  Measurement and estimation of parameters are essential for science and
engineering, where the main quest is to find out the highest achievable
precision with given resources and design schemes to attain it. Two schemes,
the sequential feedback scheme and the parallel scheme, are usually studied in
quantum parameter estimation. While the sequential feedback scheme represents
the most general scheme, it remains unknown whether it can outperform the
parallel scheme for any quantum estimation tasks. In this Letter we show that
the sequential feedback scheme has a 3-fold improvement over the parallel
scheme for Hamiltonian parameter estimations on 2-dimensional systems, and an
order of $O(d+1)$ improvement for Hamiltonian parameter estimation on
$d-$dimensional systems. We also show that, contrary to the conventional
belief, it is possible to simultaneously achieve the highest precision for
estimating all three components of a magnetic field, which sets a benchmark on
the local precision limit for the estimation of a magnetic field.
