  In this work, the measurement transition as well as precision measurement
advantages of single-photon-added coherent state after postselected von Neumann
measurement are investigated. We noticed that the weak-to-strong measurement
transition characterized by the shifts of pointer's position and momentum
variables occurred in continuously by controlling a dimensionless parameter
associated with system-pointer coupling. We calculate the ratio between the
signal-to-noise ratio of nonpostselected and postselected measurements, and the
latter is used to find the quantum Fisher information. We found that the
single-photon-added coherent pointer state can improve the precision of the
measurement processes such as signal-to-noise ratio and parameter estimation
after postselected von Neumann measurement characterized by postselection and
weak value. Furthermore, contrary to the results of several previous studies,
we found that the anomalous large weak values can't improve the precision
measurement processes related to single-photon-added coherent state.
