On variance component estimation with pseudo-observations
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On variance component estimation with pseudo-observations E. Mysen1 Received: 5 January 2018 / Accepted: 7 August 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract A common approach in geodesy is to rescale observation noise covariance blocks to compensate for errors in stochastic modelling. Each block represents a batch of observations, which is assumed to depend on parameters that are specific to that batch only, and on global parameters that may also be involved in other batches. In the presented work, the covariance rescaling using variance component estimation is given in a form that depends explicitly on the number of batch specific parameters. A transformation of the observations is applied to demonstrate that variance component estimation based on batch estimates of global parameters does not utilize the available information. Keywords Variance component estimation · Piecewise linear functions · Degrees of freedom · Pseudo-observations · Completeness Mathematics Subject Classification 62F10 Point estimation
1 Motivation In some geodetic problems the observations are, for computational convenience or feasibility, first processed in batches to produce batchwise parameter solutions and their error covariances. When the goal is to produce a reference frame, the batches are called sessions and their sizes are defined by periods of time, stretching from one day to 2 weeks (Altamimi et al. 2016). Final parameter estimates can then be obtained, conveniently and without the loss of information (Brockmann 1997, pp. 21–23), by treating the batchwise solutions as observations. Even though the stochastic model for these pseudo-observations is perfectly correct, the fact that this approach is rigorous is not trivial since the number of effective observations is significantly reduced.
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E. Mysen [email protected] Geodetic Institute, Norwegian Mapping Authority (NMA), 3507 Hønefoss, Norway
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GEM - International Journal on Geomathematics
With this in mind, one can turn to the determination of the stochastic model of the fundamental observations themselves, which is important to address since the optimal parameter estimates are functions of the true observation noise covariance. In the computation of reference frames, a stochastic model is often adopted in which the observation noise covariance of each session, or an equivalent, is postulated to be correct except for a scale factor (e.g. Altamimi et al. 2002). The scale factors of each session have, for instance, been determined iteratively by a variance component estimation scheme based on pseudo-observations (VCEP). An advantage of this algorithm is that data from each session do not need to be reanalyzed, but presumes that little information is lost compared to more fundamental variance component methods, like the one based on the information content of the observation residuals1 (VCEO). Applications of pseudo-observation based weighting include Altamimi et al. (2011) and Seitz et al. (2012), and it is expected that VCEO and VC
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