Distributed maximum a posteriori probability estimation for tracking of dynamic systems

We present a framework for the estimation of time-varying random signals with wireless sensor networks. Given a continuous time model, sensors collect noisy observations according to the discrete-time equivalent system defined by the sampling period of observations. Estimation is performed locally using a maximum a posteriori probability estimator (MAP) within a time window. To incorporate information from neighboring sensors we introduce Lagrange multipliers to penalize the disagreement between estimates. We show that the distributed (D-)MAP algorithm is able to track dynamical signals with an error characterized in terms of problem constants. This error vanishes with the sampling period if the log-likelihood function satisfies a smoothness condition.