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New techniques for recursive identification of systems described by nonlinear ordinary differential equation models are discussed. The model is of black-box state space type, where the right-hand side function is estimated as a multi-variate polynomial in the states and inputs, with the parameters selected to be the polynomial coefficients. An algorithm based on Kalman filtering techniques is derived, where a numerical differentiation scheme, used for generation of approximate state variables is a key ingredient. The Kalman-filter-based algorithm is, for example, suitable for initialization of a previously published recursive prediction error method (RPEM) based on the same model. In this brief, the algorithm performance of the Kalman-filter-based method is compared to that of the RPEM using a numerical example. Another example shows that the success rate of the RPEM is increased from 70% to 100%, when the proposed algorithm is used for generation of initial estimates for the RPEM. The Kalman-filter-based algorithm is also used for finding initial parameters for the RPEM when applied to live data from a laboratory process - a system of cascaded tanks. Based on the experimental results, this brief discusses advantages and disadvantages of different algorithms and differentiation schemes.
Date of Publication: July 2008