  It is a common phenomenon in nature and technology that a system under
perturbations exits a regime of its usual dynamics. Often it is possible to
define a potential function whereby a potential well can be associated with a
usual or persistent dynamics, and a potential barrier needs to be overcome to
escape the regime associated with the usual dynamics. We develop an algorithm
to determine the potential barrier height experimentally, provided that we have
control over the noise strength. We are concerned with the situation when the
experiment requires large resources of time or computational power, and wish to
find a protocol that provides the best estimate in a given amount of time. The
optimal noise strength to use is found to be very simply related to the
potential barrier height, and we propose an iterative method for the
estimation.
