How to Calibrate your Enemy's Capabilities? Inverse Filtering for Counter-Autonomous Systems

We consider the following adversarial Bayesian signal processing problem involving “us” and the “enemy”: an enemy observes our state in noise; updates its posterior distribution of the state and then chooses an action based on this posterior. Given knowledge of “our” state and sequence of enemy's actions observed in noise, we consider two problems: (i) How can the enemy's posterior distribution be estimated? Estimating the posterior is an inverse filtering problem involving a random measure - we formulate and solve several versions of this problem in a Bayesian setting. (ii) How can the enemy's observation likelihood be estimated? This tells us how accurate the enemy's sensors are. We compute the maximum likelihood estimator for the enemy's observation likelihood given our measurements of the enemy's actions where the enemy's actions are in response to estimating our state. The above questions are motivated by the design of counter-autonomous systems: given measurements of the actions of a sophisticated autonomous enemy, how can a counter-autonomous system estimate the underlying belief of the enemy, predict future actions and therefore guard against these actions.