State Estimation for Nonlinear Dynamic Systems Based on Improved Dual Set-membership Filtering

This paper introduces an improved dual set membership filter (IDSMF) for state estimation in nonlinear systems with unknown but bounded noise, which is common in applications such as target tracking, robot control, and navigation where noise characteristics are hard to determine precisely. To address the performance degradation caused by linearization in traditional filtering methods when dealing with highly nonlinear systems, the paper utilizes semi-infinite programming to convert the nonlinear system into linear system, thus avoiding linearization errors and enabling a more accurate calculation of the minimal ellipsoid covering the system state. Additionally, an adaptive process noise up dating step is introduced to enhance the algorithm's adaptability and robustness by adjusting the process noise bounds in real-time based on current estimation error and system dynamics, better reflecting the system's uncertainty and optimizing filtering performance. To make the algorithm suitable for online real-time applications and reduce computational complexity, an efficient solution strategy based on the first-order Frank-Wolfe method is proposed, which significantly decreases computational resource consumption without compromising filtering accuracy. The stability of the proposed dual set membership filter in a specific nonlinear dynamic system is verified by theoretical analysis and simulation experiments. Compared with the existing methods, the proposed filter has higher estimation accuracy and computational efficiency. The adaptive process noise updating step further improves the algorithm's adaptability and robustness under different conditions, ma king it a more reliable and efficient solution for state estimation of nonlinear systems.