  We investigate simultaneous estimation of multi-parameter quantum estimation
with time-dependent Hamiltonians. We analytically obtain the maximal quantum
Fisher information matrix for two-parameter in time-dependent three-level
systems. The optimal coherent control scheme is proposed to increase the
estimation precisions. In a example of a spin-1 particle in a uniformly
rotating magnetic field, the optimal coherent Hamiltonians for different
parameters can be chosen to be completely same. However, in general, the
optimal coherent Hamiltonians for different parameters are incompatibility. In
this situation, we suggest a variance method to obtain the optimal coherent
Hamiltonian for estimating multiple parameters simultaneously, and obtain the
optimal simultaneous estimation precision of two-parameter in a three-level
Landau-Zener Hamiltonian.
