Robust least-squares estimation with harmonic regressor: high order algorithms

A new robust and computationally efficient solution to least-squares problem in the presence of round-off errors is proposed. The properties of a harmonic regressor are utilized for design of new combined algorithms of direct calculation of the parameter vector. In addition, an explicit transient bound for estimation error is derived for classical recursive least-squares (RLS) algorithm using Lyapunov function method. Different initialization techniques of the gain matrix are proposed as an extension of RLS algorithm. All the results are illustrated by simulations.