In this paper we study the structure of finite dimensional estimation algebras with state dimension 3 and rank 2 arising from a nonlinear filtering system by using the theories of the Euler operator and underdetermined partial differential equations. The structure of the Wong Omega-matrix is shown to be linear. The fundamental strategy we use in this paper to prove these results is to show that if they were not true, then infinite sequences could be constructed in the finite dimensional estimation algebra.