tailieunhanh - Báo cáo hóa học: " Erratum to “A New Class of Particle Filters for Random Dynamic Systems with Unknown Statistics”"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Erratum to “A New Class of Particle Filters for Random Dynamic Systems with Unknown Statistics” | Hindawi Publishing Corporation EURASIP Journal on Applied Signal Processing Volume 2006 Article ID 78708 Pages 1-2 DOI ASP 2006 78708 Erratum to A New Class of Particle Filters for Random Dynamic Systems with Unknown Statistics Joaquin Miguez 1 Monica F. Bugallo 2 and Petar M. Djuric2 1 Departamento de Teoria de la Senalylas Comunicaciones Universidad Carlos III de Madrid 28911 Leganes Spain 2 Department of Electrical and Computer Engineering Stony Brook University Stony Brook NY 11794 USA Received 28 August 2005 Accepted 9 November 2005 Recommended for Publication by Marc Moonen We have found an error in the proof of Lemma 1 presented in our paper A New Class of Particle Filters for Random Dynamic Systems with Unknown Statistics EURASIP Journal on Applied Signal Processing 2004 . In the sequel we provide a restatement of the lemma and a corrected and simpler proof. We emphasize that the original result in the said paper still holds true. The only difference with the new statement is the relaxation of condition 3 which becomes less restrictive. Copyright 2006 Hindawi Publishing Corporation. All rights reserved. Lemma 1 in 1 should be as follows. Lemma 1. Let x ff1 be a set of particles drawn at time t using the propagation pdf pM x let y1 t be a fixed bounded sequence of observations let AC x I yt 0 be a continuous cost function bounded in S x pt e with a minimum at x x pt and let Bt A c x i M 1 - 0 o be a set function t t i 1 defined as Bt a c x c y b AC x I yt . 1 t t i 1 t xeA If the following three conditions are met 1 Any ball with center at x pt has a nonzero probability under the propagation density that is opt PM x dx Y 0 e 0 2 2S xlF e 2 the supremum of the function b AC I for points outside S x pt e is a finite constant that is Sout sup ffiAe xt I yt o 3 xtEil S xopt e 3 the expected value of 1 pt x i M1 satisfies lim e 1 I 0 4 M0 pt x i M1 M then lim Pr M o Bt SM x pt e . Í u i M BA lxt 1 Ỗ where Pr denotes probability that is lim M o M opt Pt S