OOSM-Adaptive Sequential Tobit Kalman Filter (OS-TKF) for Distributed X-Ray Pulsar-Based Navigation Systems

To address the filtering challenges associated with censored and out-of-sequence measurements (OOSMs) within distributed X-ray pulsar-based navigation (DXNAV) systems, an OOSM-adaptive Sequential Tobit Kalman Filter (OS-TKF) is developed. Initially, the Sequential Tobit Kalman Filter is derived to process censored measurements in such navigation systems, thereby improving measurement efficiency and on-board computational performance. To tackle the challenges posed by OOSMs, the state estimation backstepping technique is employed, providing the necessary backtracking states and observation covariance. These OOSMs are subsequently integrated into the filtering process, where forward updates of both the state and the covariance are conducted, realizing the processing of the OOSMs within the current filtering period. Moreover, the navigation filter is adapted into a sequential processing format to optimize calculation efficiency. Finally, the OS-TKF is presented in detail along with its application scheme and is applied to the DXNAV system. Simulation results demonstrate that the proposed method can effectively handle censored measurements and integrate OOSMs into the state update process, thereby significantly enhancing the positioning accuracy of the DXNAV system.