English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Approximating the solution of the nonlinear filtering problem with Gaussianmixtures has been a very popular method since the 1970s. However, the vastmajority of such approximations are introduced in an ad-hoc manner withouttheoretical grounding. This work is a continuation of [4, 5], where wedescribed a rigorous Gaussian mixture approximation to the solution of thefiltering problem. We deduce here a refined estimate of the rate of convergenceof the approximation. We do this by proving a central limit type theorem forthe error process. We also find the optimal variances of the Gaussian measuresare of order $1/\sqrt{n}$. This implies, in particular, that the mean squareerror of the approximation as defined in [4, 5] is of order $1/n$.

A central limit type theorem for Gaussian mixture approximations to the nonlinear filtering problem