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A Stochastic Nonlinear Dynamical System for Smoothing Noisy Eye Gaze Data

Thoa Thieu, Roderick Melnik

TL;DR

The paper tackles smoothing of noisy eye gaze data, where pixel-location accuracy is degraded by tracker limitations, calibration drift, lighting changes, and blinks. It introduces a stochastic nonlinear dynamical model and applies an Extended Kalman Filter to propagate and correct gaze state estimates using $x_t$, $z_t$, $f$, $h$, $Q$, and $R$. Through synthetic and real gaze-data experiments, the EKF achieves lower RMSE than a simple moving average, demonstrating improved position and velocity estimates and robustness to data gaps. The approach offers practical benefits for gaze-tracking applications and related time-series smoothing tasks, with potential extensions to multimodal tracking and deeper learning integrations.

Abstract

In this study, we address the challenges associated with accurately determining gaze location on a screen, which is often compromised by noise from factors such as eye tracker limitations, calibration drift, ambient lighting changes, and eye blinks. We propose the use of an extended Kalman filter (EKF) to smooth the gaze data collected during eye-tracking experiments, and systematically explore the interaction of different system parameters. Our results demonstrate that the EKF significantly reduces noise, leading to a marked improvement in tracking accuracy. Furthermore, we show that our proposed stochastic nonlinear dynamical model aligns well with real experimental data and holds promise for applications in related fields.

A Stochastic Nonlinear Dynamical System for Smoothing Noisy Eye Gaze Data

TL;DR

The paper tackles smoothing of noisy eye gaze data, where pixel-location accuracy is degraded by tracker limitations, calibration drift, lighting changes, and blinks. It introduces a stochastic nonlinear dynamical model and applies an Extended Kalman Filter to propagate and correct gaze state estimates using , , , , , and . Through synthetic and real gaze-data experiments, the EKF achieves lower RMSE than a simple moving average, demonstrating improved position and velocity estimates and robustness to data gaps. The approach offers practical benefits for gaze-tracking applications and related time-series smoothing tasks, with potential extensions to multimodal tracking and deeper learning integrations.

Abstract

In this study, we address the challenges associated with accurately determining gaze location on a screen, which is often compromised by noise from factors such as eye tracker limitations, calibration drift, ambient lighting changes, and eye blinks. We propose the use of an extended Kalman filter (EKF) to smooth the gaze data collected during eye-tracking experiments, and systematically explore the interaction of different system parameters. Our results demonstrate that the EKF significantly reduces noise, leading to a marked improvement in tracking accuracy. Furthermore, we show that our proposed stochastic nonlinear dynamical model aligns well with real experimental data and holds promise for applications in related fields.

Paper Structure

This paper contains 14 sections, 15 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Model description
  3. Stochastic State Transition Model
  4. Stochastic Measurement Model
  5. Combining the Stochastic Dynamics in EKF
  6. Prediction (Propagation of State Uncertainty).
  7. Update (Correcting State Estimate Based on Measurements).
  8. The Role of Stochastic Dynamics in the Eye-Tracking Context.
  9. SMA Filtering
  10. Root Mean Square Error (RMSE)
  11. Numerical results
  12. Example 1
  13. Example 2
  14. Conclusions and discussion

Figures (2)

  • Figure 1: Comparison of EKF and SMA filters in estimating position and velocity: theoretical versus filtered estimates.
  • Figure 2: Comparison of EKF and SMA filters in estimating position and velocity: real-eye gaze tracking data and filtered estimates. Here, we use the data from Judd2009.