Fisher Information Approach for Masking the Sensing Plan: Applications in Multifunction Radars

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 article 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 formulate an MDP, which is regularized by the determinant of the adversary's FIM. This results in the perturbations to the total cost of operation, state–action costs, and the transition matrix. In addition, we propose a maximum-entropy-based convex lower bound for the FIM-constrained MDP, whose solution can serve as an initialization point for the proposed nonlinear optimization problem. This convex lower bound aligns with existing work that employs the same maximum entropy criteria to mask the sensing plan. Numerical results show that the introduction of minor perturbations to the MDP's state–action costs, 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. We demonstrate this by comparing the error in the estimate of the transition kernel under different criteria: the FIM criteria, the maximum entropy criteria, a sensing plan where actions are chosen uniformly, and the unmasked sensing plan.