The DIA-Estimator for Positional Integrity: Design and Computational Challenges

Abstract

AbstractThe geodetic method of positional data processing is usually not one of position estimation only, nor one of model testing only, but usually one in which estimation and testing are combined. The Detection, Identification and Adaptation (DIA)-estimator captures the statistical intricacies of this combination, providing a unifying framework for rigorous analyses of positional integrity and quality control procedures. However, to be able to establish fit-for-purpose quality control, not only solutions for the forward problem (quality of control) need to be available, but also for the inverse problem (control of quality). With the DIA-estimator and its multi-modal probability density function (PDF), we have solutions available for the forward problem, but not yet for the inverse problem. That is, no objective methods and strategies are currently available that allow one to design DIA-estimators specifically for given fit-for-purpose quality criteria. In this invited contribution we present and illustrate some of the underlying design and computational challenges that are brought forward by the complexities of the inverse problem. This relates, amongst others, to the DIA-variables, such as the chosen partitioning of the misclosure space, and to the ‘winner-takes-all’ structure of the DIA-class of estimators currently employed. To appreciate the fundamental differences with the traditional estimation-only approaches, we also show how the position probability distribution, and therefore the quality of positioning, is affected and driven by the combination of estimation and testing. For an underpinning of the design and computational challenges various numerical and graphical examples are presented.