Joint two-stage multi-innovation recursive least squares parameter and fractional-order estimation algorithm for the fractional-order input nonlinear output-error autoregressive model

This paper mainly investigates the issue of parameter identification for the fractional-order input nonlinear output error autoregressive (IN-OEAR) model. In order to avoid the problem of large computation of redundant parameter estimation, the output form of the system can be expressed by a linear combination of unknown parameters through the key term separation. Through employing the hierarchial identification principle, the fractional-order IN-OEAR model is decomposed into two sub-models with a smaller number of parameters. On the basis of the recursive identification methods, a recursive least squares sub-algorithm and a gradient stochastic sub-algorithm are proposed to estimate the parameters and the fractional-order, respectively. With the aim of achieving more accurate parameter estimates, a two-stage multi-innovation least recursive algorithm is proposed by means of the multi-innovation identification theory. The numerical simulation results test the effectiveness of the proposed methods.

Automated summary

This paper investigates the parameter identification issue for the fractional-order input nonlinear output error autoregressive (IN-OEAR) model. By expressing the output form of the system as a linear combination of unknown parameters through key term separation, the problem of large computation of redundant parameter estimation is avoided. The fractional-order IN-OEAR model is decomposed into two sub-models with a smaller number of parameters using the hierarchical identification principle. Recursive least squares and gradient stochastic sub-algorithms are proposed for parameter and fractional-order estimation, respectively. A two-stage multi-innovation least recursive algorithm is proposed to achieve more accurate parameter estimates based on the multi-innovation identification theory. Numerical simulation results demonstrate the effectiveness of the proposed methods.