# Inverse Filtering for Hidden Markov Models with Applications to Counter-Adversarial Autonomous Systems

arXiv: https://arxiv.org/abs/2001.11809 · HTML: https://mlsanity.com/paper/2001.11809/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2020.

## Built on by (most cited first, 8 of 8)

- [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)
- [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)
- [Provably Efficient Action-Manipulation Attack Against Continuous Reinforcement Learning](https://mlsanity.com/paper/2411.13116/) (2024)
- [Inverse Unscented Kalman Filter](https://mlsanity.com/paper/2304.01698/) (2023)
- [Inverse Particle Filter](https://mlsanity.com/paper/2407.16623/) (2024)

## Abstract (arXiv)

Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following inverse filtering problem: Given a sequence of posterior distributions from a Bayesian filter, what can be inferred about the transition kernel of the state, the observation likelihoods of the sensor and the measured observations? For finite-state Markov chains observed in noise (hidden Markov models), we show that a least-squares fit for estimating the parameters and observations amounts to a combinatorial optimization problem with non-convex objective. Instead, by exploiting the algebraic structure of the corresponding Bayesian filter, we propose an algorithm based on convex optimization for reconstructing the transition kernel, the observation likelihoods and the observations. We discuss and derive conditions for identifiability. As an application of our results, we illustrate the design of counter-adversarial systems: By observing the actions of an autonomous enemy, we estimate the accuracy of its sensors and the observations it has received. The proposed algorithms are evaluated in numerical examples.