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 combination of system and channel, using the data processing inequality and a robust version of the Shannon lower bound, a necessary condition for channel capacity in 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 for Shannon capacity in terms of its rate of expansion is necessary and sufficient in estimation with uniform almost sure asymptotically zero estimation error. The satisfactory performance of the proposed technique is illustrated using simulation.