We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of cooling and confining a single quantum degree of freedom, and compare it to current schemes in which the measurement signal is fed back directly in the manner usually considered in existing treatments of quantum feedback. The two approaches to feedback are to a certain extent complementary, and they may be combined to achieve the best results. The resulting combined feedback, performed on a linear system, is closely analogous to classical LQG control theory with residual feedback.