  We propose a new protocol for on-line quantum system estimation on the basis
of continuous weak-measurements with the help of compressive sensing and the
optimization algorithm. By directly measuring the state of the probe system, we
indirectly obtain the measurement operators of the estimated system. The
continuous weak measurements for a dynamic evolution open quantum system enable
us to derive the time-varying measurement operators of the estimated system.
Compressed sensing is used to reduce the number of the measurements needed and
to improve the efficiency of the estimation. This approach to the on-line state
estimation provides a novel solution to the problem of closed-loop quantum
feedback control.
