Inverse Cubature and Quadrature Kalman filters

Recent developments in counter-adversarial system research have led to the development of inverse stochastic filters that are employed by a defender to infer the information its adversary 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 nonlinearities and, to this end, develop inverse cubature KF (I-CKF) and inverse quadrature KF (I-QKF). Numerical experiments demonstrate the estimation accuracy of our I-CKF and I-QKF with the recursive Cramér-Rao lower bound as a benchmark. Autonomous cognitive agents continually sense their surroundings and optimally adapt themselves in response to changes in the environment.