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We consider a network of sensors deployed to sense a spatio-temporal field and infer parameters of interest about the field. We are interested in the case where each sensor's observation sequence is modeled as a state-space process that is perturbed by random noise, and the models across sensors are parametrized by the same parameter vector. The sensors collaborate to estimate this parameter from their measurements, and to this end we propose a distributed and recursive estimation algorithm, which we refer to as the incremental recursive prediction error algorithm. This algorithm has the distributed property of incremental gradient algorithms and the on-line property of recursive prediction error algorithms.