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For a wireless sensor network (WSN) with a large number of low-cost,battery-driven, multiple transmission power leveled sensor nodes of limitedtransmission bandwidth, then conservation of transmission resources (power andbandwidth) is of paramount importance. Towards this end, this paper considersthe problem of power scheduling of Kalman filtering for general linearstochastic systems subject to data packet drops (over a packet-droppingwireless network). The transmission of the acquired measurement from the sensorto the remote estimator is realized by sequentially transmitting every singlecomponent of the measurement to the remote estimator in one time period. Thesensor node decides separately whether to use a high or low transmission powerto communicate every component to the estimator across a packet-droppingwireless network based on the rule that promotes the power scheduling with theleast impact on the estimator mean squared error. Under the customaryassumption that the predicted density is (approximately) Gaussian, leveragingthe statistical distribution of sensor data, the mechanism of power scheduling,the wireless network effect and the received data, the minimum mean squarederror estimator is derived. By investigating the statistical convergenceproperties of the estimation error covariance, we establish, for general linearsystems, both the sufficient condition and the necessary condition guaranteeingthe stability of the estimator.

Power Scheduling of Kalman Filtering in Wireless Sensor Networks with Data Packet Drops