Based on a special machine learning approach, consisting of an artificial neural network (ANN) as approximation function and an extended Kalman filter (EKF) as optimisation method, a methodology for the identification of geodetic systems is derived in this thesis. This ANN-EKF learning approach is enhanced by the consideration of data-, model- or data- and model-related uncertainties. Depending on the geodetic application, one aspect of each of the three groups of uncertainties is considered. The systems to be identified are a robot arm, for which the position uncertainty is to be improved by calibration, and real estates whose value is to be determined. While the robot arm is a controllable, data-producible system with a realisable reference and low local heterogeneity; real estates are a system which is limited in inputs, in data samples, in the realisation of a reference and exhibits little empirical evidence andstrong local heterogeneity.The differences in the geodetic systems result in different research objectives. The robot arm system provides a controlled environment (data can be generated, a reference can be realised) and knowledge about geometric/physical laws is available. Thus, it is possible to pursue two enhancements of the ANN-EKF learning approach for the robot arm application. These base on data- and model-related uncertainties and are mainly supported by the EKF. The inherent variance propagation in the EKF enables accounting for the random variability of the measurements. Realistic random variabilities of the robot arm positions measured by a reference are derived. Due to the existing system description in the EKF, it is alsopossible to integrate a geometric system into the ANN-EKF learning method. The aim is to create a methodological framework that allows the incompleteness of the model to be reduced.Real estate is a limited and complex system. The biggest limiting factor of real estate valuation based on the German purchase price collection is the small data sample. The data sample is enlarged by aggregating submarkets to achieve an advantageous ANN-EKF learning. Although this increases the sample size, it is also likely to increase the complexity of the system. The incomplete data causes a model-related uncertainty. Therefore, the interaction between data- and model-related uncertainty is analysed.The first finding deals with the effects of considering data-related uncertainties in the ANN-EKF learning. The best generalisation result (minimum test error) is achieved by considering realistic data-related uncertainties in the ANN-EKF learning of the robot arm position  corrections. The learning procedure becomes more expressive due to a meaningful setting of the learning rate. In addition, insignificant ANN parameters are eliminated and smaller model structures can be achieved. The second finding concerns the development of a framework for the integration of a parametric model into ANN-EKF learning to enable a reduction in model-related uncertainty. The integrated ANN-EKF approach is built as a residual model. Testing the functionality based on simulated data shows a necessary introduction of an additional ANN iteration to achieve the adaptivity of machine learning (ML) approaches. The analysis of model complexity as a function of reduced data samples enables the derivation of minimum samplesizes for ANN-EKF learning and corresponds to the third finding. The methods of cross-validation (CV) and structural risk minimisation (SRM) in the down-sampling procedure are used and adapted for the purposes of the geodetic systems. While the SRM determines a critical number of required samples at 5000, the CV provides a stable region starting from 9000 samples for a spatially aggregated data set.The aggregation of submarkets is an appropriate approach for enlarging the sample size. The real estate valuation on basis of cross submarket ANN-EKF learning is comparable to local  valuation methods.The first two findings relate to two current topics in scientific machine learning (sciML). These are the consideration of uncertainties in ML and physics-informed machine learning (PIML), which are of interest for many fields of application such as earth observation. The developed toolbox of the ANN-EKF learning method enables the consideration of these two aspects. Finding three complements this toolbox to test these approaches of included prior information on smaller model complexities or smaller sample sizes.