Shannon Entropy And Tracking Dynamic Systems Over Noisy Channels

This paper is concerned with the estimation of state trajectory of linear discrete time dynamic systems subject to parametric uncertainty over the compound erasure channel that uses feedback channel intermittently. For this combined system and channel, using the data processing inequality and a robust version of the Shannon lower bound, a necessary condition on channel capacity for estimation of state trajectory at the receiver giving almost sure asymptotically zero estimation error is presented. Then, an estimation technique over the compound erasure channel that includes an encoder, decoder and a sufficient condition under which the estimation error at the receiver is asymptotically zero almost surely is presented. This leads to the conclusion that over the compound erasure channel, a condition on Shannon capacity in terms of the rate of expansion of the Shannon entropy is a necessary and sufficient condition for estimation with uniform almost sure asymptotically zero estimation error. The satisfactory performance of the proposed technique is illustrated using simulation.