Distributed subspace projection over Wireless Sensor Networks with unreliable links

The inaccuracy of the measurements collected by sensor nodes in a Wireless Sensor Network motivates the use of appropriate techniques for reducing this observation error. One of the most widely used method consists of projecting orthogonally the observation signal onto a subspace of interest. The in-network processing nature of these architectures suggests that such a method should be performed in a distributed manner, through successive local communications between neighbors and under a time-varying network topology. Existing approaches to this technique assume an ideal scenario, where these communications are not subject to interferences, packet losses or fading. In this work, we propose a new technique, which under unreliable communications, projects the initial observation onto a proper subspace in a totally distributed fashion. We analyze the deviation from the optimal projection due to packet losses, and compare it with the initial observation error. We also consider the additional error due to an inaccurate choice of the subspace. Simulation results are presented to show the efficiency and validity of our approach.