Belief consensus and distributed hypothesis testing in sensor networks

In this paper, we address distributed hypothesis testing (DHT) in sensor networks and Bayesian networks using the average-consensus algorithm of Olfati-Saber & Murray. As a byproduct, we obtain a novel belief propagation algorithm called Belief Consensus. This algorithm works for connected networks with loops and arbitrary degree sequence. Belief consensus allows distributed computation of products of n beliefs (or conditional probabilities) that belong to n different nodes of a network. This capability enables distributed hypothesis testing for a broad variety of applications. We show that this belief propagation admits a Lyapunov function that quantifies the collective disbelief in the network. Belief consensus benefits from scalability, robustness to link failures, convergence under variable topology, asynchronous features of average-consensus algorithm. Some connections between small-word networks and speed of convergence of belief consensus are discussed. A detailed example is provided for distributed detection of multi-target formations in a sensor network. The entire network is capable of reaching a common set of beliefs associated with correctness of different hypotheses. We demonstrate that our DHT algorithm successfully identifies a test formation in a network of sensors with self-constructed statistical models.

[1]  Yaakov Bar-Shalom,et al.  Tracking methods in a multitarget environment , 1978 .

[2]  D. Reid.  An algorithm for tracking multiple targets , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[3]  Jason Speyer,et al.  Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[4]  Y. Bar-Shalom.  Tracking and data association , 1988 .

[5]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[6]  Hugh F. Durrant-Whyte,et al.  A Fully Decentralized Multi-Sensor System For Tracking and Surveillance , 1993, Int. J. Robotics Res..

[7]  N. K. Bose,et al.  Multitarget tracking in clutter: fast algorithms for data association , 1993 .

[8]  Hugh F. Durrant-Whyte,et al.  A decentralized Bayesian algorithm for identification of tracked targets , 1993, IEEE Trans. Syst. Man Cybern..

[9]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[10]  Satish Kumar,et al.  Next century challenges: scalable coordination in sensor networks , 1999, MobiCom.

[11]  Wendi B. Heinzelman,et al.  Adaptive protocols for information dissemination in wireless sensor networks , 1999, MobiCom.

[12]  Miodrag Potkonjak,et al.  Coverage problems in wireless ad-hoc sensor networks , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[13]  Sekhar Tatikonda,et al.  Loopy Belief Propogation and Gibbs Measures , 2002, UAI.

[14]  Feng Zhao,et al.  Scalable Information-Driven Sensor Querying and Routing for Ad Hoc Heterogeneous Sensor Networks , 2002, Int. J. High Perform. Comput. Appl..

[15]  Ian F. Akyildiz,et al.  Sensor Networks , 2002, Encyclopedia of GIS.

[16]  R. Murray,et al.  Consensus protocols for networks of dynamic agents , 2003, Proceedings of the 2003 American Control Conference, 2003..

[17]  S. Venkatesh,et al.  Distributed Bayesian hypothesis testing in sensor networks , 2004, Proceedings of the 2004 American Control Conference.

[18]  Sonia Martínez,et al.  Coverage control for mobile sensing networks , 2002, IEEE Transactions on Robotics and Automation.

[19]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[20]  Mehran Mesbahi,et al.  Agreement over random networks , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[21]  R. Olfati-Saber,et al.  Consensus Filters for Sensor Networks and Distributed Sensor Fusion , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[22]  Venkatesh Saligrama Murat Alanyali Onur Savas.  Asynchronous Distributed Detection in Sensor Networks ∗ , 2005 .

[23]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[24]  William T. Freeman,et al.  Constructing free-energy approximations and generalized belief propagation algorithms , 2005, IEEE Transactions on Information Theory.

[25]  R. Olfati-Saber,et al.  Distributed Kalman Filter with Embedded Consensus Filters , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[26]  Richard M. Murray,et al.  Approximate distributed Kalman filtering in sensor networks with quantifiable performance , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[27]  R. Olfati-Saber.  Ultrafast consensus in small-world networks , 2005, Proceedings of the 2005, American Control Conference, 2005..

[28]  Benjamin Van Roy,et al.  Consensus Propagation , 2005, IEEE Transactions on Information Theory.

[29]  R. Olfati-Saber,et al.  Distributed Fault Diagnosis using Sensor Networks and Consensus-based Filters , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.