Robust M-estimation-based maximum correntropy Kalman filter

Area of Science:

• Signal Processing
• Control Systems Engineering
• Statistical Inference

Background:

• Kalman filters are susceptible to impulsive noise, degrading performance.
• Information-theoretic learning (ITL) offers data-driven robustness but can diverge with small bandwidths.
• M-estimation provides statistical robustness independent of bandwidth.

Purpose of the Study:

• To develop a robust Kalman filter framework mitigating impulsive noise effects.
• To combine the strengths of M-estimation and ITL for enhanced filter performance.
• To extend the framework to nonlinear systems using unscented Kalman filtering.

Main Methods:

• A novel framework integrating M-estimation weighting with an ITL-based Kalman filter.
• Utilizing unscented Kalman filtering to adapt the algorithm for nonlinear dynamics.
• Employing Monte Carlo simulations for rigorous performance evaluation.

Main Results:

• The proposed framework effectively suppresses the divergence of ITL-based filters at low kernel bandwidths.
• Improved filter performance is achieved across a range of kernel bandwidths.
• Demonstrated robustness and effectiveness in handling impulsive noise, even in nonlinear scenarios.

Conclusions:

• The fused M-estimation and ITL Kalman filter offers superior robustness and stability against impulsive noise.
• The unscented Kalman filter extension successfully addresses nonlinear system challenges.
• This framework presents a significant advancement for state estimation in noisy environments.