  The maximum-marginal-a-posteriori success rate of statistical decision under
multivariate Gaussian error distribution on an integer lattice is almost
rigorously calculated by using union-bound approximation and Monte Carlo
integration. These calculations are applied to the revelation of the various
possible realizations of the reliable and short-period integer ambiguity
resolution in precise carrier-phase relative positioning by GPS/GNSS. The
theoretical foundation and efficient methodology are systematically developed,
and two types of the enhancement of union-bound approximation are proposed and
examined.
  The results revealed include an extremely high reliability under the
condition of accurate carrier-phase measurements and a large number of visible
satellites, its heavy degradation caused by the slight amount of differentiated
ionospheric delays due to the nonvanishing baseline length between rover and
reference receivers, and the advantages of the use of the multiple carrier
frequencies. The succeeding initialization of the integer ambiguities is shown
to overcome the disadvantageous condition of the nonvanishing baseline length
effectively due to the reasonably assumed temporal and spatial constancy of
differentiated ionospheric delays.
