For a wireless sensor network (WSN) with a large number of low-cost, battery-driven, multiple transmission power leveled sensor nodes of limited transmission bandwidth, then conservation of transmission resources (power and bandwidth) is of paramount importance. Towards this end, this paper considers the problem of power scheduling of Kalman filtering for general linear stochastic systems subject to data packet drops (over a packet-dropping wireless network). The transmission of the acquired measurement from the sensor to the remote estimator is realized by sequentially transmitting every single component of the measurement to the remote estimator in one time period. The sensor node decides separately whether to use a high or low transmission power to communicate every component to the estimator across a packet-dropping wireless network based on the rule that promotes the power scheduling with the least impact on the estimator mean squared error. Under the customary assumption that the predicted density is (approximately) Gaussian, leveraging the statistical distribution of sensor data, the mechanism of power scheduling, the wireless network effect and the received data, the minimum mean squared error estimator is derived. By investigating the statistical convergence properties of the estimation error covariance, we establish, for general linear systems, both the sufficient condition and the necessary condition guaranteeing the stability of the estimator.