Model Structure Identification: Development and Assessment of a Recursive Prediction Error Algorithm

The paper aims to develop a more systematic approach to the problem of model structure identification for continuous time (physically based) mathematical models with discrete observations. An introduction to the model structure identification problem is first presented. The approach to this problem is the application of a modified version of the extended Kalman filter, originally defined in [23]. This filter is tested using artificial data. The results obtained lead to a further discussion of the filter's stability properties and also to a metaphor for model structures. Further study of the numerical properties of the algorithm reveal that its stability can be improved. An alternative algorithm, the so called recursive prediction error algorithm, is modified to a Kalman-like algorithm in continuous-discrete formulation. This algorithm is also tested using artificial data. The RPE-type of filter has better stability properties and appears to be very robust to initial conditions. Its applicability to environmental case studies is set out through the application of the filter to a familiar case study. Applications of this type of filter is valuable for validation/verification of environmental and/or economical models that include a set of ordinary differential equations