A Novel LiDAR–Inertial Odometry Using Tightly Coupled Iterated Set-Membership Filter

This work presents a novel tightly coupled LiDAR-inertial odometry (LIO) method using a Set-Membership Filter (SMF). While most filtering methods in LiDAR odometry rely on the Gaussian assumption, SMF operates under unknown-but-bounded (UBB) measurement noise. It achieves information fusion by formulating a semi-definite programming (SDP) problem without requiring explicit analytical formulas. We improve the SMF framework to provide a more suitable integration of LiDAR and IMU measurements. In the prediction step, a decoupled formulation is introduced in combination with IMU propagation, resulting in a prediction model that differs from that of the Extended Kalman Filter (EKF). In the update step, we relax the original computationally intensive SDP formulation to further reduce computational complexity and employ an iterative approach to eliminate linearization errors. This not only avoids the need to formulate a new SDP for higher-order error estimation but also improves the LiDAR point cloud registration rate. To evaluate the effectiveness of SMF in LiDAR odometry, the proposed filter is integrated into three state-of-the-art LIO systems and tested extensively on benchmark datasets and field experiments. Experimental results demonstrate that SMF achieves comparable or even higher accuracy, enhancing overall system performance.