Inverse Extended Kalman Filter—Part I: Fundamentals
Himali Singh, Arpan Chattopadhyay, Kumar Vijay Mishra · IEEE Transactions on Signal Processing · 2023
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 ofinverse 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 aninverse 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 spacebased EKF to handle incomplete system model information.