Modelling and estimating trajectory points from RTK-GNSS based on an integrated modelling approach

Abstract

The sparse Gaussian process regression (GPR) has been used to model trajectory data from Real time kinematics-global navigation satellite system (RTK-GNSS). However, upon scrutinizing the model residuals; the sparse GPR model poorly fits the data and exhibits presence of correlated noise. This work attempts to address these issues by proposing an integrated modeling approach called GPR-LR-ARIMA where the sparse GPR was integrated with the linear regression with autoregressive integrated moving average errors (LR-ARIMA) to further enhance the description of the trajectory data. In this integrated approach, the predicted trajectory points from the GPR were further described by the LR-ARIMA. Simulation of the GPR-LR-ARIMA on three sets of trajectory data indicated better model fit, revealed in the normally distributed model residuals and symmetrically distributed scatter plots. Correlated noise was also successfully eliminated by the model. The GPR-LR-ARIMA outperformed both the GPR and LRARIMA by its ability to improve mean-absolute-error in 2-dimension positioning by up to 86%. The GPR-LR-ARIMA contributes to enhancement of positioning accuracy of dynamic GNSS measurements in localization and navigation system with good model fit.