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arxiv: 2605.18417 · v1 · pith:LKC2F5GKnew · submitted 2026-05-18 · 📡 eess.SP

A Fast Robust Adaptive filter using Improved Data-Reuse Method

Yi Peng , Haiquan Zhao , Jinhui Hu This is my paper

Pith reviewed 2026-05-19 23:58 UTC · model grok-4.3

classification 📡 eess.SP
keywords adaptive filterrobust algorithmdata reuseerrors-in-variablestotal least squaresacoustic echo cancellationonline censoringmean-square deviation
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The pith

The RTGA-IDROC algorithm merges total least squares with robust adaptation and improved data reuse to handle input noise while speeding early convergence.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes the RTGA-IDROC algorithm that unites the total least squares approach for errors-in-variables input noise with a robust generalized adaptive function suited to varied noise conditions. An improved data reuse technique reuses recent samples to accelerate the initial phase of adaptation without degrading the final steady-state accuracy. Online censoring limits the extra computation that reuse would otherwise impose, and the censoring threshold is adjusted for real-valued signals. Local stability analysis and a closed-form expression for steady-state mean-square deviation are derived. Simulations in system identification and acoustic echo cancellation confirm gains over prior robust methods.

Core claim

The RTGA-IDROC algorithm possesses the advantages of both the total least squares strategy and the robust generalized adaptive function. This algorithm not only effectively handles input noise under the errors-in-variables model but also achieves excellent performance across diverse noise environments. An improved data reuse method enables faster convergence in the early stages of iteration without compromising steady-state performance, with the added complexity controlled by an online censoring strategy.

What carries the argument

The improved data reuse method paired with online censoring, which reuses recent data samples for quicker early adaptation while selectively skipping updates to keep complexity low.

If this is right

  • The algorithm handles input noise under the errors-in-variables model more effectively than standard robust filters.
  • Faster early convergence occurs in diverse noise environments while steady-state error remains comparable.
  • Online censoring keeps the computational cost of data reuse manageable for real-time use.
  • Local stability holds and the steady-state mean-square deviation can be predicted analytically.
  • Superior tracking is observed in both system identification and acoustic echo cancellation tasks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same reuse-plus-censoring pattern could be applied to other adaptive algorithms that suffer slow initial convergence.
  • Adjusting the censoring threshold for real-valued signals hints at similar domain-specific tuning for complex-valued or vector cases.
  • The approach may reduce the number of samples needed for acceptable performance in resource-constrained devices.

Load-bearing premise

The noise and input statistics satisfy the modeling assumptions required for the local stability analysis and the derived steady-state mean-square deviation.

What would settle it

An experiment that injects input noise whose variance or correlation structure departs markedly from the assumed model and checks whether measured convergence rate or final MSD deviates from the theoretical prediction.

Figures

Figures reproduced from arXiv: 2605.18417 by Haiquan Zhao, Jinhui Hu, Yi Peng.

Figure 1
Figure 1. Figure 1: EIV model The remainder of this paper is organized as follows. Section II reviews the EIV model and presents the IDR method and real-domain OC strategy. Section III provides a detailed derivation of the RTGA-OC algorithm. Section IV presents a comprehensive analysis of the RTGA-OC algorithm, covering its local performance, mean stability, and steady-state behavior. The computational complexity of the RTGA-… view at source ↗
Figure 2
Figure 2. Figure 2: Graphical depiction of the underlying principle for the (a) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparative visualization of the RTGA function against [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Performance curves of the RTGA-IDROC algorithm under [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Performance comparison under Gaussian noise [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Performance comparison under Cases 2 to 5: (a) Case 2, (b) [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: AEC environment: (a) the schematic diagram of AEC model, [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: NMSD Performance comparison under: (a) Gaussian noise, [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: ERLE Performance comparison under: (a) Gaussian noise, [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Validation of the theoretical steady-state MSD with [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
read the original abstract

