  Pose-Graph optimization is a crucial component of many modern SLAM systems.
Most prominent state of the art systems address this problem by iterative
non-linear least squares. Both number of iterations and convergence basin of
these approaches depend on the error functions used to describe the problem.
The smoother and more convex the error function with respect to perturbations
of the state variables, the better the least-squares solver will perform. In
this paper we propose an alternative error function obtained by removing some
non-linearities from the standard used one - i.e. the geodesic error function.
Comparative experiments conducted on common benchmarking datasets confirm that
our function is more robust to noise that affects the rotational component of
the pose measurements and, thus, exhibits a larger convergence basin than the
geodesic. Furthermore, its implementation is relatively easy compared to the
geodesic distance. This property leads to rather simple derivatives and nice
numerical properties of the Jacobians resulting from the effective computation
of the quadratic approximation used by Gauss-Newton algorithm.
