A robust navigation algorithm without GNSS based on deep learning and variational Bayesian filter

Integrated navigation systems, combining inertial navigation system (INS) and global navigation satellite system (GNSS), are extensively used in land vehicle navigation. However, they often exhibit poor performance during GNSS outages and lack robustness in challenging urban environments. In order to reduce reliance on GNSS and fully leverage the vehicle dynamics hidden in the data, this study proposes a novel robust navigation algorithm without GNSS, based on deep learning and variational Bayesian methods. Firstly, a cascaded long and short term memory (LSTM) model with an 'attitude-velocity' two-step sequential structure is proposed. By incorporating quaternions, it overcomes the non-differentiable property of attitude caused by its bounded nature, resulting in more accurate attitude predictions. Subsequently, the attitude prediction results are utilized to enhance speed prediction, leading to a significant improvement in accuracy. Building upon the cascaded LSTM model, variational Bayesian filtering is employed to further address the complex time-varying error of its results. Through an adaptive data fusion of LSTM predictions and INS data, the data fluctuations are reduced, and the accuracy is significantly improved. The efficacy of the proposed robust navigation algorithm is validated through multiple vehicle experiments conducted on diverse paths. Experimental results demonstrate that even in scenarios where GNSS fails continuously for 15 min, the proposed algorithm maintains of speed and horizontal attitude errors within 0.6 m s-1 (root mean squared error (RMSE)) and 0.3 degrees (RMSE) respectively. Consequently, the proposed algorithm has broad application prospects in GNSS-denied environments such as building occlusion, underground parking garages, and indoor positioning. In addition, we also provide attempts to improve the model for situations such as odometer assistance and different motion states.