  The optimal phase estimation strategy is derived when partial a priori
knowledge on the estimated phase is available. The structure of the optimal
measurements, estimators and the optimal probe states is analyzed. The results
fill the gap in the literature on the subject which until now dealt almost
exclusively with two extreme cases: almost perfect knowledge (local approach
based on Fisher information) and no a priori knowledge (global approach based
on covariant measurements). Special attention is paid to a natural a priori
probability distribution arising from a diffusion process.
