Distributed Bayesian Fault diagnosis in Collaborative Wireless Sensor Networks. Hichem Snoussi ISTIT/M2S, University of Technology of Troyes, 12, rue Marie Curie, 10000, France Email: snoussi@utt.fr C´ edric Richard ISTIT/M2S, University of Technology of Troyes, 12, rue Marie Curie, 10000, France Email: richard@utt.fr Abstract— In this contribution, we propose an efficient col- laborative strategy for online change detection, in a distributed sensor network. The collaborative strategy ensures the efficiency and the robustness of the data processing, while limiting the required communication bandwith. The observed systems are assumed to have each a finite set of states, including the abrupt change behavior. For each discrete state, an observed system is assumed to evolve according to a linear state-space model. An efficient Rao-Blackwellized collaborative particle filter (RB- CPF) is proposed to estimate the a posteriori probability of the discrete states of the observed systems. The Rao-Blackwellization procedure combines a sequential Monte Carlo filter with a bank of distributed Kalman filters. Only sufficient statistics are communicated between smart nodes. The spatio-temporal selection of the leader node and its collaborators is based on a trade-off between error propagation, communication constraints and information content complementarity of distributed data. I. I NTRODUCTION In this paper, the signal processing objective is to online detect the state change of a system observed by a sensor network. The efficient online state detection, in an automatic way, is very important for the system functioning security. In fact, according to each state, the system should adopt a specific behavior. For example, an autonomous robot must be able to detect its state and carry out repairs if necessary, without human intervention, by processing the data received from the on-board sensors [1], [2]. One can also mention the use of the sensor networks for the monitoring of production systems in order to face the industrial risks, the monitoring of the houses for safety or the house automation, the air and transport control in general, intelligent alarms for the prevention of natural disasters. With such systems, the automatic control of an event or an incident rests on the reliability of the network for a an efficient and robust decision-making. For the above purpose, collaborative information processing in sensor networks is becoming a very attractive field of research. In such a sensor network, the sensors role is not limited to detect and transmit the data to a central unit where they are processed. Individual sensors have the capability to process the data and transmit only pertinent information to a fusion unit. The sensors have the ability to collaborate, exchange information to ensure an optimal decision. Such sensors are called smart sensors or smart nodes. Contrary to the centralized approach, the system does not depend on a unique processing unit whose damaging leads to the entire system failure. Every smart sensor is able to play a central role and provide a suboptimal decision. The system is thus very robust against a probable foreign attack or a technical failure of the central unit. In addition, as collected data are locally processed, only pertinent information is exchanged between smart nodes, limiting hence the required channel communication bandwidth. In fact, in a centralized network, all sensors transmit raw data to a unique processing unit, increasing the required communication bandwidth. Concerning the data processing at each smart node and the fusion rule, we adopt a probabilistic approach to model the system dynamics. The system is described by a jump Markov linear Gaussian model where the conditional Gaussians depend on the discrete state of the system and also on the sensor. The state change detection is resumed in the posterior marginal probability of the discrete state. To solve the inference prob- lem, we use the particle filter as an approximate Monte Carlo inference method able to deal with the intractable analytical aspect of the dynamical system update. Our contribution consists in proposing and implementing a collaborative dis- tributed particle filter for estimating the marginal a posteriori probabilities of the system discrete states. Recently, distributed particle filters were proposed in literature [3], [4]. In the previously proposed distributed particle filters, the conditional distributions of the distributed collected data (likelihoods) are assumed to be independent. Therefore, applying these particle filters to the jump Markov models, one needs to consider jointly the continuous and the discrete states of the system. As shown in [1], in a centralized processing, the particle filtering of the joint state leads to poor results. Our contribution consists thus in extending the Rao-Blackwellized approach, proposed in [1], in a distributed environment. The leader node collaborates with the remaining nodes at each time step. The temporal selection of the leader node is based on a trade-off between information relevance, communication cost and propagation error. The spatial selection of the leader collaborators relies on the same trade-off except that the information relevance takes an information complementarity form. The main difficulty of the spatial collaboration, within the Rao-Blackwellized distributed particle filter, is the fact that the sensors marginal likelihoods are no more independent. We show in the proposed collaborative strategy how to circumvent this difficulty while propagating only sufficient second order