Joint iterative state and parameter estimation for bilinear systems with autoregressive noises via the data...

Area of Science:

• Control Systems Engineering
• Signal Processing
• Nonlinear System Identification

Background:

• Bilinear state-space systems present unique challenges in state and parameter estimation due to inherent nonlinearity.
• Accurate estimation is crucial for control, diagnostics, and modeling of these complex systems.
• Colored noise further complicates estimation, requiring advanced filtering techniques.

Purpose of the Study:

• To develop a robust iterative algorithm for the joint state and parameter estimation of bilinear state-space systems.
• To address the challenges posed by nonlinearity and colored noise in these systems.
• To enhance the accuracy and efficiency of estimation methods for bilinear systems.

Main Methods:

• Modification of Kalman filtering for state estimation in bilinear systems.
• Development of a Kalman filtering-based multi-innovation gradient-based iterative (KF-MIGI) algorithm for parameter estimation.
• Introduction of a data filtering-based KF-MIGI algorithm incorporating adaptive filtering to handle colored noise.

Main Results:

• The proposed KF-MIGI algorithm demonstrates effective joint state and parameter estimation.
• The data filtering-based approach significantly improves estimation accuracy in the presence of colored noise.
• Numerical examples validate the superior performance of the proposed iterative algorithm compared to standard gradient methods.

Conclusions:

• The novel iterative algorithm provides an effective solution for the joint state and parameter estimation of bilinear systems with colored noise.
• The integration of adaptive data filtering enhances robustness and accuracy, outperforming existing methods.
• This work contributes a valuable tool for researchers and engineers working with complex nonlinear dynamic systems.