# Inverse Unscented Kalman Filter

arXiv: https://arxiv.org/abs/2304.01698 · HTML: https://mlsanity.com/paper/2304.01698/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 85 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 12 of 12)

- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Identifying Cognitive Radars -- Inverse Reinforcement Learning using Revealed Preferences](https://mlsanity.com/paper/1912.00331/) (2019)
- [How to Calibrate your Adversary's Capabilities? Inverse Filtering for Counter-Autonomous Systems](https://mlsanity.com/paper/1905.07230/) (2019)
- [Adversarial Radar Inference: Inverse Tracking, Identifying Cognition and Designing Smart Interference](https://mlsanity.com/paper/2008.01559/) (2020)
- [Inverse Filtering for Hidden Markov Models with Applications to Counter-Adversarial Autonomous Systems](https://mlsanity.com/paper/2001.11809/) (2020)
- [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)
- [Inverse-Inverse Reinforcement Learning. How to Hide Strategy from an Adversarial Inverse Reinforcement Learner](https://mlsanity.com/paper/2205.10802/) (2022)
- [Counter-Adversarial Learning with Inverse Unscented Kalman Filter](https://mlsanity.com/paper/2210.00359/) (2022)
- [Maximum Correntropy Unscented Filter](https://mlsanity.com/paper/1608.07526/) (2016)
- [Inverse Cubature and Quadrature Kalman filters](https://mlsanity.com/paper/2303.10322/) (2023)

## Abstract (arXiv)

Rapid advances in designing cognitive and counter-adversarial systems have motivated the development of inverse Bayesian filters. In this setting, a cognitive 'adversary' tracks its target of interest via a stochastic framework such as a Kalman filter (KF). The target or 'defender' then employs another inverse stochastic filter to infer the forward filter estimates of the defender computed by the adversary. For linear systems, the inverse Kalman filter (I-KF) has been recently shown to be effective in these counter-adversarial applications. In the paper, contrary to prior works, we focus on non-linear system dynamics and formulate the inverse unscented KF (I-UKF) to estimate the defender's state based on the unscented transform, or equivalently, statistical linearization technique. We then generalize this framework to unknown systems by proposing reproducing kernel Hilbert space-based UKF (RKHS-UKF) to learn the system dynamics and estimate the state based on its observations. Our theoretical analyses to guarantee the stochastic stability of I-UKF and RKHS-UKF in the mean-squared sense show that, provided the forward filters are stable, the inverse filters are also stable under mild system-level conditions. We show that, despite being a suboptimal filter, our proposed I-UKF is a conservative estimator, i.e., I-UKF's estimated error covariance upper-bounds its true value. Our numerical experiments for several different applications demonstrate the estimation performance of the proposed filters using recursive Cram'er-Rao lower bound and non-credibility index (NCI).