  Counter-adversarial system design problems have lately motivated the
development of inverse Bayesian filters. For example, inverse Kalman filter
(I-KF) has been recently formulated to estimate the adversary's
Kalman-filter-tracked estimates and hence, predict the adversary's future
steps. The purpose of this paper and the companion paper (Part I) is to address
the inverse filtering problem in non-linear systems by proposing an inverse
extended Kalman filter (I-EKF). The companion paper proposed the theory of
I-EKF (with and without unknown inputs) and I-KF (with unknown inputs). In this
paper, we develop this theory for highly non-linear models, which employ
second-order, Gaussian sum, and dithered forward EKFs. In particular, we derive
theoretical stability guarantees for the inverse second-order EKF using the
bounded non-linearity approach. To address the limitation of the standard
I-EKFs that the system model and forward filter are perfectly known to the
defender, we propose reproducing kernel Hilbert space-based EKF to learn the
unknown system dynamics based on its observations, which can be employed as an
inverse filter to infer the adversary's estimate. Numerical experiments
demonstrate the state estimation performance of the proposed filters using
recursive Cram\'{e}r-Rao lower bound as a benchmark.
