Distributed function and time delay estimation using nonparametric techniques

In this paper we analyze the problem of estimating a function from different noisy data sets collected by spatially distributed sensors and subject to unknown temporal shifts. We propose a novel approach based on non-parametric Gaussian regression and reproducing kernel Hilbert space theory that exploit compact and accurate representations of function estimates. As a first result, suitable minimization of inner products in reproducing kernel Hilbert spaces is used to obtain a novel time delay estimation technique when attention is restricted only to two signals. Then, we derive both a centralized and a distributed estimator to simultaneously identify the unknown function and delays for a generic number of networked sensors subject to a restricted communication graph. Numerical simulations are used to test the effectiveness of the proposed approaches.