Fractional system identification based on improved NLJ algorithm

This paper presents an improved new Luus-Jaakola (NLJ) algorithm which is applied to the fractional order system identification. The discretization of the fractional order system is the precondition of the system identification. However, whether it is based on the definition or the direct approximation, the discretization will increase the complexity of the system architecture and make the system identification much more difficult. In this context, the traditional NLJ algorithm still appears to be of low efficiency and poor stability of the identification result. To address this problem, this article introduces the concept of bi-directional iterative calculation. By comparing the fitting errors, the set of parameters resulting to the smaller error is selected as the initial value of the next iteration, through which the identification efficiency has been improved greatly. Meanwhile, the improved algorithm is applied to two forms of fractional identification with constrained and unconstrained, respectively, just in order to verify the correctness and efficiency of the improved algorithm.