Target Tracking Using the Invariant Extended Kalman Filter with Numerical Differentiation for Estimating Curvature and Torsion

TL;DR

The paper addresses real-time target tracking from position measurements by deriving $v$, $a$, and $j$ from position data using adaptive input/state estimation (AISE) for numerical differentiation. It then embeds these estimates in the Frenet-Serret frame to model motion on the Lie group $SE(3)$ and uses the invariant extended Kalman filter ($IEKF$) to estimate position and velocity. The proposed FS-IEKF-AISE method couples AISE-based differentiation with invariant filtering and is validated through numerical demonstrations that compare against prior techniques. The results indicate robust real-time performance and improved accuracy in dynamic scenarios, highlighting the method's practical utility for real-world target tracking.

Abstract

The goal of target tracking is to estimate target position, velocity, and acceleration in real time using position data. This paper introduces a novel target-tracking technique that uses adaptive input and state estimation (AISE) for real-time numerical differentiation to estimate velocity, acceleration, and jerk from position data. These estimates are used to model the target motion within the Frenet-Serret (FS) frame. By representing the model in SE(3), the position and velocity are estimated using the invariant extended Kalman filter (IEKF). The proposed method, called FS-IEKF-AISE, is illustrated by numerical examples and compared to prior techniques.