The Implementation and Evaluation of Learning Approaches in State Filtering

Abstract:

State estimation uses measurements of a system's output to estimate the state. A particular method within state estimation is filtering, which estimates the state using measurements up to and including the current time. Common filters are the Kalman filter, the Extended Kalman filter and the Particle filter for unconstrained linear and nonlinear systems respectively. Moving Horizon Estimation is an alternative filter that accounts for state constraints; however, these filters are reliant on an accurate system model. Thus, when the model is uncertain, an alternative strategy is to develop a filter that, using neural networks, learns the filtering task from data. Such black-box filters has been implemented but needs further evaluation. A black-box filter requires much data for training and it does not consider constraints. Therefore, this thesis implements and evaluates two state filters: a DNN filter that is completely based on a neural network and the MHENet that incorporates a neural network into the filtering pipeline and allows for constraints on the state. The DNN filter has been implemented and evaluated for one-dimensional linear and nonlinear systems. The MHENet is evaluated for linear one- and two-dimensional systems. The tests show that Kalman filter and the Particle filter outperform the DNN filter in terms of tolerance to model uncertainty. Also, the DNN filter experiences difficulties during training when the states to be estimated diverges. The MHENet is shown to outperform the Kalman filter when the model is uncertain and when constraints are imposed on the state. Lastly, the MHENet is shown to perform better than the DNN filter for linear one-dimensional system showing the benefits of including structural knowledge in the filter setup.