Weak Form Mitter Conjecture on Nonmaximal Rank Estimation Algebra:State Dimension 4 and Rank 3  

作　　者：JIAO Xiaopei YAU Stephen Shing-Toung 

机构地区：[1]Department of Applied Mathematics,University of Twente,Enschede 7522 NB,Netherlands [2]Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China [3]Beijing Institute of Mathematical Sciences and Applications(BIMSA),Beijing 101408,China

出　　处：《Journal of Systems Science & Complexity》2025年第1期27-78,共52页系统科学与复杂性学报(英文版)

基　　金：supported by the Tsinghua University Education Foundation fund under Grant No.042202008.

摘　　要：Ever since Brockett and Clark(1980),Brockett(1981)and Mitter(1980)introduced the estimation algebra method,it becomes a powerful tool to classify finite-dimensional filtering systems.In this paper,the authors investigate estimation algebra on state dimension n and linear rank n−1,especially the case of n=4.Mitter conjecture is always a key question on classification of estimation algebra.A weak form of Mitter conjecture states that observation functions in finite dimensional filters are affine functions.In this paper,the authors shall focus on the weak form of Mitter conjecture.In the first part,it will be shown that partially constant structure of Ω is a sufficient condition for weak form Mitter conjecture to be true.In the second part,the authors shall prove partially constant structure of Ω for n=4 which implies the weak form Mitter conjecture for this case.

关 键 词：Estimation algebra finite dimensional filter Mitter conjecture state estimation 

分 类 号：O211[理学—概率论与数理统计]