Adaptive State Estimation for LQG Systems using Hybrid Kalman – LSTM Filtering under Time – Varying Noise

Abstract

This work presents a simulation-based proof of concept for a hybrid estimation framework integrating a standard Kalman filter (KF) with a lightweight Long Short–Term Memory (LSTM) network for sequential online prediction of process and measurement noise covariances. The LSTM is trained offline using nonstationary datasets generated from an XArm6 ROS 2/Gazebo model and provides adaptive covariance estimates that are injected into the Kalman recursion during closed-loop execution. The covariance predictor uses simulator-provided joint states within its temporal input window, enabling controlled evaluation under known time-varying noise conditions. The proposed estimator improves state-estimation accuracy, reduces tracking RMSE, and improves NIS/NEES consistency relative to the static Kalman filter under highly nonstationary disturbances. The results provide clear evidence of the feasibility and effectiveness of the proposed hybrid Kalman–LSTM framework for adaptive covariance estimation in closed-loop robotic control. The conducted evaluation further confirms stable, bounded, and consistent estimator performance under controlled time-varying noise conditions.