In apache.commons.math a matrix inversion is done to compute the the covariance matrix. In some cases the inversion cannot be done, because the matrix is singular. In these cases no covariances, parameter errors, ... are given. Therefore we should try to find a workaround for these cases.
One possible workaround would be to use Bootstrapping for computing the covariance matrix. http://www.math.ubc.ca/GGTSPU-argusgate02.bfr.bund.de-2872-911822-oY5FNZ88UXnQ6QGV-DAT/~keshet/MCB2012/SlidesDodo/DataFitLect3.pdf
I like this idea!
http://www.math.ubc.ca/~keshet/MCB2012/SlidesDodo/DataFitLect3.pdf