  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.
