Power scheduling for Kalman filtering over lossy wireless sensor networks

With the goal of monitoring physical processes, a wireless sensor network (WSN) is often deployed along with a fusion center to estimate the state of general linear stochastic systems. As WSNs comprise a large number of low-cost, battery-driven sensor nodes with limited transmission bandwidth, conservation of transmission resources (power and bandwidth) is of paramount importance. In this context, the present study considers power scheduling for Kalman filtering (KF) using scalar messages exchanged over wireless sensor links, where random measurement packet drops are possible. Each sensor node sequentially decides whether a high or low transmission power is needed to communicate its scalar observations based on a rule that promotes power scheduling with minimal impact on the state estimator's mean-squared error. Assuming approximately Gaussian state predictors, the minimum mean-squared error optimal power schedule is developed for KF that also accounts for dropped data packets. Leveraging statistical convergence characteristics of the estimation error covariance matrix, both sufficient and necessary conditions are established that guarantee the stability of the resultant KF estimator.