  In counter-adversarial systems, to infer the strategy of an intelligent
adversarial agent, the defender agent needs to cognitively sense the
information that the adversary has gathered about the latter. Prior works on
the problem employ linear Gaussian state-space models and solve this inverse
cognition problem by designing inverse stochastic filters. However, in
practice, counter-adversarial systems are generally highly nonlinear. In this
paper, we address this scenario by formulating inverse cognition as a nonlinear
Gaussian state-space model, wherein the adversary employs an unscented Kalman
filter (UKF) to estimate the defender's state with reduced linearization
errors. To estimate the adversary's estimate of the defender, we propose and
develop an inverse UKF (IUKF) system. We then derive theoretical guarantees for
the stochastic stability of IUKF in the mean-squared boundedness sense.
Numerical experiments for multiple practical applications show that the
estimation error of IUKF converges and closely follows the recursive
Cram\'{e}r-Rao lower bound.
