Saturated Power Control Scheme for Kalman Filtering via Wireless Sensor Networks

We investigate the Kalman filtering problem via wireless sensor networks over fading channels. When part or all of the observation measurements are lost in a random fashion, we obtain the conclusion that the packet dropout probabilities depend upon the time-varying channel gains and the transmission power levels used by the sensors. We develop a satu- rated power controller which trades off sensor energy expenditure versus state estimation accuracy. The latter is measured by the expected value of the future covariance matrices provided by the associated time-varying Kalman filter. We study the statistical convergence properties of the error covariance matrix and pointed out the existence of the admissible packet arrival probability bound.