A CNN-GRU Fusion Mathematical Model for Positioning Jump Correction in Integrated Navigation Systems

Positioning jumps are a primary cause of trajectory discontinuities in urban canyon environments, severely hindering the widespread adoption of autonomous vehicles. This paper proposes a CNN-GRU fusion-based method for correcting such positioning jumps. A complete 15-dimensional error-state extended Kalman filter (EKF) framework is established to analyze the jump generation mechanisms from three perspectives—pseudorange distortion, inertial drift, and filter gain divergence—thereby justifying the use of inertial measurement unit (IMU) time-series data for anomaly prediction. An end-to-end mapping model is further constructed, in which a one-dimensional convolutional neural network (CNN) extracts cross-channel spatial features from multi-axis inertial data, while a gated recurrent unit (GRU) captures long-term temporal error evolution. A hysteresis navigation quality factor and a piecewise Huber loss function are incorporated to enable hierarchical adaptive optimization. Experimental results demonstrate that the proposed method reduces the positioning root mean square error (RMSE) from 1.24 m to 0.70 m, achieves a jump suppression rate of 43.5%, and maintains a single-frame inference latency of 11.8 ms, meeting the real-time requirements for future autonomous driving localization.