Minimum model error estimation for poorly modeled dynamic systems

A novel strategy (which we call “minimum model error” estimation) for postexperiment optimal state estimation of discretely measured dynamic systems is developed and illustrated for a simple example. The method is especially appropriate for postexperiment estimation of dynamic systems whose presumed state governing equations are known to contain, or are suspected of containing, errors. The hew method accounts for errors in the system dynamic model equations in a rigorous manner. Specifically, the dynamic model error terms in the proposed method do not require the usual Kalman filter-smoother process noise assumptions of zero-mean, symmetrically distributed random disturbances, nor do they require representation by assumed parameterized time series (such as Fourier series); Instead, the dynamic model error terms require no prior assumptions other than piecewise continuity. Estimates of the state histories, as well as the dynamic model errors, are Obtained as part of the solution of a two-point boundary value problem. The state estimates are continuous and optimal in a global sense, yet the algorithm processes the measurements sequentially. The example demonstrates the method and shows it to be quite accurate for state estimation of a poorly modeled dynamic system.