Reducing the observation error in a WSN through a consensus-based subspace projection

An essential process in a Wireless Sensor Network is the noise mitigation of the measured data, by exploiting their spatial correlation. A widely used technique to achieve this reduction is to project the measured data into a proper subspace. We present a low complexity and distributed algorithm to perform this projection. Unlike other algorithms existing in the literature, which require the number of connections at every node to be larger than the dimension of the involved subspace, our algorithm does not require such dense network topologies for its applicability, making it suitable for a larger number of scenarios. Our proposed algorithm is based on the execution of several consensus processes, and therefore the mixing weights that drive the iterative process can be much more easily computed by using information local to each particular node. These two main advantages makes our approach more suitable for large networks composed by simple and power limited nodes. Simulations results are presented to show that our algorithm performs the projection faster and, in several scenarios, consuming less energy than other existing works in the related literature.