Estimation of 3D facial dynamics with nonlinear filters for position tracking*

This study presents a comparative evaluation of three nonlinear state estimation filters, the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF), for the task of 3D facial landmark tracking. Using a publicly available dataset, we assess each filter's performance under both deterministic (noise-free) and stochastic (noisy) conditions. Metrics such as mean squared error (MSE), convergence rates of state and covariance estimates, and consistency over time are used to quantify tracking performance. Results show that the EKF consistently outperforms the UKF and PF, achieving faster convergence and lower estimation error, particularly in scenarios characterized by mild nonlinearity. Heatmap analyses under varying noise conditions further highlight the EKF's robustness and accuracy, especially in low-noise regimes, while PF performance deteriorates with increased process noise. Our findings suggest that while UKF and PF offer advantages in highly nonlinear or non-Gaussian environments, the EKF provides the best trade-off between computational efficiency and estimation accuracy for the facial tracking task studied in mild nonlinearity.