A robust gradient-adaptive lattice filtering algorithm

Sunming Zhang

doi:10.1016/j.sigpro.2026.110587

A robust gradient-adaptive lattice filtering algorithm

2026-03-06

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DOI：10.1016/j.sigpro.2026.110587

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Convergence rate and robustness are two important metrics for adaptive filters. This paper proposes a robust gradient-adaptive lattice (RGAL) filtering algorithm. It achieves parameter estimation via a two-stage update process. First, the reflection coefficients of the lattice structure are updated using the gradient descent method to achieve input signal decorrelation; then, the filter weights are updated by minimizing a linear cost function in the form of a rational fraction, enhancing the stability of the adaptive filter in impulsive noise environments. This robust cost function approaches to the mean-square error (MSE) for small errors, ensuring good convergence performance, while tending to an upper bound in the presence of large errors to effectively suppress outliers. By using the linear relationship between the backward prediction error and the original input signal of the lattice structure, we derive the stability condition for the step-size and the steady-state excess MSE (EMSE). Simulation results demonstrate that the developed RGAL achieves fast convergence rate and strong robustness against impulsive interference.

Keywords:

RGAL

adaptive filter

robustness

convergence rate

impulsive noise

A robust gradient-adaptive lattice filtering algorithm

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