On estimation across analog erasure links with and without acknowledgements

Consider the problem of estimating a linear time-invariant process across communication links that erase data stochastically. We compare the stability and performance for two protocols: when the sensor transmits new data only on obtaining an acknowledgement for previously transmitted data (so-called Transmission Control Protocol (TCP)-like protocols) and when the source transmits new data at every time step (so called User Datagram Protocol (UDP)-like protocols). We show that the effect of acknowledgements and retransmissions on performance is case dependent. 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 error covariance. When either multiple sensors or multiple links are present, we prove that TCP-like protocols may perform better than the UDP-like protocols.