An Extended Kalman Filter with Remainder Terms and Correlation Compensation for Nonlinear State Monitoring and Soft...

Area of Science:

• Control Systems Engineering
• Signal Processing
• Data Science

Background:

• Nonlinear state monitoring and soft sensing are crucial in networked systems for real-time variable reconstruction.
• The Extended Kalman Filter (EKF) is a standard method but suffers from accuracy degradation and potential divergence due to neglecting higher-order terms in linearization.
• Existing methods often ignore the statistical impact of remainder terms and error correlations, limiting performance.

Purpose of the Study:

• To develop an improved nonlinear estimation method that addresses the limitations of the conventional Extended Kalman Filter (EKF).
• To enhance the accuracy and robustness of state estimation in systems with strong nonlinearities.
• To incorporate higher-order information and error correlations into the filtering process.

Main Methods:

• Proposes the Remainder Error Extended Kalman Filter (REKF), which replaces neglected higher-order Taylor expansion terms with remainder terms.
• Utilizes least squares for incremental identification of these remainder terms to refine the EKF update.
• Constructs a higher-order filtering framework for joint state and remainder-related variable estimation, considering induced error correlations.

Main Results:

• Numerical simulations on nonlinear models show the proposed REKF outperforms the conventional EKF in estimation performance.
• The REKF effectively improves nonlinear state estimation accuracy, particularly for state monitoring and soft sensing applications.
• Accounting for higher-order remainder information and correlations enhances filtering stability and precision.

Conclusions:

• The REKF offers a significant advancement over the traditional EKF for nonlinear estimation tasks.
• This method is particularly beneficial for networked sensing systems facing challenges from strong state evolution nonlinearity.
• The REKF provides a more accurate and reliable approach to state monitoring and soft sensing.