Higher-Order Statistics-based methods for order and parameter estimation of continuous-time errors-in-variables fractional models

This paper considers the problem of dynamic Errors-In-Variables identification by fractional model. First, differentiation orders are fixed and the differential equation coefficients are estimated using two estimators based on Higher-Order Statistics (third-order cumulants). Then, all differentiation orders are set as integer multiples of a commensurate order. The fractional third-order based least squares algorithm (ftocls) and the fractional third-order based iterative least squares algorithm (ftocils) are extended to estimate the commensurate order with a nonlinear optimization algorithm. A simulation example is used to demonstrate the performance of the proposed methods.