Online Learning With Joint State and Model Estimation - Götte, Ricarda‐Samantha; Timmermann, Julia (Proceedings in applied mathematics and mechanics, 2025)
ABSTRACT Model‐based state observers require high‐quality models to deliver accurate state estimates. However, due to time or cost shortage, modeling simplifications or numerical issues, models often have severe inaccuracies that may lead to insufficient and deficient control. Instead of attempting to iteratively model these deviations, we address the challenge by the concept of joint estimation. Thus, we assume a linear combination of suitable functions to approximate the inaccuracies. The parameters of the linear combination are supposed to be time invariant and augment the model's state. Subsequently, the parameters can be identified simultaneously to the states within the observer. Referring to the principle of Occam's razor, the parameters are claimed to be sparse. Our former work shows that estimating states and model inaccuracies simultaneously by a sparsity promoting unscented Kalman filter yields not only high accuracy but also provides interpretable representations of underlying inaccuracies. Based on this work, our contribution is twofold: First, we apply our approach finally on a real‐world test bench, namely a golf robot. Within the experimental setting, we investigate closed loop behavior as well as how suitable functions need to be chosen to approximate the inaccuracies in a physically interpretable way. Results do not only provide high state estimation accuracy but also meaningful insights into the system's inaccuracies. Second, we discuss and establish a method to automatically adapt and update the model based on collected data of the linear combination during operation. Examining past parameter estimates by principal component analysis, a moving window is utilized to extract the most dominant functions. These are kept characterizing the model inaccuracies, while nondominant functions are automatically neglected and refilled with novel function candidates. After analysis and rebuilding, this updated function set is subsequently fed back into the joint estimation loop and deployed for further estimation. Hence, we give a holistic paradigm of how to analyze and combat model inaccuracies while ensuring high state estimation accuracy. Within this setting, we once more investigate closed loop behavior and yield promising results. In conclusion, we show that the proposed observer provides a helpful tool to guarantee high estimation accuracy for models with severe inaccuracies or for situations with occurring deviations during operation, for example, due to mechanical wear or temperature changes.