Distributed Detection/Isolation Procedures for Quickest Event Detection in Large Extent Wireless Sensor Networks

We study a problem of distributed detection of a stationary point event in a large extent wireless sensor network ($\wsn$), where the event influences the observations of the sensors only in the vicinity of where it occurs. An event occurs at an unknown time and at a random location in the coverage region (or region of interest ($\ROI$)) of the $\wsn$. We consider a general sensing model in which the effect of the event at a sensor node depends on the distance between the event and the sensor node; in particular, in the Boolean sensing model, all sensors in a disk of a given radius around the event are equally affected. Following the prior work reported in \cite{nikiforov95change_isolation}, \cite{nikiforov03lower-bound-for-det-isolation}, \cite{tartakovsky08multi-decision}, {\em the problem is formulated as that of detecting the event and locating it to a subregion of the $\ROI$ as early as possible under the constraints that the average run length to false alarm ($\tfa$) is bounded below by $\gamma$, and the probability of false isolation ($\pfi$) is bounded above by $\alpha$}, where $\gamma$ and $\alpha$ are target performance requirements. In this setting, we propose distributed procedures for event detection and isolation (namely $\mx$, $\all$, and $\hall$), based on the local fusion of $\CUSUM$s at the sensors. For these procedures, we obtain bounds on the maximum mean detection/isolation delay ($\add$), and on $\tfa$ and $\pfi$, and thus provide an upper bound on $\add$ as $\min\{\gamma,1/\alpha\} \to \infty$. For the Boolean sensing model, we show that an asymptotic upper bound on the maximum mean detection/isolation delay of our distributed procedure scales with $\gamma$ and $\alpha$ in the same way as the asymptotically optimal centralised procedure \cite{nikiforov03lower-bound-for-det-isolation}.
Comment: Submitted to IEEE Transactions on Signal Processing, Mar. 10, 2011. Revised on Jul. 17, 2011. A part of this work was presented in Forty-Seventh Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, USA, Sep. - Oct. 2009