At present, various applications have a high demand for navigation systems. With the example of self-driving cars, the navigation system has to provide pinpoint accuracy for positioning. Inertial navigation system (INS) and global positioning system (GPS) are some of the common ways to navigate. However, these two systems have the disadvantages of continuity, cumulative error, divergence over time, and reliability. A solution based on the extended Kalman filter (EKF) and long- and short-term memory (LSTM) is proposed in this study to correct the divergence due to cumulative errors in INS. It has been proven effective by a number of studies to combine a Kalman filter with GPS and INS data. However, there are still issues in the integration of the Kalman filter with INS/GPS, such as random error model, noise resistance, and observability of inertial sensors. The proposed system is designed to incorporate deep learning to comb through long-, medium-, and short-term memories as well as predict INS and GPS errors using recurrent neural network (RNN), as LSTM is used to learn INS errors while the GPS is working well and to predict GPS errors when GPS signals are lost. Unlike the traditional way of learning, LSTM contains time variants. To verify the accuracy of the proposed design, the EKF is introduced as a means to compare with LSTM. EKF is very suitable for more flexible coordination between INS and GPS, so EKF is used for deep learning comparison with LSTM for prediction and control in a nonlinear environment. Then, the LSTM deep learning is used to correct the predictions. This computation reduces the errors in position and speed. Finally, an emulation model developed in MATLAB is used to simulate the INS–GPS integrated system error compensation model. The experiment results indicate that the errors in parameters are the smallest with the integration of LSTM in INS and GPS, thus providing the effects of error correction and compensation.