“RLS Algorithm with Convex Regularization”, Home
IEEE Signal Process. Lett.,
vol. 18, pp. 470-473, Aug. 2011.
E. M. Eksioglu and
A. Korhan Tanc. [pdf]
MATLAB code to generate the curves
in Fig.1:
Abstract—In this letter the RLS
adaptive algorithm is considered in the system identification setting. The RLS
algorithm is regularized using a general convex function of the system impulse
response estimate. The normal equations corresponding to the convex regularized
cost function are derived, and a recursive algorithm for the update of the tap
estimates is established. We also introduce a closed-form expression for
selecting the regularization parameter. With this selection of the
regularization parameter, we show that the convex regularized RLS algorithm
performs as well as, and possibly better than, the regular RLS when there is a
constraint on the value of the convex function evaluated at the true weight
vector. Simulations demonstrate the superiority of the convex regularized RLS
with automatic parameter selection over regular RLS for the sparse system
identification setting.