Robust multi-innovation full parameter identification for separable fractional-order systems based on online measurements

Abstract

In fractional-order systems, the simultaneous estimation of system parameters and the differential order is challenging, especially when measurements contain outliers, which may significantly degrade the identification performance. Currently, although robust principal component analysis methods can separate outliers, they are essentially offline batch processing techniques and cannot simultaneously perform online matrix recovery and parameter estimation. This results in a key limitation of these methods, making them unsuitable for real-time applications. Thus, we propose an online robust parameter estimation framework for fractional-order systems. In this framework, the outlier detection problem is converted into a matrix decomposition problem, in which the information matrix is recovered online by formulating a Sylvester equation. This proposed framework can automatically detect outliers in real-time and adaptively estimate parameters simultaneously. Moreover, this framework incorporates a multi-innovation strategy to fully utilize historical data, and its sliding window mechanism ensures the feasibility of real-time data updates. Subsequently, a robust multi-innovation gradient-based iterative (RMIGI) algorithm is derived for simultaneous full parameter estimation. Finally, the effectiveness and superiority of the RMIGI method are demonstrated through Monte Carlo simulations and a circuit case study, supported by a theoretical analysis that proves its convergence via a contraction inequality and characterizes its computational complexity.