  Entropy notions for $\varepsilon$-incremental practical stability and
incremental stability of deterministic nonlinear systems under disturbances are
introduced. The entropy notions are constructed via a set of points in state
space which induces the desired stability properties, called an approximating
set. We provide conditions on the system which ensures that the approximating
set is finite. Lower and upper bounds for the two estimation entropies are
computed. The construction of the finite approximating sets induces a robust
state estimation algorithm for systems under disturbances using quantized and
time-samples measurements.
