Improvement of Baarda’s external reliability measure

The reliability theory has been an important element of the classical geodetic adjustment theory and methods in a linear Gauss-Markov model since Baarda invented reliability in 1968. Although geodetic reliability has been widely investigated and applied to a variety of geodetic, photogrammetric, and remote sensing problems, there is no report of theoretical progress to improve further Baarda's reliability measures among linear models. We propose the power of the effect of the minimum detectable outlier on parameters as an alternative external reliability measure, present a regularized external reliability, and demonstrate for the first time that the external reliability measure of Baarda's type is not the best and can be significantly improved through regularization for inverse ill-posed problems. An ill-posed regression example is used to illustrate the regularized external reliability measure, which is shown to perform much better than the external reliability measure of Baarda's type.