Residual least-squares collocation: use of covariance matrices from high-resolution global geopotential models

Martin Willberg, Philipp Zingerle, Roland Pail

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

The paper presents a modified formulation of least-squares collocation. This residual least-squares collocation (RLSC) includes a remove–compute–restore procedure with a high-resolution global geopotential model (GGM) and a topographic gravitational potential model. In contrast to previous approaches, in RLSC, the remaining input residuals are modeled with error covariance matrices instead of signal covariance matrices. Therefore, we include the full variance–covariance information of a high-resolution GGM, namely the XGM2016, to the procedure. The included covariance matrices are anisotropic and location-dependent and enable a realistic error modeling of a target area. This fact represents an advantage over covariance matrices derived from signal degree variances or empirical covariance fitting. Additionally, due to the stochastic modeling of all involved components, RLSC provides realistic accuracy estimates. In a synthetic closed-loop test case with a realistic data distribution in the Andes we demonstrate the advantages of RLSC for regional geoid modeling and quantify the benefit which results mainly from a rigorously handled high-resolution GGM. In terms of root mean square deviations from the true reference solution, RLSC delivers an improvement of about 30% compared to a standard LSC approach, where the benefit is particularly pronounced in areas with a sparse data distribution. This improved performance, together with the fact that the resulting stochastic error estimates better reflect the true errors, might be an important aspect for the application of RLSC to derive gravity potential values and their uncertainties at reference stations of the international height reference system.

Original languageEnglish
Pages (from-to)1739-1757
Number of pages19
JournalJournal of Geodesy
Volume93
Issue number9
DOIs
StatePublished - 1 Sep 2019

Keywords

  • Covariance function
  • High-resolution GGM
  • Least-squares collocation
  • Regional geoid modeling
  • Remove–compute–restore
  • XGM2016

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