## 1 Introduction  
Recently, space situational awareness (SSA) [1; 2; 3] has attracted more and more attention, because of its broad applications in space surveillance, tracking of objects in Earth orbit, monitoring the conditions of Earth's magnetosphere, ionosphere and thermosphere, etc. Among the varieties of SSA systems, the space-based sensor network [4] (e.g., distributed satellite system) has many advantages compared with ground-based ones, since there is no atmosphere and weather problems for space-based sensor networks. Object tracking is a key problem in SSA, because many space missions highly depend on the results of object tracking, i.e., threat detection, cooperative search and collision avoidance. Kalman filter-based estimation [5; 6] plays a key role among tracking methods, due to its ability of real-time estimation and non-stationary process tracking. The main challenging problem in tracking objects in Earth orbit is the strong nonlinear dynamics of objects. Existing approximate nonlinear filters can be roughly classified into two categories: linearization and sampling approaches. The linearization approach is based on linearizing the nonlinear dynamics and measurement map and then employing the classical Kalman filter equations. For example, the extended Kalman filter (EKF) [7; 8] puts the Jacobians of dynamics and measurement maps into the structure of the Kalman filter to estimate the state and corresponding covariance. It should be noted that the EKF is highly effective and has a broad range of applications [9; 10]. The sampling approach is to use a collection of state samples to approximate the state estimate and its error covariance, i.e., uncertain Kalman filter (UKF) [11; 12] and cubature Kalman filter (CKF) [13]. In [5], the authors studied the spacecraft tracking problem using sampled-data Kalman filters. Notice that UKF introduces a nonzero scaling parameter, which defines a non-zero center of sampling points. The CKF does not entail any free parameter and is more accurate than the UKF [14]. There exist many works studying the centralized estimation method, which need a central node to fuse information from the whole network [15; 16]. For example, in [15], the authors proposed a fusion method based on the cubature information filter for the target tracking problem. However, when it comes to a distributed setting and the central node failure, information is exchanged only between neighbors. Most of the existing distributed Kalman filters include consensus terms in the Kalman filter structure [17; 18; 19; 20; 21; 22]. For example, [PERSON] [18] constructed a Kalman consensus filter (KCF), in which the estimates of each node are provided by consensus on measurement information. The work in [17] proposed an optimal KCF and then proved the convergence property. However, KCF in [17] is not scalable, since it needs all-to-all communications. Additionally, [PERSON] et al. [23; 24] studied KCF for switching communication topologies. The work in [19] considered the KCF with consensus on the inverse covariance matrix and the information vector. It should be noted that the works in [19] only need communication once between two sample instances and do not need any global information. When it comes to the nonlinear case, the main difficulty is that the joint (all-sensor) likelihood function is not available for each sensor. Several distributed Bayesian filters were proposed to solve the problem [20; 25; 26]. In [25], a likelihood consensus-based distributed Bayesian filtering was studied, where the joint likelihood function was approximated by the consensus algorithm, and a distributed particle filter was proposed. Nevertheless, particle filters suffer from the burden of computational complexity, which is not suitable for real-time applications. In [20], the authors extended the results of [19] to a class of nonlinear systems and proposed a distributed extended Kalman filter.