Distributed detection of Gauss–Markov signals using diffusion Kalman filtering

This paper addresses the problem of distributed detection of Gauss–Markov signals in adaptive networks, where nodes make individual decisions by exchanging information with their neighbours and no fusion centre is used. Relying on the connection between the log-likelihood ratio (LLR) and the innovations process, a distributed detection algorithm for Gauss–Markov signals is proposed based on diffusion Kalman filtering. To perform hypothesis testing, a LLR is constructed using the innovations estimated by the diffusion Kalman filter. The detection performance of the new algorithm is analysed by deriving approximate expressions for the probability of false alarm and detection. The mean and mean-square value of the test statistic, and the probability of detection and receiver operating characteristics of the algorithm are demonstrated by way of Monte Carlo simulations, where a good agreement between theoretical and simulation results is observed. Simulations also confirm the improved detection performance of the proposed algorithm over non-cooperative detection and show that the performance of the algorithm converges to that of the centralized scheme.