We consider distributed state estimation in a wireless sensor network without a fusion center. Each sensor performs a global estimation task-based on the past and current measurements of all sensors-using only local processing and local communications with its neighbors. In this estimation task, the joint (all-sensors) likelihood function (JLF) plays a central role as it epitomizes the measurements of all sensors. We propose a distributed method for computing, at each sensor, an approximation of the JLF by means of consensus algorithms. This "likelihood consensus" method is applicable if the local likelihood functions of the various sensors (viewed as conditional probability density functions of the local measurements) belong to the exponential family of distributions. We then use the likelihood consensus method to implement a distributed particle filter and a distributed Gaussian particle filter. Each sensor runs a local particle filter, or a local Gaussian particle filter, that computes a global state estimate. The weight update in each local (Gaussian) particle filter employs the JLF, which is obtained through the likelihood consensus scheme. For the distributed Gaussian particle filter, the number of particles can be significantly reduced by means of an additional consensus scheme. Simulation results are presented to assess the performance of the proposed distributed particle filters for a multiple target tracking problem.Centralized estimation techniques transmit sensor data to a possibly distant fusion center [1]. This may require energyintensive communications over large distances or complex multi-hop routing protocols, which results in poor scalability. Centralized techniques are also less robust, and less suitable if the estimation results have to be available at the sensors (e.g., in sensor-actuator networks [4]). Furthermore, the fusion center must be aware of the measurement models and, possibly, additional parameters of all sensors. By contrast, decentralized estimation techniques without a fusion center use innetwork processing and neighbor-to-neighbor communications to achieve low energy consumption as well as high robustness and scalability. The sensors do not require knowledge of the network topology, and no routing protocols are needed.There are two basic categories of decentralized estimation techniques. In the first, information is transmitted in a sequential manner from sensor to sensor [5]- [7]. In the second, each sensor diffuses its local information in an iterative process using broadcasts to a set of neighboring sensors (e.g., [8]). This second category is more robust but involves an increased communication overhead. It includes consensusbased estimation techniques, which use distributed algorithms for reaching a consensus (on a sum, average, maximum, etc.) in the network [9], [10]. Examples are gossip algorithms [10], consensus algorithms [11], and combined approaches [12].In this paper, we consider a decentralized wireless sensor network architecture without a fusion center and use con...

We propose a distributed implementation of the Gaussian particle filter (GPF) for use in a wireless sensor network. Each sensor runs a local GPF that computes a global state estimate. The updating of the particle weights at each sensor uses the joint likelihood function, which is calculated in a distributed way, using only local communications, via the recently proposed likelihood consensus scheme. A significant reduction of the number of particles can be achieved by means of another consensus algorithm. The performance of the proposed distributed GPF is demonstrated for a target tracking problem. Index Terms-Gaussian particle filter, distributed particle filter, likelihood consensus, target tracking, wireless sensor network.

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