# What Did Your Adversary Believe? Optimal Filtering and Smoothing in Counter-Adversarial Autonomous Systems

arXiv: https://arxiv.org/abs/1910.07332 · HTML: https://mlsanity.com/paper/1910.07332/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2019.

## Built on by (most cited first, 1 of 1)

- [Counter-Adversarial Learning with Inverse Unscented Kalman Filter](https://mlsanity.com/paper/2210.00359/) (2022)

## Abstract (arXiv)

We consider fixed-interval smoothing problems for counter-adversarial autonomous systems. An adversary deploys an autonomous filtering and control system that i) measures our current state via a noisy sensor, ii) computes a posterior estimate (belief) and iii) takes an action that we can observe. Based on such observed actions and our knowledge of our state sequence, we aim to estimate the adversary's past and current beliefs -- this forms a foundation for predicting, and counteracting against, future actions. We derive the optimal smoother for the adversary's beliefs (we treat the problem in a Bayesian framework). Moreover, we demonstrate how the smoother can be computed for discrete systems even though the corresponding backward variables do not admit a finite-dimensional characterization. Finally, we illustrate our results in numerical simulations.