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How to Calibrate Your Adversary's Capabilities Inverse Filtering for Counter-Autonomous Systems (Preprint)

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We consider an adversarial Bayesian signal processing problem involving us and an adversary. The adversary 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 adversarys actions observed in noise, we consider three problems i How can the adversarys 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 adversarys observation likelihood be estimated This tells us how accurate the adversarys sensors are. We compute the maximum likelihood estimator for the adversarys observation likelihood given our measurements of the adversarys actions where the adversarys actions are in response to estimating our state. iii How can the state be chosen by us to minimize the covariance of the estimate of the adversarys observation likelihood Our state can be viewed as a probe signal which causes the adversary to act so choosing the optimal state sequence is an input design problem. The above questions are motivated by the design of counter-autonomous systems given measurements of the actions of a sophisticated autonomous adversary, how can our counter-autonomous system estimate the underlying belief of the adversary, predict future actions and therefore guard against these actions.

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  • Statistics and Probability

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