SYSTEM IDENTIFICATION USING NEWTON–RAPHSON METHOD BASED ON SYNERGY OF HUBER AND PSEUDO–HUBER FUNCTIONS

Abstract

In real situations the presence of outliers is unavoidable and that is why the distribution of a disturbance is non-Gaussian. A synthesis of an algorithm of identification based on the Newton-Raphson method is considered for this case. The method requires that the loss function should be twice differentiable. Huber loss function, relevant for the treatment of outliers, has just the first derivative. In order to overcome the problem, the pseudo- Huber loss function is introduced. This function behaves similarly to the Huber loss function and has derivatives of an arbitrary order. In this paper, the pseudo- Huber loss function is used for the second derivative of functional in the Newton-Raphson procedure. The main contributions of the paper are: (i) Design of a new robust recursive algorithm based on the synergy of Huber and pseudo – Huber functions; (ii) The convergence analysis.