Service for Geodesy and Astrometry (IVS). Thereby, an intra-technique combination utilizing the individual contributions of multiple Analysis Centres (AC) is applied.For the contribution to the upcoming ITRF2020 solution, sessions containing 24h VLBI observations from 1979 until the end of 2020 are processed by 10 to 12 ACs and submitted to the IVS Combination Centre. The required SINEX format includes datum-free normal equations containing station coordinates and source positions as well as full sets of Earth Orientation Parameters (EOP). For ensuring a consistently combined solution, time series of EOPs, source positions and station coordinates as well as a VLBI-only Terrestrial Reference Frame (VTRF) and a Celestial Reference Frame (CRF) were generated and further investigated.One possibility to assess the quality of the IVS contribution to the ITRF2020 solution is to carry out internal as well as external comparisons of the estimated EOP. Thereby, estimates of the individual ACs as well as external time series (e.g. IERS C04, Bulletin A, JPL-Comb2018) serve as a reference. The evaluation of the contributions by the ACs, the combination procedure and the results of the combined solution for station coordinates, source positions and EOPs will be presented.

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Non Linear Economic Time Series as a Testbed for Dynamic Macro Models

SSRN Electronic Journal ◽

10.2139/ssrn.3447782 ◽

2019 ◽

Author(s):

Michael Wood

Keyword(s):

Time Series ◽

Economic Time Series ◽

Non Linear ◽

Economic Time

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Nonlinear Time Series Analysis with R

10.1093/oso/9780198782933.001.0001 ◽

2018 ◽

Author(s):

Ray Huffaker ◽

Marco Bittelli ◽

Rodolfo Rosa

Keyword(s):

Time Series ◽

Time Series Analysis ◽

Particle Physics ◽

Linear Time ◽

Nonlinear Time Series ◽

Nonlinear Time Series Analysis ◽

Series Analysis ◽

Linear Behavior ◽

Non Linear ◽

Scientific Principles

In the process of data analysis, the investigator is often facing highly-volatile and random-appearing observed data. A vast body of literature shows that the assumption of underlying stochastic processes was not necessarily representing the nature of the processes under investigation and, when other tools were used, deterministic features emerged. Non Linear Time Series Analysis (NLTS) allows researchers to test whether observed volatility conceals systematic non linear behavior, and to rigorously characterize governing dynamics. Behavioral patterns detected by non linear time series analysis, along with scientific principles and other expert information, guide the specification of mechanistic models that serve to explain real-world behavior rather than merely reproducing it. Often there is a misconception regarding the complexity of the level of mathematics needed to understand and utilize the tools of NLTS (for instance Chaos theory). However, mathematics used in NLTS is much simpler than many other subjects of science, such as mathematical topology, relativity or particle physics. For this reason, the tools of NLTS have been confined and utilized mostly in the fields of mathematics and physics. However, many natural phenomena investigated I many fields have been revealing deterministic non linear structures. In this book we aim at presenting the theory and the empirical of NLTS to a broader audience, to make this very powerful area of science available to many scientific areas. This book targets students and professionals in physics, engineering, biology, agriculture, economy and social sciences as a textbook in Nonlinear Time Series Analysis (NLTS) using the R computer language.

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