  We present a new procedure for quantum state reconstruction based on weak
continuous measurement of an ensemble average. By applying controlled evolution
to the initial state new information is continually mapped onto the measured
observable. A Bayesian filter is then used to update the state-estimate in
accordance with the measurement record. This generalizes the standard paradigm
for quantum tomography based on strong, destructive measurements on separate
ensembles. This approach to state estimation can be non-destructive and
real-time, giving information about observables whose evolution cannot be
described classically, opening the door to new types of quantum feedback
control.
