System identification and nonlinear filtering: Lie algebras

This paper is continuation of our previous work ([1], [2], [3]) to understand the identification problem of linear system theory from the viewpoint of nonlinear filtering. The estimation algebra of the identification problem is a subalgebra of a current algebra. It therefore follows that the estimation algebra is embeddable as a Lie algebra of vector fields on a finite dimensional manifold. These features permit us to develop a Wei-Norman type procedure for the associated Cauchy problem and reveal a set of functionals of the observations that play the role of joint sufficient statistics for the identification problem.