If the off-diagonal elements of a covariance matrix are positive than the covariance ellipse is rotated 45 degrees, and vice versa if negative.[^1]
The equation of an ellipse that is represented by a covariance matrix is[^1]
$$
\begin{bmatrix}
x(t) \ y(t)\end{bmatrix}\begin{bmatrix}
v_{1x} & v_{2x} \
v_{1y} & v_{2y}
\end{bmatrix}
\begin{bmatrix}
\sqrt{\lambda_1}\cos(t) \
\sqrt{\lambda_2}\sin(t)
\end{bmatrix}$$
With \(v_{nx}\) and \(v_{ny}\) begin the eigenvectors of the covariance matrix, and \(\sqrt{\lambda_n}\) being the eigenvalues.[^1]
If there are any zeros in the off-diagonal elements then there is no correlation.[^1
[[Ellipse]]
[[Error Ellipses]] – 95% of points fall in the ellipse.
[[Covariance]]
[[N4SID]] – uses covariance matrices to identify system parameters
[[Covariance Update for Inertial Navigation]]
- HowDrawEllipse