On the use of a relay for Kalman filtering over packet dropping links

This paper considers the use of a relay to improve the performance of Kalman filtering over i.i.d. packet dropping links. We consider a situation with two sensors and one relay, where the relay can either i) forward the measurement of the first sensor to the gateway/fusion center, ii) forward the measurement of the second sensor to the gateway, or iii) perform a simple network coding operation. Using an upper bound to the expected error covariance matrix as a performance measure, we characterize situations where either one of the three schemes for the relay will give the best performance. Numerical simulations of the expected error covariance matrix confirm this qualitative behaviour.