  Relativistic effects on the precision of quantum metrology for particle
detectors, such as two-level atoms are studied. The quantum Fisher information
is used to estimate the phase sensitivity of atoms in non-inertial motions or
in gravitational fields. The Unruh-DeWitt model is applicable to the
investigation of the dynamics of a uniformly accelerated atom weakly coupled to
a massless scalar vacuum field. When a measuring device is in the same
relativistic motion as the atom, the dynamical behavior of quantum Fisher
information as a function of Rindler proper time are obtained. It is found out
that monotonic decrease in phase sensitivity is characteristic of dynamics of
relativistic quantum estimation. To improve relativistic quantum metrology, we
reasonably take into account two reflecting plane boundaries perpendicular to
each other.
