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The present paper is concerned with a sensor network, where each sensor is modeled by either a linear or nonlinear sensing system. These sensors team up in observing either static or dynamic random targets and transmit their observations through noisy communication channels to a fusion center (FC) for locating/tracking the targets. Physically, the network is limited by energy resource. According to the available sum power budget, we develop a novel technique for power allocation to the sensor nodes that enables the FC produce the best linear estimate in terms of the mean square error (MSE). Regardless of whether the sensor measurements are linear or nonlinear, the targets are scalar or vectors, static or dynamic, the corresponding optimization problems are shown to be semidefinite programs (SDPs) of tractable optimization and thus are globally and efficiently solved by any existing SDP solver. In other words, new tractably computational algorithms of distributed Bayes filtering are derived with full multisensor diversity achieved. Intensive simulation shows that these algorithms clearly outperform previously known algorithms.