## Least-squares support vector machine-based Kalman filtering for GNSS navigation with dynamic model real-time correction

The accuracy of Kalman filtering (KF) relies on the quality of the observations as well as the dynamic model. However, the dynamic model is usually assumed to be invariant, which is not realistic in real global navigation satellite system (GNSS) navigation applications due to unexpected vehicular motion. A new algorithm is proposed to enhance the KF by using the least-squares support vector machine (LSSVM) technique. The LSSVM-enhanced KF (LSSVM-KF) adaptively estimates the dynamic modelling bias from historical information, and then uses the bias estimate to compensate the dynamic model. The algorithm treats the dynamic model bias as a time-variant ambiguous function which is trained with the LSSVM. A *k*-fold cross-validation method is developed to tune the training parameters of the LSSVM. With the corrected dynamic model, the KF is implemented to estimate the navigation parameters. To integrate LSSVM with KF, the unscented transformation is introduced to numerically compute the covariance of the LSSVM training. To verify the algorithm, simulation, semi-simulation and real GNSS vehicular experiments were carried out. The results show that the LSSVM-KF can adequately adapt to time-variant dynamics and achieve a reliable and accurate GNSS navigation solution.