An innovative parameter estimation for fractional order systems with impulse noise

Area of Science:

• Control Systems Engineering
• Signal Processing
• Nonlinear Dynamics

Background:

• Parameter estimation for fractional order systems is challenging, especially with impulse noise.
• Conventional methods like least squares are sensitive to outliers and noise.

Purpose of the Study:

• To develop a robust parameter estimation method for fractional order linear systems corrupted by impulse noise.
• To improve the accuracy and reliability of parameter estimation in noisy environments.

Main Methods:

• Utilized an approximate least absolute error (ALAE) objective function to mitigate impulse noise effects.
• Designed a novel parameter estimation approach combining stochastic gradient descent, a fractional order parameter update law, and the ALAE criterion.
• Incorporated a fractional order parameter update law for enhanced algorithmic convergence and flexibility.

Main Results:

• The proposed method demonstrates improved estimation accuracy compared to conventional techniques.
• Enhanced robustness against impulse noise was achieved through the ALAE function.
• The fractional order parameter update law facilitated a wider selection range for the update order and smoother algorithm convergence.

Conclusions:

• The novel parameter estimation approach offers superior performance and robustness for fractional order linear systems in the presence of impulse noise.
• Mathematical analysis and numerical examples validate the effectiveness of the proposed method.