On Kalman Filtering with Fading Wireless Channels Governed by Power Control

Abstract

We study stochastic stability for Kalman filtering over fading wireless channels where variable channel gains are counteracted by the use of power control to alleviate the effects of packet drops. The Kalman filter and the controller are located at a single gateway which acquires data from the wireless sensors. We establish sufficient conditions which ensure that the Kalman filter covariance matrix is exponentially bounded in norm. The conditions obtained are then used to formulate stabilizing optimal power allocation laws which minimize the total sensor power budget. In deriving the optimal power allocation laws, both statistical channel information and full channel information are considered. The effect of system instability on the power budget is also investigated for both these cases.

Stability of State Estimation over Sensor Networks with Markovian Fading Channels*

“…The latter is determined by the individual conditional transmission success probabilities φ E (j), and can therefore be influenced by designing the power control policies, see (11). The situation generalizes that investigated for the simpler case of having independent channel gains in our recent work Quevedo et al (2011).…”

“…In view of (6), power control can be used to counteract fading effects; see Pantazis and Vergados (2007); Quevedo et al (2010Quevedo et al ( , 2011. In the present work, we consider power control laws to be of the form:…”