Simultaneous ML estimation of state and parameters for hyperbolic systems with noisy boundary conditions

A method to estimate simultaneously states and parameters of a discrete-time hyperbolic system with noisy boundary conditions is presented. This method is based on maximization of a likelihood (ML) function. The ML function leads to a two-point boundary value problem of considerable complexity. Restricted discrete-time problems, the large dimension of the state vector and the direct solution of the two-point boundary value problem may lead to a huge computational load. An alternative computational method is proposed which is much faster and makes use of specific features of the hyperbolic system. Although this technique is described for linear systems, possible extension to nonlinear systems are also briefly discussed