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In this paper, we develop an energy-efficient distributed estimation method that can be used in applications such as the estimation of a diffusive source and the localization and tracking of an acoustic target in wireless sensor networks. We first propose a statistical measurement model in which we separate the linear and nonlinear parameters. This modeling strategy reduce the processing complexity. We then study the distributed implementation of the Gauss-Newton method in the maximum likelihood estimation. After that we propose a fully distributed estimation approach based on an incremental realization of the Gauss-Newton method. We derive three modifications of the basic algorithm to improve the distributed processing performance while still considering the energy restriction. We implement the idea of information-driven collaborative signal processing and provide a sensor-node scheduling scheme in which the Cramer-Rao bound (CRB) is used as the performance and information utility measure to select the next sensor node. Numerical examples are used to study the performance of the distributed estimation, and we show that of the methods considered here, the proposed multiple iteration Kalman filtering method has the most advantages for wireless sensor networks.