  Recent research in inverse cognition with cognitive radar has led to the
development of inverse stochastic filters that are employed by the target to
infer the information the cognitive radar may have learned. Prior works
addressed this inverse cognition problem by proposing inverse Kalman filter
(I-KF) and inverse extended KF (I-EKF), respectively, for linear and non-linear
Gaussian state-space models. However, in practice, many counter-adversarial
settings involve highly non-linear system models, wherein EKF's linearization
often fails. In this paper, we consider the efficient numerical integration
techniques to address such non-linearities and, to this end, develop inverse
cubature KF (I-CKF), inverse quadrature KF (I-QKF), and inverse
cubature-quadrature KF (I-CQKF). For the unknown system model case, we develop
reproducing kernel Hilbert space (RKHS)-based CKF. We derive the stochastic
stability conditions for the proposed filters in the
exponential-mean-squared-boundedness sense and prove the filters' consistency.
Numerical experiments demonstrate the estimation accuracy of our I-CKF, I-QKF,
and I-CQKF with the recursive Cram\'{e}r-Rao lower bound as a benchmark.
