High-efficiency unscented Kalman filter for multi-target trajectory estimation

High-efficiency trajectory estimation for massive resident space objects plays an important role in space situational awareness to protect space assets. The unscented Kalman filter (UKF) has been widely utilized in trajectory estimation for decades due to its high level of accuracy. However, its efficiency suffers from the time-consuming propagation of Sigma points in the unscented transformation for multiple-target trajectory estimation, especially in space-based observation scenarios with limited computing resources. The conventional UKF, essentially based on finite difference, relies heavily on small integration steps to maintain the precision of the unscented transformation, contradicting the simultaneous requirement for both accuracy and efficiency. To address this issue, we propose a high-efficiency UKF called F-UKF. It utilizes the feedback-accelerated Picard iteration (FAPI) method, an integration-correction method with large-step computing capability, to accelerate the propagation of Sigma points. Furthermore, we propose another more efficient UKF, referred to as EF-UKF, by extending the FAPI method to perform the propagation of Sigma points concurrently. The numerical results show that the proposed methods are highly efficient for multi-target trajectory estimation.