Modeling RTK-GNSS Trajectory Data using Sparse Gaussian Process Models

The Gaussian process regression (GPR) has been applied to model trajectory points from Global Navigation Satellite System (GNSS). Trajectory modeling using GP in previous works did not demonstrate its performance when training the GP using various kernel functions. In addition, residuals were not analyzed to ascertain the goodness of fit. In this paper, we aim to develop sparse GPR model with the best performing covariance function to model trajectory data collected using the RTK-GNSS (Real-Time Kinematics-Global Navigation Satellite Systems) in a sub-urban area. The sparse GPR was trained on three data sets collected using five types of kernel or covariance functions. The model was validated using 10-fold cross validation. The Bayesian information (BIC) and mean square error (MAE) from the cross-validation were used to identify the best performing kernel function. Subsequently sparse GPR model with the best kernel was implemented to predict the trajectory. Model residuals were analyzed using the autocorrelation, partial correlation, histograms and QuantileQuantile (Q-Q) plot. The sparse GPR could improve positioning errors ranging from 9.93 % to 34.91 %. However, the analyses on the residuals reveal poor model fit and the presence of correlation in the data.