## 1 Introduction
In [26], the authors proposed a distributed cubature information filter (DCIF), which was used for the cooperative space object tracking problem. However, in [26], information of the whole network is need, which may not be suitable for application. Therefore, we need to investigate a more scalable distributed Bayesian filter. In this paper, a distributed sensor network architecture without a fusion center is considered, and a global estimation (global estimation means that the measurements of all sensors are processed by one sensor) task is performed by consensus algorithms through local processing and communicating with neighbors such that the final global estimate is obtained locally at each sensor. We first discuss the distributed Bayesian filter (DBF) by maximizing a posterior estimation method. Then K-L divergence-based consensus is used to approach the global posterior estimation. In order to improve the effectiveness and practicality of DBF, the cubature rules are adopted to formulate a distributed cubature Kalman filter. Notice that K-L divergence as an information metric has been used in several Kalman filters [19; 27; 28; 29; 30]. Similar to [19], K-L divergence in our paper is used to measure the difference of posterior distributions between sensors. The contributions of this paper are summarized as follows:  
1. A distributed Bayesian filter is developed, which can be treated as an extension of the traditional Bayesian filter [7] and an extension of distributed linear filters [18; 19; 31] to a nonlinear case. By maximizing a posterior estimation method, we show that the global posterior estimation can be achieved by consensus of each local posterior distribution, where the consensus of PDFs is obtained by an information-theoretic approach. 2. Based on the developed distributed Bayesian filter structure, a distributed cubature Kalman filter (DCKF) is proposed, which can improve the effectiveness and practicality for applications. Different from the design in [26], the only global information we required is the number of sensor, which is more suitable for applications. 3. The cooperative space object tracking problem is studied. Different from [26], we focus on the scenario in which the communication topology may change due to the blockage of the Earth. Moreover, we also consider the case that measurement mapping of each sensor may differ, which will lead to the problem of weak observability for some sensors. The issues of weak observability and blockage are handled by the proposed DCKF. The remainder of paper is organized as follows. The problem formulation is given in Section 2. Then, the distributed Bayesian filter is discussed, while a fully-distributed cubature Kalman filter is proposed in Section 3. Following that, numerical simulations on space object tracking are shown in Section 4. The discussions are provided in Section 5. Finally, the conclusion of this paper is provided in Section 6. Notations: The superscript \"\(\top\)\" represents the transpose. \(\mathbb{E}\{x\}\) denotes the mathematical expectation of the stochastic variable \(x\). \(diag\{\cdot\}\) represent the diagonalization scalar elements. \(tr(P)\) is the trace of the matrix \(P\), and \(var(x)\) is the variance of \(x\). \(p(\cdot)\) denotes the probability density function (PDF), and \(\mathbb{N}(0,U)\) is the Gaussian distribution with mean zero and variance matrix \(U\).