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 files. The time-series representation characterizes and distinguishes JTRF from ITRF and DTRF, both adopting a parameterized representation.

The ultimate goal of the JPL frame products is to unify all of the space geodetic inputs into a self-consistent frame. 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.

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Plots showing VLBI and GNSS Co-Observing Tsukuba

Kalman Filter

Kalman filtering is one of the elective approaches in recursive optimal state estimation. Widely applied to a variety of disciplines and applications ranging from:

  • oceanography,
  • global sea level rise,
  • precise satellite orbit determination,
  • GPS positioning,
  • VLBI data analyses,
  • Earth rotation,
  • combination of loosely constrained positions inferred from SG and terrestrial geodesy,
  • and studies of correlations of the radial component of position time series at SG co-located sites

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.

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Plot demonstrating Kalman Filter and RTS Smoother

Rauch-Tung-Striebel (RTS) Smoother​

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 Wu et al. [2015], whereas for an in-depth coverage of the subject, the interested reader is addressed to, e.g., Gelb [1974] and Simon [2006].

References

Abbondanza, C., T. M. Chin, R. S. Gross, M. B. Heflin, J. W. Parker, B. S Soja, T. van Dam, and X. Wu (2017), JTRF2014, the JPL Kalman filter, and smoother realization of the International Terrestrial Reference System, J. Geophys. Res. Solid Earth, 122, 8474– 8510, doi:10.1002/2017JB014360.

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, Adv. Space Res., 65(4), 1235– 1249, doi:10.1016/j.asr.2019.11.016.

Chin, T. M. (2023), Square-Root formulas for Kalman filter, information filter, and RTS smoother: Links via boomerang prediction residual, Interplanetary Network Progress Report, 42-233, 1–23, https://ipnpr.jpl.nasa.gov/progress_report/42-233/42-233A.pdf.

Gelb, A (1974), Applied Optimal Estimation, MIT Press, Cambridge, Mass.

Simon, D. (2006), Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches, Wiley, Hoboken, N. J.

Wu, X., C. Abbondanza, Z. Altamimi, T. M. Chin, X. Collilieux, R. S. Gross, M. B. Heflin, Y. Jiang, and J. W. Parker (2015), KALREF—A Kalman filter and time series approach to the International Terrestrial Reference Frame realization, J. Geophys. Res. Solid Earth, 120, 3775–3802, doi:10.1002/2014JB011622.

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