This paper deals with the problem of tracking a moving target by means of a network of geographically dispersed nodes with Doppler sensing, communication and processing capabilities, free of any centralized coordination. The contribution is twofold. First, a suitable nonlinear observability decomposition is introduced in order to single out state coordinates that can be fully observed from a single Doppler sensor. Then, based on such a decomposition, a novel consensus filter for distributed Doppler-only tracking is developed and its performance is evaluated via computer simulations.