On Estimation Across Analog Erasure Links With and Without Acknowledgements

We study the effect of feedback from the receiver through the transmission layer protocol on the problem of estimating a linear time-invariant process across communication links that erase data stochastically. We compare the stability and performance for two cases: i) when the transmission layer protocol provides acknowledgements for any data successfully transmitted and the sensor transmits new data only on obtaining such an acknowledgement for previously transmitted data (so-called transmission control protocol (TCP)-like protocols), and ii) when there is no feedback from the estimator and the source transmits new data at every time step (so-called user datagram protocol (UDP)-like protocols). Due to the latency introduced by acknowledgements and retransmissions, it is often assumed that such feedback will necessarily degrade control/estimation performance. We show that this statement does not hold in general. When a single sensor transmits data across a single link, we prove that TCP-like protocols always perform worse than UDP-like protocols in the sense of minimizing the error covariance. When either multiple sensors or multiple links are present, we prove that feedback may lead to better performance.