  We consider Bayesian estimate of static magnetic field, characterized by a
prior Gaussian probability distribution, in systems of a few electron quantum
dot spins interacting with infinite temperature spin environment via hyperfine
interaction. Sudden transitions among optimal states and measurements are
observed. Usefulness of measuring occupation levels is shown for all times of
the evolution, together with the role of entanglement in the optimal scenario.
For low values of magnetic field, memory effects stemming from the interaction
with environment provide limited metrological advantage.
