Abstract
In this paper, we continue our program to understand the identification problem of linear system theory from the viewpoint of nonlinear filtering (see Krishnaprasad and Marcus (1981a, 1981b)). We show that the estimation Lie algebra of the identification problem is always a subalgebra of an infinite dimensional Lie algebra of a very special type, namely -- a current algebra of order zero. In the classes of problems of interest to us, such algebras are embeddable in Lie algebras of vector fields on finite ddmensional manifolds. Using a Wei-Norman type procedure we are able to solve the integration problem as well as the question of sufficient statistics.
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