Constraints on the Retrieval 3-D Velocities by Hybrid Regression Network for GNSS/INS Positioning During GNSS Outages

The integrated navigation system frequently degrades to an inertial navigation system (INS) standalone in complex urban environments due to recurring signal interruptions of the Global Navigation Satellite System (GNSS). Nonholonomic constraints (NHCs) and odometry assistance can effectively suppress the accumulation of INS errors during GNSS outages. However, traditional NHC requires precise compensation for inertial measuring unit (IMU) installation angles, while odometry is inaccessible in many applications. To address these challenges, we propose a novel velocity hybrid regression network (VHRNet), which integrates the superiority of convolutional neural network (CNN) and Transformer for IMU data mining. This network establishes a mapping between IMU outputs and virtual NHC and odometry measurement to apply 3-D velocity full constraints without IMU installation angles compensation and hardware-wheeled odometry. Moreover, a low-complexity adaptive optimization model in the variance domain is introduced, which can adaptively adjust noise covariance to mitigate the impact of gross errors and frequent stopping events. Land vehicle experiments demonstrate that VHRNet effectively improves the prediction accuracy of 3-D velocities, achieving 0.028, 0.562, and 0.034 m/s in lateral, forward, and vertical directions, respectively. Compared to classic time series prediction models, the prediction accuracy for the 3-D velocity improves by more than 12.5%, 21.7%, and 17.0%. In various GNSS outage scenarios, the positioning performance of the pseudo-3-D velocity constraint method significantly surpasses the traditional method with precise installation angle compensation. Notably, when GNSS outages for 120 s, positioning accuracy improves by 87.3% compared to single INS. In addition, the implementation of a noise-adaptive model yields more precise and robust positioning results.