In this work, a multi-sensor transmit power control design problem for remote state estimation over a packet-dropping network is investigated. In this problem, a remote estimator collects measurement innovations from each individual sensor node for data fusion, where the dropouts of data packets may occur over the communication network. Subject to an energy constraint, we propose a transmit power controller for each sensor based on a quadratic form of the measurements' incremental innovation. Under this specific form of transmit power controller which is proved to preserve the Gaussianity of the a posteriori state estimation, we derive the minimum mean squared error (MMSE) estimate for the remote state estimator with a closed-form recursion of the expected estimation error covariance. Performance analysis is also provided. For scalar systems, an upper bound of the expected estimation error variance is optimized subject to a limited energy budget over the parameters of the proposed power controller. Numerical comparisons with other controllers are made to illustrate the performance of our approach. (C) 2018 Elsevier Ltd. All rights reserved.