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Robust Gradient Estimation Algorithm for a Stochastic System with Colored Noise
Wentao Liu,Weili Xiong 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.2
This paper studies the parameter estimation algorithms of a finite impulse response system with colored noise. To suppress the negative effects of the colored noises, a novel gradient-based algorithm is developed by means of the cost function of the continuous mixed p-norm (CMPN). It combines the p-norms for 1 6 p 6 2, which control the proportions of the error norms and generate an adjustable gain to adapt the data quality. Moreover, to improve the convergence rate, a CMPN multi-innovation gradient recursive algorithm is derived through expanding the innovation scalar to the innovation vector. Finally, two examples are given to demonstrate the validity of the proposed algorithms.
Wentao Liu,Weili Xiong 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.1
This paper discusses the parameter estimation problems for the output-error moving average (OEMA) systems under stochastic environments. The estimation problems with unknown inner variables and unmeasurable noise terms existed in the information vector are solved by the auxiliary model framework. Meanwhile, the algorithms utilize the continues mixed p-norm (CMPN) method to control the proportions of the error norms, which take into account each p-norm of errors for 1 6 p 6 2. To improve the identification accuracy further, a multiinnovation CMPN optimization algorithm is developed by expanding the scalar innovation to the innovation vector. The proposed optimal algorithms offer faster tracking speed and can obtain higher parameter estimation accuracy for both stochastic white noise and α-stable noise. Two examples of identification of OEMA systems are given to validate the theoretical analysis.