When using ceres::Covariance to obtain the covariance for given parameter blocks, is it possible to obtain the covariances in the local parameter space? In most cases the LocalParameterization is used to remedy overparameterization and the covariance in the original parameter space is singular. At the moment, ceres::Covariance is returning the covariance in the original parameter space. Is there any way to return the local parameter covariance? Or does that require manually solving for the covariance by evaluating the jacobian and forward/back substituting for the covariance columns?Thanks in advance.
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Hi Sameer,I'm interested in doing some consistency analysis on an optimization over SE3 poses, and so I'm interested in obtaining the covariance over the tangent space to check for bias and consistency as the original parameter space is overparameterized and doesn't represent the uncertainty of the degrees of freedom being optimized.Do you think it would be possible to add an option to the covariance estimation to return the covariance in terms of the local parameters? If not I think the only other option is manually evaluate the Jacobian and forward/backward solve for each column of the covariance?
On Thursday, 27 March 2014 16:05:49 UTC-4, Sameer Agarwal wrote:Nima,Yes the covariance in the original space is singular. If you look inside CovarianceImpl, we compute the covariance matrix (if you can call it that) in the tangent space and then lift it into the ambient space using the local parameterization.So technically yes you can get access to it, but it harder to interpret that quantity. You could also just undo the lifting using the value of the local parameterization jacobian.I am curious why do you want the tangent space version of the covariance matrix?SameerOn Thu, Mar 27, 2014 at 12:55 PM, Nima Keivan <nim...@gmail.com> wrote:
When using ceres::Covariance to obtain the covariance for given parameter blocks, is it possible to obtain the covariances in the local parameter space? In most cases the LocalParameterization is used to remedy overparameterization and the covariance in the original parameter space is singular. At the moment, ceres::Covariance is returning the covariance in the original parameter space. Is there any way to return the local parameter covariance? Or does that require manually solving for the covariance by evaluating the jacobian and forward/back substituting for the covariance columns?Thanks in advance.--To unsubscribe from this group and stop receiving emails from it, send an email to ceres-solver...@googlegroups.com.
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