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.
Bagchi, A., ten Brummelhuis, P. G. J., & ten Brummelhuis, P. (1994). Parameter identification in tidal models with uncertain boundaries. Automatica, 30(5), 745-759. https://doi.org/10.1016/0005-1098(94)90166-X