Distributed detection and localization of events in large ad hoc wireless sensor networks

Abstract

We consider the problem of event detection in wireless sensor networks (WSNs) that are large in the sense that an event affects the statistics of the observations of a small number of sensors in the vicinity of where it occurs. An event occurs at a random time at a random location in the region (called the region of interest, ROI) covered by the WSN. We consider a distance based sensing model in which the physical signal sensed by a sensor at a distance d from the event is attenuated by a factor ρ(d). We formulate the problem of detecting an event as early as possible and locating it to a subregion of the ROI under the constraints that the average time to false alarm (TFA) and the average time to false isolation (TFI) are bounded by γ. This formulation is motivated by the change detection/isolation framework introduced by Nikiforov [6]. We extend the decentralized detection procedures MAX [11] and ALL [9], [5], which are designed for colocated networks, to the case of a large WSN where the event localization is also a critical issue. The extended MAX and ALL detect the change and identify a subregion where the event is located. Sensor noise can make the local decisions of ALL toggle rapidly. Motivated by this fact, we propose a distributed change detection/isolation procedure, HALL (Hysteresis modified ALL). We study the supremum average detection delay (SADD) performance of the change detection/isolation procedures MAX, ALL and HALL for a required min{TFA,TFI} ≳ γ. We show that as γ → ∞, the (asymptotic) SADD(ALL) ≤ ln γ ÷ ω0M I, SADD(HALL) ≤ ln (γ + 1) ÷ ω0(1 − 1/β)M I + C, and SADD(MAX) ≤ ln γ ÷ ω0I, where ω0, C, β and M are constants that depend on the sensor deployment, the postchange and the prechange distributions of sensor measurements, and I is the Kullback-Leibler divergence between a worst-case postchange distribution and the prechange distribution of sensor measurements. We also compare the SADD of the distributed procedures with that of the asymptotically optimal centralized procedure given by Nikiforov [6] for a Boolean sensing model. We show that the SADD performance of ALL and HALL is of the same order as that of Nikiforov's. We also provide numerical comparison of SADD and TFA for the centralized asymptotically optimal scheme [6], and the distributed schemes MAX, ALL and HALL.