New results on the performance of a well-known class of adaptive filters

The adaptation algorithms studied are introduced with the aid of an idealized identification problem involving an unknown system with a continuous vector input of known dimension and a scalar output. A misalignment vector is defined. Proof is provided for a uniform exponential convergence to zero of the norm of the misalignment vector. Upper and lower bounds to the convergence rate are derived. Attention is given to the properties of the linear system in response to a special input.