Identification of the ARX Model with Random Impulse Noise Based on Forgetting Factor Multi-error Information Entropy

Area of Science:

• Control Systems
• Signal Processing
• Information Theory

Background:

• Entropy is increasingly used in system identification.
• Traditional stochastic gradient algorithms converge slowly.
• Mean square error algorithms require more computation.

Purpose of the Study:

• Propose a novel stochastic gradient algorithm based on minimum Shannon entropy.
• Enhance the convergence speed of traditional stochastic gradient algorithms.
• Improve the accuracy of parameter estimation in system identification.

Main Methods:

• Implemented a multi-error method by stacking errors into a vector.
• Integrated a forgetting factor to adjust the step size.
• Applied the algorithm to estimate parameters of an ARX model with random impulse noise.

Main Results:

• The proposed algorithm demonstrates faster convergence than traditional gradient methods.
• Achieved more accurate parameter estimates compared to the traditional gradient algorithm.
• Validated through numerical simulations and a case study.

Conclusions:

• The novel minimum Shannon entropy-based stochastic gradient algorithm is effective.
• The integration of a multi-error method and forgetting factor accelerates convergence.
• The algorithm provides superior accuracy for ARX model parameter estimation in noisy environments.