  We demonstrate a fast, robust and non-destructive protocol for quantum state
estimation based on continuous weak measurement in the presence of a controlled
dynamical evolution. Our experiment uses optically probed atomic spins as a
testbed, and successfully reconstructs a range of trial states with fidelities
of ~90%. The procedure holds promise as a practical diagnostic tool for the
study of complex quantum dynamics, the testing of quantum hardware, and as a
starting point for new types of quantum feedback control.
