Additional Fractional Gradient Descent Identification Algorithm Based on Multi-innovation Principle for Autoregressive Exogenous Models

This paper proposed the additional fractional gradient descent identification algorithm based on the multi-innovation principle for autoregressive exogenous models. This algorithm incorporates an additional fractional order gradient to the integer order gradient. The two gradients are synchronously used to identify model parameters, thereby accelerating the convergence of the algorithm. Furthermore, to address the limitation of conventional gradient descent algorithms, which only use the information of the current moment to estimate the parameters of the next moment, resulting in low information utilisation, the multi-innovation principle is applied. Specifically, the integer-order gradient and additional fractional-order gradient are expanded into multi-innovation forms, and the parameters of the next moment are simultaneously estimated using multi-innovation matrices, thereby further enhancing the parameter estimation speed and identification accuracy. The convergence of the algorithm is demonstrated, and its effectiveness is verified through simulations and experiments involving the identification of a 3-DOF gyroscope system.