Design Method for a Higher Order Extended Kalman Filter Based on Maximum Correlation Entropy and a Taylor Network...

Area of Science:

• Control Systems Engineering
• Signal Processing
• Statistical Inference

Background:

• Kalman filters are essential for state estimation in dynamic systems.
• Nonlinear systems with unknown statistical properties and modeling errors pose significant challenges.
• Existing methods often struggle with higher-order dynamics and complex error structures.

Purpose of the Study:

• To develop a new higher order extended Kalman filter design.
• To address nonlinear random dynamic systems with modeling errors and unknown statistical properties.
• To improve state estimation accuracy in challenging dynamic environments.

Main Methods:

• System identification using multidimensional Taylor networks to transform functions into polynomial models.
• Defining higher-order polynomials as implicit variables, creating a pseudolinear model.
• Integrating maximum correlation estimation with Kalman filtering for parameter and state estimation.
• Developing an extended dimensional linear state and measurement model.

Main Results:

• A novel higher order extended Kalman filter was successfully designed.
• The proposed method effectively models nonlinear random dynamic systems with unknown statistical properties.
• Digital simulations verified the effectiveness and improved performance of the new filter.

Conclusions:

• The developed higher order extended Kalman filter provides a robust solution for systems with modeling errors.
• Combining maximum correlation entropy and Taylor networks offers a powerful approach for nonlinear system identification and filtering.
• The proposed filter demonstrates significant potential for applications requiring accurate state estimation under uncertainty.