Structure theorem for six-dimensional estimation algebras

The problem of classification of finite-dimensional estimation algebras was formally proposed by Brockett in his lecture at International Congress of Mathematicians in 1983. Due to the difficulty of the problem, in the early 1990s Brockett suggested that one should understand the low-dimensional estimation algebras first. In this paper, We extend Yau and his coauthors´ work of the Mitter conjecture for low dimensional estimation algebras in nonlinear filtering problem. And we apply the results to give classification of estimation algebras of dimension six.