On the computation of confidence regions and error ellipses: a critical appraisal

Customary confidence regions do not truly reflect in the majority of our geodetic applications the confidence one can have in one’s produced estimators. As it is common practice in our daily data analyses to combine methods of parameter estimation and hypothesis testing before the final estimator is produced, it is their combined uncertainty...

A mean-squared-error condition for weighting ionospheric delays in GNSS baselines

Although ionosphere-weighted GNSS parameter estimation is a popular technique for strengthening estimator performance in the presence of ionospheric delays, no provable rules yet exist that specify the needed weighting in dependence on ionospheric circumstances. The goal of the present contribution is therefore to develop and present the...

On a unified framework for linear nuisance parameters

Estimation problems in the presence of deterministic linear nuisance parameters arise in a variety of fields. To cope with those, three common methods are widely considered: (1) jointly estimating the parameters of interest and the nuisance parameters; (2) projecting out the nuisance parameters; (3) selecting a reference and then taking...

Least-squares variance component estimation

Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible because it works with a user-defined weight matrix; and it is attractive because it allows one to...