  We investigate the estimation technique called quantum state smoothing
introduced by Guevara and Wiseman [Phys.~Rev.~Lett.~{\bf 115}, 180407 (2015)],
which offers a valid quantum state estimate for a partially monitored system,
conditioned on the observed record both prior and posterior to an estimation
time. Partial monitoring by an observer implies that there may exist records
unobserved by that observer. It was shown that, given only the observed record,
the observer can better estimate the underlying true quantum states, by
inferring the unobserved record and using quantum state smoothing, rather than
the usual quantum filtering approach. However, the improvement in estimation
fidelity, originally examined for a resonantly driven qubit coupled to two
vacuum baths, was also shown to vary depending on the types of detection used
for the qubit's fluorescence. In this work, we analyse this variation in a
systematic way for the first time. We first define smoothing power using an
average purity recovery and a relative average purity recovery, of smoothing
over filtering. Then, we explore the power for various combinations of
fluorescence detection for both observed and unobserved channels. We next
propose a method to explain the variation of the smoothing power, based on
multi-time correlation strength between fluorescence detection records. The
method gives a prediction of smoothing power for different combinations, which
is remarkably successful in comparison with numerically simulated qubit
trajectories.
