Gaussian Process Based Multi-Rate Observer for the Dynamic Positioning Error of a Measuring Machine

In this paper, a Kalman filter (KF) based method for the accurate estimation of the dynamic positioning error of the tool-center-point (TCP) of a high-precision measuring machine is presented. A generalizing approach consisting of a linear physical model of the dynamic TCP deviations and a data-based model, which is realized as an additive Gaussian process (GP) trained on the physical model error, is applied. On one hand, the TCP position can be measured using a novel camera-based sensor which yields the absolute positioning error at a relatively slow sampling rate. On the other hand, the GP predicts the model mismatch at the fast base sample rate and can be treated as an additional pseudo measurement. A multirate (MR) observer in the KF framework yields an improved estimate of the TCP position compared to a KF using only the camera measurements. Simulation results show the potential of the proposed MR-KF approach using a combined physical and data-based model.