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

Abstract Accurate navigation state estimation is critical for navigation and control systems, where internal states must be inferred from noisy sensor inputs. However, conventional Extended Kalman Filter (EKF) methods often struggle with nonlinearities and data noise. To address these challenges, a hybrid approach is proposed that combines EKF with Long Short-Term Memory (LSTM) networks and multi-head attention mechanisms. By leveraging temporal dependencies, this method improves future state predictions. The Genetic Algorithm (GA) further enhances the EKF’s adaptability by optimizing the process noise covariance matrix (Q%). Incorporating 1D convolutional (Conv1D) layers enables effective feature extraction from accelerometer and gyroscope data, boosting estimation accuracy. Compared to traditional EKF techniques, the hybrid EKF-LSTM model with attention and GAoptimized Q values demonstrates significantly better performance, achieving notable reductions in Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE). This robust framework strengthens the reliability of state estimation in smartphone-based and sensor-driven navigation systems, offering a promising solution for dynamic and noisy environments.