Maximum Correntropy Recursive Filtering for Inverse Cognition with Non-Gaussian Noise

The objective of inverse cognition is to estimate the state of the defender as inferred by the adversarial system, based on the behavior of the attacker under noisy conditions. In linear systems, the inverse extended Kalman filter (IKF) is typically employed for estimation; however, its performance significantly deteriorates in non-Gaussian noise environments. To address this issue, we propose an inverse maximum entropy recursive filter. First, we utilize the forward maximum entropy Kalman filter (MCKF) to accurately estimate the state of the defender. Subsequently, using both MCKF's state estimate and that of the actual defender, we generate a prior estimate and formulate a state equation for our inverse filtering process. Finally, leveraging a cost function derived from the maximum correlation coefficient criterion (MCC), we implement a fixed-point algorithm to achieve optimal estimates and updated posterior estimates. Simulation results demonstrate that the performance of our proposed inverse maximum entropy Kalman filter algorithm surpasses that of existing algorithms in non-Gaussian noise environments.