  In this work, we consider the problem of online (real-time, single-shot)
estimation of static or slow-varying parameters along quantum trajectories in
quantum dynamical systems. Based on the measurement signal of a
continuously-monitored quantum system, we propose a recursive algorithm for
computing the maximum likelihood estimate of unknown parameters using an
approach based on stochastic gradient ascent on the log-likelihood function. We
formulate the algorithm in both discrete-time and continuous-time and
illustrate the performance of the algorithm through simulations of a simple
two-level system undergoing homodyne measurement from which we are able to
track multiple parameters simultaneously.
