Working group: Expert-based data analysis and quality processes

Optimal and sequential estimation of states based on arbitrary observations in the state space. In addition to linear systems, mainly non-linear systems are also taken into account. The aim is to make the approaches as efficient and robust as possible against outliers. In addition, pre-existing knowledge is to be integrated into the filter algorithm as priori knowledge and thus lead to an improved estimate. The focus is also on methods with which normally distributed system and measurement noise as well as arbitrary and multimodal system and measurement noise can be mastered.

Efficiency is increased by modelling and optimising measurement processes. The modelling of measurement processes with suitable modelling methods and the determination of the necessary level of detail is a focus of the research field. Furthermore, suitable optimisation methods for optimising the efficiency of the respective measurement processes are validated.

This research field deals with the adaptation of Bayesian inference, centred on Bayes' theorem, to some geodetic applications. Based on Bayes' theorem, unknown parameters are determined and hypothesis tests for the parameters are tested. The applications are carried out in linear and non-linear models. In addition, robust estimates against outliers and the Bayes filter are derived. As some analytical integrations for parameter estimation, for the definition of uncertainty ranges or for testing hypotheses cannot be derived, numerical methods based on Monte Carlo procedures were developed and applied.

In the area of classical parameter estimation, various deterministic trend models are analysed on the one hand, e.g. regression and basis function models (B-splines, polynomials, etc.). On the other hand, the focus is on the realistic modelling of stochastic models in the form of covariance matrices. In the area of hypothesis testing, suitable optimality criteria (e.g. based on uniform best invariance) are developed for various modelling scenarios. If outliers are to be expected in the measurement data, the least squares method is replaced by a robust estimation procedure. For this purpose, we analyse M, R, maximum likelihood, LMS and RANSAC estimators, among others. In addition to outliers, data gaps are also a major problem in parameter estimation. In order to solve this problem, we are investigating robust expection-maximisation algorithms that are able to fill data gaps with stochastic prior information.

In addition to the typical spatial reference, geodetic measurement series often also have a time reference. This applies in particular to the measurement noise, whose characteristics can often be modelled with the help of stochastic processes. Stochastic processes in the form of autoregressive moving average (ARMA) processes are particularly interesting here, as they are described by relatively few coefficients, which also have direct relationships to the autocovariance function or the power density spectrum. This means that coloured measurement noise in particular can be modelled efficiently and meaningfully both in the time domain and in the spectral domain.