# Inverse Extended Kalman Filter -- Part I: Fundamentals

arXiv: https://arxiv.org/abs/2201.01539 · HTML: https://mlsanity.com/paper/2201.01539/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 80 references that are in the map.
- First posted on arXiv 5 Jan 2022.

## Builds on (most cited first, 6 of 6)

- [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)
- [How to Protect Your Privacy? A Framework for Counter-Adversarial Decision Making](https://mlsanity.com/paper/2004.04119/) (2020)

## Built on by (most cited first, 6 of 6)

- [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)
- [Inverse Unscented Kalman Filter](https://mlsanity.com/paper/2304.01698/) (2023)
- [Inverse Particle Filter](https://mlsanity.com/paper/2407.16623/) (2024)
- [Nonlinear Dynamical Systems for Automatic Face Annotation in Head Tracking and Pose Estimation](https://mlsanity.com/paper/2502.15179/) (2025)

## Abstract (arXiv)

Recent advances in counter-adversarial systems have garnered significant research attention to inverse filtering from a Bayesian perspective. For example, interest in estimating the adversary's Kalman filter tracked estimate with the purpose of predicting the adversary's future steps has led to recent formulations of inverse Kalman filter (I-KF). In this context of inverse filtering, we address the key challenges of non-linear process dynamics and unknown input to the forward filter by proposing an inverse extended Kalman filter (I-EKF). The purpose of this paper and the companion paper (Part II) is to develop the theory of I-EKF in detail. In this paper, we assume perfect system model information and derive I-EKF with and without an unknown input when both forward and inverse state-space models are non-linear. In the process, I-KF-with-unknown-input is also obtained. We then provide theoretical stability guarantees using both bounded non-linearity and unknown matrix approaches and prove the I-EKF's consistency. Numerical experiments validate our methods for various proposed inverse filters using the recursive Cram'er-Rao lower bound as a benchmark. In the companion paper (Part II), we further generalize these formulations to highly non-linear models and propose reproducing kernel Hilbert space-based EKF to handle incomplete system model information.