  For a general class of translationally invariant systems with a specific
category of nonlinearity in the output, this paper presents necessary and
sufficient conditions for global observability. Critically, this class of
systems cannot be stabilized to an isolated equilibrium point by dynamic output
feedback. These analyses may help explain the active sensing movements made by
animals when they perform certain motor behaviors, despite the fact that these
active sensing movements appear to run counter to the primary motor goals. The
findings presented here establish that active sensing underlies the maintenance
of observability for such biological systems, which are inherently nonlinear
due to the presence of the high-pass sensor dynamics.
