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

Multi-parameter estimation along quantum trajectories with Sequential Monte Carlo methods