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Abstract:
The geodetic method of positional data processing is usually not one of position estimation only, nor one of model testing only, but usually one where estimation and testing are combined. The DIA-estimator captures the statistical intricacies of this combination, thus providing a unifying framework for the 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 multimodal probability density function (PDF), we have solutions available for the forward problem, but not so for the inverse problem. That is, no objective methods and strategies are currently available that allow one to design DIA-estimators specifically for explicitly formulated 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 partitionings of the misclosure spaces, and to the ‘winner-takes-all’ structure of the DIA-class estimators currently employed. For an underpinning of the design and computational challenges various numerical and graphical examples will be provided. The challenges that will be provided represent samples of fertile grounds for the typical researcher interested in geodetic data processing and modelling, and eager to take up a difficult challenge and/or looking for research opportunities that can make a difference.
