COVARIANCE ANALYSIS OF THE MINIMUM MODEL ERROR ESTIMATOR
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Minimum model error estimation has been an important smoothing approach for the state and parameter estimation of nonlinear dynamical systems. The analyst typically obtains the best estimates of the state trajectory and the time varying model error term as a byproduct of the measurement data processing using the minimum model error estimator. However, the lack of covariance information associated with the state estimation error is a theoretical gap that prevented estimation theorists from adopting this smoothing procedure widely. In this paper, we derive expressions governing the covariance of the state estimation error for minimum model error estimation framework. Investigations will be carried out using a linear and nonlinear statistical analysis of the estimation error. Relationships of the minimum model error framework with classical smoothing solutions will be explored and the statistical similarities will be delineated. Numerical examples illustrate the calculation strategies outlined in the paper.
