  The state estimation of continuous-time nonlinear systems in which a subset
of sensor outputs can be maliciously controlled through injecting a potentially
unbounded additive signal is considered in this paper. Analogous to our earlier
work for continuous-time linear systems in \cite{chong2015observability}, we
term the convergence of the estimates to the true states in the presence of
sensor attacks as `observability under $M$ attacks', where $M$ refers to the
number of sensors which the attacker has access to. Unlike the linear case, we
only provide a sufficient condition such that a nonlinear system is observable
under $M$ attacks. The condition requires the existence of asymptotic observers
which are robust with respect to the attack signals in an input-to-state stable
sense. We show that an algorithm to choose a compatible state estimate from the
state estimates generated by the bank of observers achieves asymptotic state
reconstruction. We also provide a constructive method for a class of nonlinear
systems to design state observers which have the desirable robustness property.
The relevance of this study is illustrated on monitoring the safe operation of
a power distribution network.
