# Inverse Cubature and Quadrature Kalman filters

arXiv: https://arxiv.org/abs/2303.10322 · HTML: https://mlsanity.com/paper/2303.10322/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 58 references that are in the map.
- First posted on arXiv 18 Mar 2023.

## Builds on (most cited first, 8 of 8)

- [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)
- [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)
- [Outlier-robust Kalman filters with mixture correntropy](https://mlsanity.com/paper/1907.00307/) (2019)

## Built on by (most cited first, 2 of 2)

- [Inverse Unscented Kalman Filter](https://mlsanity.com/paper/2304.01698/) (2023)
- [Inverse Particle Filter](https://mlsanity.com/paper/2407.16623/) (2024)

## Abstract (arXiv)

Recent research in inverse cognition with cognitive radar has led to the development of inverse stochastic filters that are employed by the target to infer the information the cognitive radar may have learned. Prior works addressed this inverse cognition problem by proposing inverse Kalman filter (I-KF) and inverse extended KF (I-EKF), respectively, for linear and non-linear Gaussian state-space models. However, in practice, many counter-adversarial settings involve highly non-linear system models, wherein EKF's linearization often fails. In this paper, we consider the efficient numerical integration techniques to address such non-linearities and, to this end, develop inverse cubature KF (I-CKF), inverse quadrature KF (I-QKF), and inverse cubature-quadrature KF (I-CQKF). For the unknown system model case, we develop reproducing kernel Hilbert space (RKHS)-based CKF. We derive the stochastic stability conditions for the proposed filters in the exponential-mean-squared-boundedness sense and prove the filters' consistency. Numerical experiments demonstrate the estimation accuracy of our I-CKF, I-QKF, and I-CQKF with the recursive Cram'er-Rao lower bound as a benchmark.