A Stochastic Newton-Raphson Method with Noisy Function Measurements

Abstract

This letter shows that traditional Newton-Raphson (NR) method cannot achieve zero-convergence in presence of additive noise without adding a multiplicative gain. Furthermore, this gain needs to converge to zero. This article proposes a novel recursive algorithm providing optimal iterative-varying gains associated with the NR method. The development of the proposed optimal algorithm is based on minimizing a stochastic performance index. The estimation error covariance matrix is shown to converge to zero for linearized functions while considering additive zero-mean white noise. In addition, the proposed approach is capable of overcoming common drawbacks associated with the traditional NR method. Simulation results are included to illustrate the performance capabilities of the proposed algorithm. We show that the proposed recursive algorithm provides significant improvement over the traditional NR method.