A Hilbertian Projection Approach with Dictionary Dividing Strategy: Accelerating Nonlinear Estimation Algorithm with Multiscale Gaussians

A novel dictionary dividing scheme for online non-linear estimation algorithms with multiscale Gaussians is pro-posed to perform a projection in an appropriate reproducing kernel Hilbert space. The proposed dictionary dividing strategy mitigates the in equivalence of the norm of multiscale Gaussians, which leads to degradations of adaptation speed for certain Gaussians. Based on a Hilbertian projection with the dictionary dividing strategy, a fast nonlinear estimation algorithm, which adapts scales and centers of Gaussians as well as its heights, is presented. The numerical example shows that using the Hilber-tian projection with the proposed dictionary dividing scheme ameliorates the adaptation speed of Gaussian heights.