On Joint State Estimation and Model Learning using Gaussian Process Approximations

Techniques for state estimation is a cornerstone of essentially every sector of science and engineering, ranging from aeronautics and automotive engineering to economics and medical science. Common to state estimation methods, is the specification of a mathematical model of the underlying system in question. Typically, this is done a priori, i.e., the mathematical model is derived based on known physical relationships and any unknown parameters of the model are estimated from experimental data, before the process of state estimation is even started. Another approach is to jointly estimate any unknown model parameters together with the states, i.e., while estimating the state of the system, the parameters of the model are also estimated (learned). This can be done either offline or it can be done online, i.e., the parameters are learned after the state estimation procedure is “deployed” in practice. A challenge with online parameter estimation, is that it complicates the estimation procedures and typically increases the computational burden, which limits the applicability of such methods to models with only a handful of parameters. This thesis aims to investigate how online joint state estimation and parameter learning can be done using a class of models that is physically interpretable, yet flexible enough to be able to model complex dynamics. Particularly, it is of interest to construct an estimation procedure that is applicable to problems of a large scale, which is challenging due to a high computational burden because the models typically need to contain many parameters. Further, the ability to detect sudden deviations in the behavior of the observed system with respect to the learned model is investigated. The studied model class consists of an a priori specified part providing a coarse description of the dynamics of the considered system and a generic model part that describes any dynamics that is unknown a priori and is to be learnt from data online. In particular, a subclass of these models, in which it is assumed that the spatial correlation of the underlying process is limited, is studied. A computationally efficient method to perform joint state estimation and parameter learning using this model class is proposed. In fact, the proposed method turns out to be nearly computationally invariant to the number of model parameters, enabling online inference in models with a large number of parameters, in the order of tens of thousands or more, while retaining the interpretability. Lastly, the method is applied to the problem of learning motion patterns in ship traffic in a harbor area. The method is shown to accurately capture vessel behavior going in and out of port. Further, a method to detect whether the vessels are behaving as expected, or anomalously, is developed. After initially learning the vessel behaviors from historical data, the anomaly detection method is shown to be able to detect artificially injected anomalies