Distributed Kalman Filtering Over Sensor Networks With Unknown Random Link Failures

In this letter we consider the distributed consensus-based filtering problem for linear time-invariant systems over sensor networks subject to random link failures when the failure sequence is not known at the receiving side. We assume that the information exchanged, traveling along the channel, is corrupted by a noise and hence, it is no more possible to discriminate with certainty if a link failure has occurred. Therefore, in order to process the only significant information, we endow each sensor with detectors which decide on the presence of link failures. At each sensor the proposed approach consists of three steps: 1) failure detection; 2) local data aggregation; and 3) Kalman consensus filtering. Numerical examples show the effectiveness of this method.

I. Introduction

In recent years the fast technological developments in the area of sensor networks have attracted a considerable amount of research on the problem of distributed estimation. In the context of the ongoing Internet of Things era, distributed estimation and control, by successfully exploiting the communication among the nodes of the underlying network, are currently being adopted to deal with several applications, e.g., in the domains of telecommunications [4] and intelligent transportation systems [24]. In particular, the typical scenario of distributed estimation consists of a group of autonomous sensors that are deployed in a monitored region and cooperate in some monitoring task by sharing their local information via wireless communication links. In this framework the estimation process is distributed in the sense that no central elaboration is assumed and each node of the sensor network utilizes both the local information and the messages from the neighbors to generate an estimate [5], [12], [13], [15]–[17], [21]. Even if the use of shared information across neighbors improves the local estimate, there is no guarantee for the consensus of the estimates across the network. To this aim, several consensus procedures have been proposed [1]–[3], [16]. In practical applications temporary link failures are an important issue, due to power constraints, multipath fading, background noise or external attacks. This problem has been widely investigated for centralized estimation algorithms [6], [22] and in the consensus problem of random networks [8], [10], [11], [23]. In the context of sensor networks and distributed consensus algorithms the topology design of the network in presence of link failures and other communication constraints is investigated in [9]. The convergence rate of the consensus in presence of failure is studied in [19] and [20]. The recent paper [14] proposes a two-stage Kalman-consensus filtering approach over unreliable channels when the link failures are known at the receiving side. In these conditions sufficient conditions for the boundedness of the estimation error covariance are provided.