Continuous-time system modelling using the weighted-parabola-overlapping numerical integration method

Abstract

Numerical integration is a widely used method in scientific areas where the uniform integral interval can be selected optionally. Simpson integration and Newton-Cotes formula, for example, are available in many textbooks and software. However, in system science, the data may come from practical sampled continuous systems. Sometimes the sampling interval is non-uniform and the integration values at each sampled point are needed. For example, when the parameters of a continuous system model need to be estimated by least squares, we want the integration value at each sampling point. In that case, trapezoidal numerical integration is mostly adopted, which has only first-order algebraic accuracy (the straight line). When sampled points are fewer, the errors of numerical integration such as noise can interfere with the modelling. We propose a weighted-parabola-overlapping (WPO) numerical integration method, which possesses third-order algebraic accuracy and needs nearly the same computation of second-order powe...