On variance component estimation with pseudo-observations

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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.