Distributed Detection Fusion via Monte Carlo Importance Sampling

摘要

Distributed detection fusion with high-dimension conditionally dependentobservations is known to be a challenging problem. When a fusion rule is fixed,this paper attempts to make progress on this problem for the large sensornetworks by proposing a new Monte Carlo framework. Through the Monte Carloimportance sampling, we derive a necessary condition for optimal sensordecision rules in the sense of minimizing the approximated Bayesian costfunction. Then, a Gauss-Seidel/person-by-person optimization algorithm can beobtained to search the optimal sensor decision rules. It is proved that thediscretized algorithm is finitely convergent. The complexity of the newalgorithm is $O(LN)$ compared with $O(LN^L)$ of the previous algorithm where$L$ is the number of sensors and $N$ is a constant. Thus, the proposed methodsallows us to design the large sensor networks with general high-dimensiondependent observations. Furthermore, an interesting result is that, for thefixed AND or OR fusion rules, we can analytically derive the optimal solutionin the sense of minimizing the approximated Bayesian cost function. In general,the solution of the Gauss-Seidel algorithm is only local optimal. However, inthe new framework, we can prove that the solution of Gauss-Seidel algorithm issame as the analytically optimal solution in the case of the AND or OR fusionrule. The typical examples with dependent observations and large number ofsensors are examined under this new framework. The results of numericalexamples demonstrate the effectiveness of the new algorithm.