Adaptive fusion of correlated local decisions

In this paper, an adaptive fusion algorithm is proposed for an environment where the observations and local decisions are dependent from one sensor to another. An optimal decision rule, based on the maximum posterior probability (MAP) detection criterion for such an environment, is derived and compared to the adaptive approach. In the algorithm, the log-likelihood ratio function can be expressed as a linear combination of ratios of conditional probabilities and local decisions. The estimations of the conditional probabilities are adapted by reinforcement learning. The error probability at steady state is analyzed theoretically and, in some cases, found to be equal to the error probability obtained by the optimal fusion rule. The effect of the number of sensors and correlation coefficients on error probability in Gaussian noise is also investigated. Simulation results that conform to the theoretical analysis are presented at the end of the paper.