Estimation of parameters in the linear-fractional models

The linear-fractional model (LFM) is a fraction function whose numerator and denominator are linear in parameters. The LFM is a group of models nonlinear in parameters. The estimation methods for nonlinear models can be applied to the FLM. However, the parameters in an LFM can naturally be divided into two groups: those in the numerator and those in the denominator. When the parameters in the denominator are known, the standard least squares algorithm for the linear model can be used to estimate the parameters in the numerator. On the other hand, when parameters in the numerator are known, by a reciprocal transformation, the standard least squares algorithm for the linear model can again be used to estimate the parameters in the denominator. From this observation, we develop a recursive least-squares algorithm for estimation of parameters in the LFM when both groups has unknown parameters. The basic idea is to estimate the parameters in the numerators for a given initial parameters in the denominator using the standard least squares algorithm for the linear model, and then to estimate the parameters in the denominator with the previous estimates of parameters in the denominator using the standard least squares algorithm for the linear model when new data is available. The simulation results validated the convergence of the proposed algorithm and also showed the superior performance of the algorithm proposed over some existing algorithm.