  Many accretion-powered pulsars rotate in magnetocentrifugal disequilibrium,
spinning up or down secularly over multi-year intervals. The magnetic dipole
moment $\mu$ of such systems cannot be inferred uniquely from the time-averaged
aperiodic X-ray flux $\langle L(t) \rangle$ and pulse period $\langle P(t)
\rangle$, because the radiative efficiency of the accretion is unknown and
degenerate with the mass accretion rate. Here we circumvent the degeneracy by
tracking the fluctuations in the unaveraged time series $L(t)$ and $P(t)$ using
an unscented Kalman filter, whereupon $\mu$ can be estimated uniquely, up to
the uncertainties in the mass, radius and distance of the star. The analysis is
performed on Rossi X-ray Timing Explorer observations for $24$ X-ray transients
in the Small Magellanic Cloud, which have been monitored regularly for $\sim
16$ years. As well as independent estimates of $\mu$, the analysis yields
time-resolved histories of the mass accretion rate and the Maxwell stress at
the disk-magnetosphere boundary for each star, and hence auto- and
cross-correlations involving the latter two state variables. The inferred
fluctuation statistics convey important information about the complex accretion
physics at the disk-magnetosphere boundary.
