  This paper proposes an efficient method for the simultaneous estimation of
the state of a quantum system and the classical parameters that govern its
evolution. This hybrid approach benefits from efficient numerical methods for
the integration of stochastic master equations for the quantum system, and
efficient parameter estimation methods from classical signal processing. The
classical techniques use Sequential Monte Carlo (SMC) methods, which aim to
optimize the selection of points within the parameter space, conditioned by the
measurement data obtained. We illustrate these methods using a specific
example, an SMC sampler applied to a nonlinear system, the Duffing oscillator,
where the evolution of the quantum state of the oscillator and three
Hamiltonian parameters are estimated simultaneously.
