Fisher Information Approach for Masking the Sensing Plan: Applications in Multifunction Radars (2403.15966v1)

Abstract: How to design a Markov Decision Process (MDP) based radar controller that makes small sacrifices in performance to mask its sensing plan from an adversary? The radar controller purposefully minimizes the Fisher information of its emissions so that an adversary cannot identify the controller's model parameters accurately. Unlike classical open loop statistical inference, where the Fisher information serves as a lower bound for the achievable covariance, this paper employs the Fisher information as a design constraint for a closed loop radar controller to mask its sensing plan. We analytically derive a closed-form expression for the determinant of the Fisher Information Matrix (FIM) pertaining to the parameters of the MDP-based controller. Subsequently, we constrain the MDP with respect to the determinant of the FIM. Numerical results show that the introduction of minor perturbations to the MDP's transition kernel and the total operation cost can reduce the Fisher Information of the emissions. Consequently, this reduction amplifies the variability in policy and transition kernel estimation errors, thwarting the adversary's accuracy in estimating the controller's sensing plan.