Robust nonlinear parameter estimation for bounded error models using Isomap

This paper proposes a robust parameter estimation method for nonlinear models with bounded errors. The purpose of this method is to characterize the set of all the parameter vectors consistent with the data, model structure and error bounds. This set is called the feasible parameter set (FPS). The method uses Isomap to construct a mapping which can approximate the homeomorphism between the FPS boundary and the n-1-sphere (n is the number of parameters). Once this mapping is established, it can be used to map the n-1-sphere into an approximation of the FPS boundary. The performance of the proposed method is provided by two examples. The simulation results show that the proposed method exhibits superior accuracy compared with the support vector machine method.