Steepening Squared Error Function Facilitates Online Adaptation of Gaussian Scales

Abstract

We previously proposed a joint learning scheme of Gaussian parameters (scales and centers) and coefficients for online nonlinear estimation. The instantaneous squared error cost in terms of the Gaussian scales, however, tends to have shallow slopes when the initial guess is far from optimal, causing extremely slow convergence. In this paper, we propose steepening the cost function by adding a squared distance function from the instantaneously-optimal scale. Numerical examples show that the use of the steepened cost ameliorates the convergence behaviors of the scale parameters in inappropriate initial-scale settings.