Covariance Ellipse of Actual Error for Fusion Accuracy Verification

Covariance ellipses serve as an intuitive tool for evaluating data distribution characteristics and are particularly important in validating the accuracy of fusion algorithms. By plotting the covariance ellipse of actual errors, the error distribution range and directional features after multi-source data fusion can be clearly visualized.

When implementing this verification in MATLAB, the first step involves calculating the covariance matrix of the error vector. The eigenvalues and eigenvectors of this matrix determine the ellipse's size and tilt angle. The major axis corresponds to the direction of maximum variance, while the minor axis reflects the minimum variance - a smaller ellipse area indicates higher fusion accuracy.

The Covariance Intersection (CI) fusion algorithm ensures robust fusion results through conservative covariance estimation. During verification, it's essential to compare the overlap between the theoretical covariance ellipse and the actual error ellipse: if the actual ellipse is entirely enclosed by the theoretical ellipse, the fusion method meets expected accuracy requirements; if deviations occur, noise modeling or weight allocation logic should be examined.

This verification method applies to fields like sensor fusion and state estimation, effectively revealing over-estimation or under-estimation problems while providing geometric perspective references for algorithm optimization.