I'm looking for an algorithm to fit an ellipse (tilted) to some given points in 2D. There are some around, but I need one that calculates and returns the error of the fit.

Some of the points might be "false" and I want to identify them by seeing how the error of the fit changes by excluding the points one at a time. Or is there a smarter way to identify points which "ruin the fit" of the other points to an ellipse?