New control paradigms are needed for large networks of wireless sensors and actuators in order to efficiently utilise system resources. In this study, the authors consider the problem of discrete-time state estimation over a wireless sensor network. Given a tree that represents the sensor communications with the fusion centre, the authors derive the optimal estimation algorithm at the fusion centre, and provide a closedform expression for the steady-state error covariance matrix. They then

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... nt a tree reconfiguration algorithm that produces a sensor tree that has low overall energy consumption and guarantees a desired level of estimation quality at the fusion centre. The authors further propose a sensor tree construction and scheduling algorithm that leads to a longer network lifetime than the tree reconfiguration algorithm. Examples are provided throughout the paper to demonstrate the algorithms and theory developed. * Some preliminary results [2] of this study were presented by the same authors (excluding the second author) at the 46th IEEE Conference on Decision and Control at New Orleans, 2007.