[AtsushiSakai]

Update the animation for PythonRobotics#1448 with three panels showing the estimated accelerometer x/y biases (m/s²) and gyroscope bias (deg/s), alongside their true values. The bias plots include covariance-derived ±3σ bands. The trajectory plot shows each EKF's current 3σ position ellipse, including the x/y cross-covariance, and the position-error plot tracks the bias-estimating EKF's ellipse semi-major axis. Gray shading marks the GPS outage in the error and bias plots.

The title is now GPS/IMU Fusion Localization with Bias Estimation to match the documentation.

Generated with create_animation(simulate(seed=0)) and PillowWriter at 20 fps and 90 dpi. Verified all 201 frames at 1080 × 720 pixels and visually checked the GPS-outage and final frames. This follows the previously merged animation PR #15.

[AtsushiSakai]

GPS/IMU Fusion Localization with Bias Estimation

The upper panels compare GPS/IMU fusion with bias estimation (blue), fusion without bias estimation (red dashed), and IMU-only dead reckoning (orange dotted), using the same sensor measurements.

• Position: each EKF has a current 3σ covariance ellipse centered on its estimate, with semi-axes 3√λᵢ and orientation from the position covariance eigenvectors. Dots mark the current estimates and a black cross marks the true position. The dashed blue error-plot curve is the bias-estimating EKF's ellipse semi-major axis, not a scalar position-error standard deviation.
• Biases: blue estimates and shaded estimate ± 3√Pᵢᵢ bands are shown against black dashed ground truth. True accelerometer x/y biases are 0.04 m/s² and −0.03 m/s²; true gyroscope bias is 0.4 deg/s. The band and estimate use the same units.
• Gray shading marks the 20–30 s GPS outage. Uncertainty grows during the outage and contracts with GPS corrections.

For the default seed 0, ground truth lies inside the bias-estimating EKF's position ellipse and all three bias bands at all 1,001 samples. The no-bias-estimation EKF's true position falls outside its ellipse during parts of the run. These are synthetic demonstration results, not a guarantee of coverage for other data.

The bias 3σ half-widths shrink from 0.300 → 0.0339 m/s² (x), 0.300 → 0.0296 m/s² (y), and 3.000 → 0.458 deg/s (gyro).