A distributed consensus filter for sensor networks with heavy-tailed measurement noise

Dear editor, Distributed state estimation is very important in distributed sensor networks (DSNs) [1]. The consensus estimation can make the sensor networks achieve global consistency according to the data of all nodes [2]. It is very useful for the state estimation of DSNs. The fusion center and full connection between network nodes are not required. The information only exchanges between the neighboring nodes, which eliminates the need of local observability, and the stability of the state estimation can be guaranteed by the global observability. These characteristics lead to a simplified network topology, enhanced flexibility and robustness of the network structure. An effective approach to consensus estimation is consensus on information (CI) proposed in [3], and the stability is also proved. In addition, there are other distributed state estimation methods such as [4, 5]. However, measurement outliers with the heavy-tailed feature occur relatively often in practice and they may cause the divergence of estimates of states. The consideration of this problem is absent in the consensus approaches. Recently, some robust filters using the Student-t distribution and variational Bayesian (VB) method are proposed to deal with the heavy-tailed measurement noise [6–8].