# Inverse Extended Kalman Filter -- Part II: Highly Non-Linear and Uncertain Systems

arXiv: https://arxiv.org/abs/2208.06683 · HTML: https://mlsanity.com/paper/2208.06683/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 59 references that are in the map.
- First posted on arXiv 13 Aug 2022.

## Builds on (most cited first, 10 of 10)

- [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)
- [On Computational Complexity Reduction Methods for Kalman Filter Extensions](https://mlsanity.com/paper/1512.03077/) (2015)
- [Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications](https://mlsanity.com/paper/1709.08210/) (2017)
- [How to Protect Your Privacy? A Framework for Counter-Adversarial Decision Making](https://mlsanity.com/paper/2004.04119/) (2020)
- [Inverse-Inverse Reinforcement Learning. How to Hide Strategy from an Adversarial Inverse Reinforcement Learner](https://mlsanity.com/paper/2205.10802/) (2022)
- [Robust Kalman Filtering Under Model Uncertainty: the Case of Degenerate Densities](https://mlsanity.com/paper/2108.11266/) (2021)

## Built on by (most cited first, 5 of 5)

- [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)
- [Inverse Unscented Kalman Filter](https://mlsanity.com/paper/2304.01698/) (2023)
- [Inverse Particle Filter](https://mlsanity.com/paper/2407.16623/) (2024)
- [Prognosis Of Lithium-Ion Battery Health with Hybrid EKF-CNN+LSTM Model Using Differential Capacity](https://mlsanity.com/paper/2504.13956/) (2025)

## Abstract (arXiv)

Counter-adversarial system design problems have lately motivated the development of inverse Bayesian filters. For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman-filter-tracked estimates and hence, predict the adversary's future steps. The purpose of this paper and the companion paper (Part I) is to address the inverse filtering problem in non-linear systems by proposing an inverse extended Kalman filter (I-EKF). The companion paper proposed the theory of I-EKF (with and without unknown inputs) and I-KF (with unknown inputs). In this paper, we develop this theory for highly non-linear models, which employ second-order, Gaussian sum, and dithered forward EKFs. In particular, we derive theoretical stability guarantees for the inverse second-order EKF using the bounded non-linearity approach. To address the limitation of the standard I-EKFs that the system model and forward filter are perfectly known to the defender, we propose reproducing kernel Hilbert space-based EKF to learn the unknown system dynamics based on its observations, which can be employed as an inverse filter to infer the adversary's estimate. Numerical experiments demonstrate the state estimation performance of the proposed filters using recursive Cram'er-Rao lower bound as a benchmark.