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

arXiv: https://arxiv.org/abs/1905.07230 · HTML: https://mlsanity.com/paper/1905.07230/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2019.

## Built on by (most cited first, 11 of 11)

- [Identifying Cognitive Radars -- Inverse Reinforcement Learning using Revealed Preferences](https://mlsanity.com/paper/1912.00331/) (2019)
- [Smoother Entropy for Active State Trajectory Estimation and Obfuscation in POMDPs](https://mlsanity.com/paper/2108.10227/) (2021)
- [Inverse Extended Kalman Filter -- Part I: Fundamentals](https://mlsanity.com/paper/2201.01539/) (2022)
- [Meta-Cognition. An Inverse-Inverse Reinforcement Learning Approach for Cognitive Radars](https://mlsanity.com/paper/2205.01794/) (2022)
- [Inverse Extended Kalman Filter -- Part II: Highly Non-Linear and Uncertain Systems](https://mlsanity.com/paper/2208.06683/) (2022)
- [Counter-Adversarial Learning with Inverse Unscented Kalman Filter](https://mlsanity.com/paper/2210.00359/) (2022)
- [Inverse Cubature and Quadrature Kalman filters](https://mlsanity.com/paper/2303.10322/) (2023)
- [Slow Convergence of Interacting Kalman Filters in Word-of-Mouth Social Learning](https://mlsanity.com/paper/2410.08447/) (2024)
- [Inverse Unscented Kalman Filter](https://mlsanity.com/paper/2304.01698/) (2023)
- [Inverse Particle Filter](https://mlsanity.com/paper/2407.16623/) (2024)
- [Masking Radar Cognition under Adversarial Surveillance: A Distributional Privacy Framework](https://mlsanity.com/paper/2609.07428/) (2026)

## Abstract (arXiv)

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 adversary's actions observed in noise, we consider three problems: (i) How can the adversary'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 adversary's observation likelihood be estimated? This tells us how accurate the adversary's sensors are. We compute the maximum likelihood estimator for the adversary's observation likelihood given our measurements of the adversary's actions where the adversary's 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 adversary's 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.