Parametric identification of fractional order system using Bayesian method

Abstract

In this paper, the estimation issue for fractional order system with unknown parameter and order is addressed. The Bayesian method is used for system identification. First, the framework of parameter identification algorithm is built and the conjugate prior is constructed. Then, an improved descent method is used to update the posterior distribution based on the idea of maximum likelihood function. The proposed method solves the problem of overall identification of order and parameters, and can also estimate the noise in the system. Finally, numerical experiments comparing with the optimization algorithm are completed. Experiments on prediction performance, convergence ability and time complexity verify the effectiveness and speed of the proposed algorithm.