Minimum-disturbance description for the development of adaptation algorithms and a new leakage least squares algorithm

Usual methods for the development of adaptive filters are based on a stochastic approximation of the gradient vector and Hessian matrix, or on a deterministic minimization of quadratic a posteriori output errors. Gradient-based algorithms are usually placed in the first group, whereas least squares (LS) based algorithms are placed in the second group. These are just how algorithms are usually presented and analyzed and alternative descriptions exit. This paper proposes to shed new light onto known adaptation algorithms by means of a minimum-disturbance approach to the cost function together with constraints added to improve their robustness. The resulting algorithms are able to perform extremely well in many demanding applications.