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.