  In this paper we study the notion of estimation entropy recently established
by Liberzon and Mitra. This quantity measures the smallest rate of information
about the state of a dynamical system above which an exponential state
estimation with a given exponent is possible. We show that this concept is
closely related to the $\alpha$-entropy introduced by Thieullen and we give a
lower estimate in terms of Lyapunov exponents assuming that the system
preserves an absolutely continuous measure with a bounded density, which
includes in particular Hamiltonian and symplectic systems. Although in its
current form mainly interesting from a theoretical point of view, our result
could be a first step towards a more practical analysis of state estimation
under communication constraints.
