Deep Learning Based Kalman Filter for GNSS/INS Integration: Neural Network Architecture and Feature Selection

This paper provides further details of the deep learning (DL) based integration algorithm for global navigation satellite system (GNSS) and inertial navigation system (INS) integration, where a deep neural network (DNN) is inserted into the flow of an error-state extended Kalman filter (ES-EKF) to learn the complex dynamics of the system. The proposed algorithm learns the optimal Kalman gain along with the errors in the inertial measurement units (IMU) and demonstrates superior performance over ES-EKF in terms of estimated navigation solutions and IMU errors. In this work, we analyze different implementations of the neural networks, the network architectures, and the impact of the various features to the performance of the proposed algorithm. We suggest a convolutional neural network (CNN) to extract spatial information and a long shortterm memory neural network (LSTM) to capture temporal dependencies. We justify the use of LSTM as compared to other types of recurrent neural networks (RNN). Optimal sizes for the fully connected layers, number of layers, and hidden state sizes are determined too. We report the observed difficulties in the learning, namely vanishing and exploding gradients and list the techniques we used to cope with these issues. The computational efficiency of the DL-based ES-EKF is compared to regular ES-EKF, the DL-based algorithm is supposed to fit into real-time requirements. Analysis of the impact different features have on the convergence and performance of the algorithms is carried out.