Persistence of excitation in extended least squares

In least-squares parameter estimation schemes, "persistency of excitation" conditions on the plant states are required for consistent estimation. In the case of extended least squares, the persistency conditions are on the state estimates. Here, these "persistency of excitation" conditions are translated into "sufficiently rich" conditions on the plant noise and inputs. In the case of adaptive minimum variance control schemes, the "sufficiently rich" conditions are on the noise and specified output trajectory. With sufficiently rich input signals, guaranteed convergence rates of prediction errors improve, and it is conjectured that the algorithms are consequently more robust.