Improved Kalman filtering through moment-based innovation gain strategies

This paper presents the moment-based Kalman filter (MKF), a novel sub-optimal estimation strategy designed to enhance robustness in systems subject to modeling uncertainties or external disturbances. Unlike the conventional Kalman filter, the MKF incorporates higher-order statistical moments of the innovation to inform its gain calculation, allowing for a more nuanced representation of the underlying noise and measurement error characteristics. The filter is structured as a predictor-corrector algorithm and maintains computational efficiency while offering improved adaptability in uncertain environments. A mathematical formulation of the MKF is provided, along with a proof of stability. Performance is evaluated using a simulated electrohydrostatic actuator (EHA) model undergoing a leakage fault. Results from the computational study demonstrate that the MKF provides more accurate state estimates than the standard Kalman filter, particularly under faulty or uncertain operating conditions.