This paper develops a framework for the estimation of a time-varying random signal using a distributed sensor network. Given a continuous time model sensors collect noisy observations and produce local estimates according to the discrete time equivalent system defined by the sampling period of observations. Estimation is performed using a maximum a posteriori probability estimator (MAP) within a given window of interest. To mediate the incorporation of information from other sensors we introduce Lagrange multipliers to penalize the disagreement between neighboring estimates. We show that the resulting distributed (D)-MAP algorithm is able to track dynamical signals with a small error. This error is characterized in terms of problem constants and vanishes with the sampling time as long as the log-likelihood function which is assumed to be log-concave satisfies a smoothness condition. We implement the D-MAP algorithm for a linear and a nonlinear system model to show that the performance corroborates with theoretical findings.
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