  The dynamics of many open quantum systems are described by stochastic master
equations. In the discrete-time case, we recall the structure of the derived
quantum filter governing the evolution of the density operator conditioned to
the measurement outcomes. We then describe the structure of the corresponding
particle quantum filters for estimating constant parameter and we prove their
stability. In the continuous-time (diffusive) case, we propose a new
formulation of these particle quantum filters. The interest of this new
formulation is first to prove stability, and also to provide an efficient
algorithm preserving, for any discretization step-size, positivity of the
quantum states and parameter classical probabilities. This algorithm is tested
on experimental data to estimate the detection efficiency for a superconducting
qubit whose fluorescence field is measured using a heterodyne detector.
