北京雁栖湖应用数学研究院

丘成栋

焦小沛

2023年02月21日 21:30 至 22:00

Online

Ever since Brockett, Clark and Mitter introduced the estimation algebra method, it becomes a powerful tool to classify the finite dimensional filtering system. In this paper, we investigate estimation algebra on state dimension $n$ and linear rank $n-1$, especially case of $n=4$. Mitter conjecture is always a key question on classification of estimation algebra. Weaker form of Mitter conjecture states observation functions in finite dimensional filters are affine functions. In this paper, we will focus on weaker form of Mitter conjecture. In the first part, it will be shown that a sufficient condition of weaker Mitter conjecture is partially constant structure of $Omega$. In the second part, partially constant structure of $Omega$ will be proven true and weaker Mitter conjecture hold for $n=4$ case.

焦小沛，本科毕业于上海交通大学致远学院，博士毕业于清华大学数学科学系。先后在北京雁栖湖应用数学研究院，荷兰特文特大学从事博士后工作。现研究方向包括有限维滤波理论，丘-丘滤波方法，物理信息神经网络以及生物信息学。研究兴趣主要集中于（1）利用李代数等几何工具进行偏微分方程求解与有限维滤波系统的分类；（2）设计基于物理信息神经网络的新型数值算法。