Enhancing Kalman Filter Performance: Design and Estimation with Fading-Memory Kalman Filter for Reduced Modeling Error and Improved Robustness

The Kalman filter is a widely employed algorithm for state estimation and sensor fusion in variousfields. However, its performance can degrade in the presence of modeling errors and uncertaintiesin the system dynamics. To enhance the robustness and accuracy of the Kalman filter, the conceptof a Fading-Memory Kalman Filter (FMKF) has been introduced. The FMKF incorporates a fadingmemory mechanism that effectively mitigates the impact of modeling errors and reducespermanent estimation errors. By assigning time-varying weights to past measurements andpredictions, the FMKF adaptively adjusts its influence on the current state estimation. Thismechanism allows the FMKF to better accommodate dynamic system behavior and parameterchanges. In this paper, the effectiveness of the FMKF is evaluated by comparing it with the standardKalman filter. The performance of both filters is assessed in scenarios where modeling errors arepresent, and parameter variations occur. The results demonstrate that the FMKF outperforms thestandard Kalman filter by providing more accurate and robust state estimates, even in the presenceof modeling errors. The FMKF's ability to adaptively update the weights based on the relevance ofpast information allows it to effectively handle dynamic system behavior and changing parameters.