Journal
JOURNAL OF GEODESY
Volume 77, Issue 9, Pages 514-528Publisher
SPRINGER-VERLAG
DOI: 10.1007/s00190-003-0350-5
Keywords
covariance matrices; error propagation; Gibbs sampler; Monte Carlo; gravity field modelling
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The use of sampling-based Monte Carlo methods for the computation and propagation of large covariance matrices in geodetic applications is investigated. In particular, the so-called Gibbs sampler, and its use in deriving covariance matrices by Monte Carlo integration, and in linear and nonlinear error propagation studies, is discussed. Modifications of this technique are given which improve in efficiency in situations where estimated parameters are highly correlated and normal matrices appear as ill-conditioned. This is a situation frequently encountered in satellite gravity field modelling. A synthetic experiment, where covariance matrices for spherical harmonic coefficients are estimated and propagated to geoid height covariance matrices, is described. In this case, the generated samples correspond to random realizations of errors of a gravity field model.
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