Tracking multiple space objects using multiple surveillance sensors is a critical approach in many Space Situation Awareness (SSA) applications. In this process, the uncertainties of targets, dynamics, and observations are usually represented by the probability distributions. However, precise characterization of uncertainty becomes challenging due to imperfect knowledge about some key aspects, such as birth targets and sensor detection profiles. To overcome this challenge, this paper proposes a multi-sensor possibility PHD filter based on the theory of outer probability measures. An effective compensation method is introduced to tackle variations in the fields of view of SSA sensors or instances of missed detections, aiming to mitigate the inconsistency in localized information. The proposed method is adapted to centralized and distributed sensor networks, offering effective solutions for multi-sensor multi-target tracking. The major innovation of the proposed method compared with typical methods is the proper description of epistemic uncertainty, which yields more robust performance in the scenarios of lacking some information about the system. The effectiveness of the multi-sensor possibility PHD filter is demonstrated by a comparison with conventional methods in two simulated scenarios.

Compared with a conventional unscented Kalman filter (UKF), the recently proposed marginalized unscented Kalman filter (MUKF) uses a partially sampling strategy to achieve similar filter accuracy with fewer sigma points, demonstrating its powerful ability to deal with state estimation with mixed linearity and nonlinearity. However, the hypothesis that the accuracy of MUKF is equivalent to that of UKF is not true for all systems. In this paper, it is proved that when the state equation is expressed as a differential equation, the accuracy of MUKF is equivalent to that of UKF only when the propagations of the states to be sampled and the states not to be sampled in MUKF are independent of each other. The above condition corresponds to a common problem in engineering, which is a system with measurement biases. Through theoretical proof and numerical simulation, it is verified in this paper that for the systems with measurement biases, the differences of the computed means and covariances in filtering recursions between MUKF and UKF are restricted to the same order infinitesimal as the square of the scaling parameter. To sum up, this paper evaluates the accuracy of MUKF, providing references for engineers to choose MUKF or UKF in different systems.