Vibration Displacement Extraction Based on an Auto-Tuning Kalman Smoother from GNSS

High-frequency global navigation satellite system (GNSS) is one of the most effective means for structural health monitoring. At present, most of the GNSS-based structural health monitoring research focuses on the positioning method, however, the unmodeled error caused by the complex monitoring environment and the receiver are always ignored by such technology. Most of the displacement extraction algorithms based on GNSS kinematic positioning are based on the Kalman filter and its variants, and the research on the effective determination of the process noise matrix and the measurement noise matrix is still limited. This paper aims to explore a displacement extraction method with automatic parameter tuning for structural health monitoring. An auto-tuning Kalman smoother has been introduced for extracting vibration displacement from GNSS kinematic positioning. Specifically, we divide the GNSS kinematic positioning results into a training set and a validation set, then use non-convex optimization to obtain the hyperparameters of the Kalman smoother. Finally, we extract the displacement from Kalman smoother with the tuned hyperparameters. Simulation and field experiments were carried out to verify the proposed method. The results show the feasibility and effectiveness of the method for vibration displacement extraction. For real-time kinematic positioning, the displacement extraction accuracy is improved by 9.58% compared to the traditional Kalman smoother; for precise point positioning, the displacement extraction accuracy is improved by 15.36%. The influence of the proportion of training set on the proposed method is discussed, and suggestion for the training set proportion is given.