A hybrid EKF-LSTM framework with GA-tuned noise covariance for enhanced time series forecasting

Abstract Accurate navigation state estimation is essential for control systems, where internal states must be inferred from noisy sensor inputs. Traditional Extended Kalman Filter (EKF) methods often face limitations when handling nonlinearities and sensor noise. To overcome these challenges, this study proposes a hybrid model that integrates EKF with Long Short-Term Memory (LSTM) networks and multi-head attention mechanisms to leverage temporal dependencies for improved future state prediction. Additionally, a Genetic algorithm (GA) is employed to optimize the process noise covariance matrix (Q), enhancing the adaptability of the EKF. The inclusion of 1D convolutional (Conv1D) layers enables effective feature extraction from accelerometer and gyroscope data, further boosting estimation accuracy. Compared to conventional EKF techniques, the proposed hybrid EKF-LSTM model augmented with attention and GA optimized Q achieves substantial reductions in Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE), offering a robust and reliable solution for navigation in dynamic and noisy environments.