  We analyze the estimation of a time dependent perturbation acting on a
continuously monitored quantum system. We describe the temporal fluctuations of
the perturbation by a Hidden Markov Model, and we combine quantum measurement
theory and classical filter theory into a time evolving hybrid quantum and
classical trajectory. The forward-backward analysis that permits smoothed
estimates of classical Hidden Markov Models has a counterpart in the theory of
retrodiction and Past Quantum States. As a specific example, we apply our
hybrid trajectory and Past Quantum State theory to the sensing of a fluctuating
magnetic field by microwave interrogation of a single quantum spin.
