SSUKF-FA-RBF: A Kalman-Enhanced High-Precision Positioning Framework for BeiDou Navigation Using Firefly-Optimized Neural Estimation - Li, Liang; Hong, Shunli; Liu, Xuexian (Informatica, 2025)
This study addresses the high-precision positioning requirements of the BeiDou Navigation System (BDS) by focusing on the commonly adopted BDS/Inertial Navigation System integrated navigation mode. A novel Spherical Simplex Unscented Kalman Filter (SSUKF) algorithm is proposed, featuring an improved sigma-point sampling strategy that enhances filtering accuracy while reducing computational overhead. In parallel, the Time Difference of Arrival (TDOA) method is combined with the Firefly Algorithm (FA) to optimize a Radial Basis Function (RBF) neural network, further enhancing positioning precision. Evaluation is conducted using an Ultra-Wideband TDOA dataset. Results show that the SSUKF algorithm significantly reduces positioning error. Specifically, the root means square error (RMSE) achieved by SSUKF is 0.1614 m-a reduction of 62.2% compared to the Extended Kalman Filter and 52.1% compared to the Unscented Kalman Filter. When integrated with the FA-optimized RBF neural network, the hybrid SSUKF-FA-RBF model achieves an RMSE of 0.127 m under high-noise conditions, demonstrating strong robustness and accuracy. In addition to its accuracy, the SSUKF algorithm offers improved computational efficiency, making it suitable for real-time, high-precision applications. Error analysis confirms the robustness and stability of the SSUKF-FA-RBF model across various environments. Under zero standard deviation noise, the model achieves 96.4% accuracy, 95.6% precision, and a 96.1% recall ratesubstantially outperforming comparative models. This study contributes an enhanced Kalman filtering method and an optimized positioning framework, advancing both accuracy and computational efficiency for the BDS. The proposed approach offers effective technical support for a wide range of high-precision positioning applications.