  A filtering problem for a class of quantum systems disturbed by a classical
stochastic process is investigated in this paper. The classical disturbance
process, which is assumed to be described by a linear stochastic differential
equation, is modeled by a quantum cavity model. Then the hybrid
quantum-classical system is described by a combined quantum system consisting
of two quantum cavity subsystems. Quantum filtering theory and a quantum
extended Kalman filter method are employed to estimate the states of the
combined quantum system. An estimate of the classical stochastic process is
derived from the estimate of the combined quantum system. The effectiveness and
performance of the proposed methods are illustrated by numerical results.
