Fitting of experimental data using a fractional Kalman-like observer

Area of Science:

• Control Systems Engineering
• Signal Processing
• Applied Mathematics

Background:

• Fractional calculus extends classical calculus, offering more accurate models for complex systems.
• Kalman filters are essential for state estimation in dynamic systems.
• Traditional Kalman filters are limited in modeling systems with memory effects.

Purpose of the Study:

• To introduce a fractional order Kalman filter (FOKF) for systems described by fractional differential equations.
• To enhance FOKF performance by optimizing its parameters using the cuckoo search (CS) algorithm.
• To validate the FOKF's effectiveness across various real-world and theoretical applications.

Main Methods:

• Developed a FOKF based on the Riemann-Liouville definition of fractional derivatives.
• Employed the cuckoo search (CS) optimization algorithm to tune observer order, fractional Riccati equation, and FOKF parameters.
• Utilized the Grünwald-Letnikov approximation for numerical computation of the FOKF.

Main Results:

• The proposed FOKF demonstrated effective state estimation for fractional-order systems.
• CS algorithm successfully optimized critical FOKF parameters, leading to improved accuracy.
• The FOKF showed reliable performance in diverse examples including brain activity and earthquake data.

Conclusions:

• The FOKF provides a powerful tool for analyzing and estimating states in fractional-order systems.
• Cuckoo search optimization significantly enhances the adaptability and precision of the FOKF.
• The FOKF's applicability is validated across multiple scientific and engineering domains.