Robust adaptive filtering using recursive weighted least squares with combined scale and variable forgetting factors

Area of Science:

• Signal Processing
• Adaptive Filtering
• Robust Estimation

Background:

• Non-stationary environments and impulsive noise pose significant challenges for parameter estimation.
• Traditional recursive weighted least squares methods struggle with time-varying parameters and non-Gaussian noise.
• Accurate estimation is crucial for system identification and control in dynamic systems.

Purpose of the Study:

• To propose a new adaptive robustified filter algorithm for recursive weighted least squares.
• To address the challenges of time-varying parameter estimation in non-stationary and impulsive noise environments.
• To simultaneously estimate filter parameters and noise variance.

Main Methods:

• Developed a recursive weighted least squares algorithm with combined scale and variable forgetting factors.
• Extended approximate maximum likelihood (M-estimation) for robust estimation of parameters and noise variance.
• Employed a variable forgetting factor adaptively calculated using a robustified prediction error criterion.

Main Results:

• The proposed algorithm effectively reduces the impact of impulsive noise in both stationary and non-stationary conditions.
• Simultaneous estimation of filter parameters and noise variance was achieved.
• Demonstrated feasibility in system identification using finite impulse response (FIR) filter applications.

Conclusions:

• The adaptive robustified filter provides a robust solution for time-varying parameter estimation under challenging noise conditions.
• The combined use of M-robust estimation and adaptive variable forgetting factors enhances estimation accuracy.
• The approach is suitable for practical applications in system identification and signal processing.