The Design Method of Enhanced Unscented Kalman Filter Considering UT Transform Truncation Error

Although the Unscented Kalman Filter (UKF) generally outperforms the Extended Kalman Filter (EKF) due to its superior approximation of nonlinear state transition functions, the core Unscented Transform (UT) still cannot precisely capture complex nonlinear dynamics. This inherent limitation introduces non negligible truncation errors into state estimation, leading to significantly degraded accuracy in practical applications such as high-maneuvering target tracking, robotic localization in complex environments, and high-precision inertial navigation. Crucially, UKF performance deteriorates further as system non-linearity intensifies, exemplified by scenarios like aggressive UAV maneuvers in strong winds or rapid spacecraft attitude adjustments. To address this challenge, this paper proposes a novel estimation algorithm that explicitly accounts for the UT truncation error. We developed an improved UKF method that uses this error estimate. Rigorous performance analysis and numerical simulations closely replicating real-world scenarios demonstrate the proposed method’s significant effectiveness in boosting estimation accuracy for highly complex nonlinear systems.