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A distributed parameter estimation algorithm is presented for a general nonlinear measurement model with additive Gaussian noise. We show that the Bayes-closed estimation algorithm developed by Kulhavy, when extended to the multisensor case leads to a linear fusion rule, regardless of the form of the local a posteriori densities. Specifically, the Kulhavy algorithm generates a set of reduced sufficient statistics (RSS) representing the local sensor densities, which are simply added and subtracted at the global processor to obtain optimum fusion. We discuss various approximations to the Bayes-closed algorithm which lead to a practical parameter estimator for the nonlinear measurement model, and apply such an approximate technique to the bearings-only tracking problem. The performance of the distributed tracker is compared with an alternative algorithm based on the extended Kalman filter (EKF) implemented in modified polar coordinates (MPC). It is shown that the Bayes-closed estimator does not diverge in the sense of an ordinary EKF, and hence the Bayes-closed technique can be employed in both a unidirectional and bidirectional transmission mode.