Convergence of adaptive minimum variance algorithms via weighting coefficient selection

Weighted least squares, and related stochastic approximation algorithms are studied for parameter estimation, adaptive state estimation, adaptive
N
-step-ahead prediction, and adaptive control, in both white and colored noise environments. For the fundamental algorithm which is the basis for the various applications, the step size in the stochastic approximation versions and the weighting coefficient in the weighted least squares schemes are selected according to a readily calculated stability measure associated with the estimator. The selection is guided by the convergence theory. In this way, strong global convergence of the parameter estimates, state estimates, and prediction or tracking errors is not only guaranteed under the appropriate noise, passivity, and stability or minimum phase conditions, but the convergence is also as fast as it appears reasonable to achieve given the simplicity of the adaptive scheme.