Nonparametric Estimation of Nonlinear Dynamics by Local Linear Approximation

This chapter discusses nonparametric estimation of nonlinear dynamical system models by a method of metric-based local linear approximation. By specifying a metric such as the standard metric or the square metric on the Euclidean space and a weighting function based on such as the exponential function or the cut-off function, it is possible to estimate values of an unknown vector field from experimental data. It can be shown the local linear fitting with the Gaussian kernel, or the local polynomial modeling of degree one, is included in the class of the proposed method. In addition, conducting simulation studies for estimating random oscillations, the chapter shows the method numerically works well.