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

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.