Online GPR-KF for GNSS Navigation with Unmodelled Measurement Error

To achieve the best performance for a Kalman filter (KF) for global navigation satellite system (GNSS) positioning, a comprehensive measurement model is required. However, the GNSS observations suffer from unmodelled errors resulting from multipath, interference, etc. These errors are difficult (even impossible) to model using parametric models. Inspired by Gaussian process (GP) Bayes filters with measurement and dynamic models trained with non-parametric GP regression (GPR), the unmodelled errors in the GNSS observations can be trained online based on the GPR using the measurements residuals calculated by the KF. One of the problems in using the GPR for online modelling is its high computational cost. To reduce the computational complexity, more than one forward step sliding window for the input training points and the GPR model training can be used. Furthermore, to avoid the over-prediction using the online trained GPR model, a constraint on the query point was introduced. In this study a non-linear autoregressive model was used for the online GPR model training. To verify this algorithm, both static and kinematic experiments were evaluated. The results show that the online GPR-KF algorithm can effectively improve the deteriorated GNSS positioning accuracy caused by unmodelled errors in the GNSS observations. The effectiveness of the proposed algorithm was also validated using the measurement innovation statistical test.