  The magnetic dipole moment $\mu$ of an accretion-powered pulsar in
magnetocentrifugal equilibrium cannot be inferred uniquely from time-averaged
pulse period and aperiodic X-ray flux data, because the radiative efficiency
$\eta_0$ of the accretion is unknown, as are the mass, radius, and distance of
the star. The degeneracy associated with the radiative efficiency is
circumvented, if fluctuations of the pulse period and aperiodic X-ray flux are
tracked with a Kalman filter, whereupon $\mu$ can be measured uniquely up to
the uncertainties in the mass, radius, and distance. Here the Kalman filter
analysis is demonstrated successfully in practice for the first time on Rossi
X-ray Timing Explorer observations of the X-ray transient SXP 18.3 in the Small
Magellanic Cloud, which is monitored regularly. The analysis yields $\mu =
8.0^{+1.3}_{-1.2} \, \times \, 10^{30} \, {\rm G \, cm^3}$ and $\eta_0 =
0.04^{+0.02}_{-0.01}$, compared to $\mu = 5.0^{+1.0}_{-1.0} \times 10^{30} \,
{\rm G \, cm^3}$ as inferred traditionally from time-averaged data assuming
$\eta_0=1$. The analysis also yields time-resolved estimates of two hidden
state variables, the mass accretion rate and the Maxwell stress at the
disk-magnetosphere boundary. The success of the demonstration confirms that the
Kalman filter analysis can be applied in the future to study the magnetic
moments and disk-magnetosphere physics of accretion-powered pulsar populations
in the Small Magellanic Cloud and elsewhere.
