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

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 discusse

Parameter identification in tidal models with uncertain boundaries

In this paper we consider a simultaneous state and parameter estimation procedure for tidal models with random inputs, which is formulated as a minimization problem. It is assumed that some model parameters are unknown and that the random noise inputs only act upon the open boundaries. The hyperbolic nature of the governing dynamical equations is exploited in order to determine the smoothed states efficiently. This enables us to also apply the procedure to nonlinear tidal models without an excessive computational load. The main aspects of this paper are that the method of Chavent (Identification and System Parameter Estimation. Proc. 5th IFAC Symp. Pergamon, Oxford, pp 85¿97, 1979), used to calculate the gradient of a criterion that is to be minimized, is now embedded in a stochastic environment and that the estimation method can also be applied to practical, large-scale problems