RBF Neural Network-Aided Robust Adaptive GNSS/INS Integrated Navigation Algorithm in Urban Environments

Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS) integrated navigation is one of the key methods for achieving precise positioning in complex urban environments. However, in some scenarios such as urban canyons, overpasses, and foliage occlusion, GNSS signals are frequently attenuated or interrupted, leading to degraded positioning accuracy when relying solely on INSs. To address this limitation, this study developed an improved GNSS/INS-integrated navigation algorithm based on a hybrid framework that combines a Robust Adaptive Kalman Filter (RAKF) with a Radial Basis Function (RBF) neural network. The RAKF allows a multi-criterion optimization strategy to be created to adaptively adjust the measurement noise covariance matrix according to GNSS data quality indicators such as PDOP, the number of satellites, and signal quality factors. This enhances the filter's robustness and outlier detection capability under degraded GNSS conditions. Meanwhile, the RBF network is trained to predict pseudo-position increments, which substitute missing GNSS measurements during signal outages to maintain continuous navigation. Real-world vehicular experiments were conducted to evaluate the proposed RBF-aided RAKF (RBF-RAKF) against three other methods: the Extended Kalman Filter (EKF), standard RAKF, and RBF-aided Kalman Filter (RBF-KF). The experimental results demonstrate that during GNSS outages the proposed method achieved root mean square (RMS) positioning errors of 0.94, 1.02, and 0.21 m in the north, east, and down directions, respectively, representing improvements of over 90% compared with conventional filters. Moreover, the algorithm maintained meter-level horizontal accuracy and sub-meter vertical precision under severe GNSS signal degradation. These results confirm that the proposed RBF-RAKF algorithm provides stable and high-precision navigation performance in challenging urban environments.