State Estimation over Sensor Networks with Correlated Wireless Fading Channels

TL;DR

This paper analyzes the stochastic stability of centralized Kalman filtering over wireless sensor networks with correlated fading channels, considering network states and power control policies, providing new stability conditions.

Contribution

It introduces a network state process modeling correlated fading channels and derives sufficient stability conditions for Kalman filtering in this context.

Findings

Stability conditions ensure exponential boundedness of the filter.

Results include previous special cases for single-sensor scenarios.

Power and bit-rate control policies are incorporated into the stability analysis.

Abstract

Stochastic stability for centralized time-varying Kalman filtering over a wireles ssensor network with correlated fading channels is studied. On their route to the gateway, sensor packets, possibly aggregated with measurements from several nodes, may be dropped because of fading links. To study this situation, we introduce a network state process, which describes a finite set of configurations of the radio environment. The network state characterizes the channel gain distributions of the links, which are allowed to be correlated between each other. Temporal correlations of channel gains are modeled by allowing the network state process to form a (semi-)Markov chain. We establish sufficient conditions that ensure the Kalman filter to be exponentially bounded. In the one-sensor case, this new stability condition is shown to include previous results obtained in the literature as special cases. The results also hold when using power and bit-rate control policies, where the transmission power and bit-rate of each node are nonlinear mapping of the network state and channel gains.