A posteriori variance factor in Covariance matrix

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Jun 30, 2023, 8:33:11 PM6/30/23
to Ceres Solver
Hi all,

As we know the Covariance matrix C = (J' S J)^{-1}, where S is a weight matrix.
In many textbooks it is mentioned that there is an a-posteriori variance factor sigma_0 (shortening it to s_0) or unit weight that is calculated by s_0^2 = (v' S v) / r, with v being the residuals and r being the degrees of freedom or redundancy with r = n-u+f,
where n = number of observations, u = number of unknowns, f = number of constraints.
Then covariance matrix is then Q = s_o^2 * C. 

Should not that be applied to the covariance values that are calculated by ceres so that the estimated covariances are scaled correctly?

Thanks in advance,

Sameer Agarwal

Jun 30, 2023, 8:45:00 PM6/30/23
to ceres-...@googlegroups.com
I believe numpy/scipy does something like this. You are welcome to apply such a scaling yourself to the output computed by Ceres.

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