Adaptive filter in complex scenarios demands algorithms that integrate fast convergence, low complexity, and robust performance under diverse noise conditions. To address this challenge, we propose a online censoring robust total generalized adaptive filter using improved data-reused method (RTGA-IDROC) algorithm. The proposed RTGA variant possesses the advantages of both the total least squares (TLS) strategy and the robust generalized adaptive (RGA) function. This algorithm not only effectively handles input noise under the errors-in-variables (EIV) model but also achieves excellent performance across diverse noise environments. Furthermore, to meet the high demand for convergence speed in practical applications, an improved data reuse (IDR) method is introduced, enabling faster convergence in the early stages of iteration without compromising steady-state performance. The increased computational complexity brought by the IDR method is mitigated using the online censoring (OC) strategy. We also modify the OC threshold for real-valued algorithms, as the original threshold was defined for the complex domain. Beyond these algorithmic enhancements, a local stability analysis for the proposed algorithm is provided, and the theoretical steady-state mean-square deviation (MSD) is derived. Finally, simulation experiments in system identification and acoustic echo cancellation (AEC) scenarios validate the superior performance of the proposed algorithm.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes the RTGA-IDROC algorithm, a robust total generalized adaptive filter that combines total least squares (TLS) and robust generalized adaptive (RGA) strategies to handle input noise under the errors-in-variables (EIV) model. It introduces an improved data-reuse (IDR) method for faster early-stage convergence, mitigated by an online censoring (OC) strategy with a modified threshold for real-valued signals. The paper provides a local stability analysis and derives the theoretical steady-state mean-square deviation (MSD), with performance validated via simulations in system identification and acoustic echo cancellation (AEC) under diverse noise conditions including impulsive noise.

Significance. If the local stability analysis and MSD derivation hold under the tested conditions and the simulations demonstrate consistent superiority without hidden parameter tuning, the work would offer a practical advance in robust adaptive filtering by balancing convergence speed, robustness to EIV noise, and computational efficiency. The combination of theoretical MSD prediction with empirical results across noise types could inform algorithm design in real-world signal processing applications.

major comments (3)
  1. [§IV] §IV (Local Stability Analysis): The derivation relies on the standard independence assumption between the regressor vector and the noise process to close the expectations. For the alpha-stable and impulsive noise cases in the AEC simulations, this assumption is typically violated; the manuscript does not show that the derived stability conditions or MSD expression remain predictive when the input has heavy tails, which directly undercuts the broad robustness claim across 'diverse noise environments'.
  2. [§V] §V (Theoretical Steady-State MSD Derivation): The IDR and OC modifications introduce additional cross-terms in the weight-error recursion that are not explicitly bounded or averaged in the provided steps. Without showing how these terms are handled under the same moment conditions used for the base RGA/TLS analysis, it is unclear whether the closed-form MSD expression accurately matches the simulated curves for the full RTGA-IDROC algorithm.
  3. [Simulation Experiments] Simulation section (system identification and AEC experiments): The abstract states that simulations validate performance, yet the reported results lack error bars, explicit data-exclusion rules for the OC threshold, and direct overlays of the theoretical MSD curves versus empirical ones under impulsive noise. This prevents verification that the derived MSD supports the observed superiority without circular fitting to the simulation parameters.
minor comments (2)
  1. [Algorithm Description] The modification of the OC threshold for real-valued signals is mentioned but the exact formula and its derivation relative to the original complex-domain version are not shown; adding this would improve reproducibility.
  2. [Figures] Figure captions for convergence and MSD plots should explicitly state the noise distributions (e.g., Gaussian, alpha-stable with specific parameters) and the number of Monte Carlo runs used.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and indicate where the manuscript will be revised to improve clarity and rigor.

read point-by-point responses

  1. Referee: [§IV] §IV (Local Stability Analysis): The derivation relies on the standard independence assumption between the regressor vector and the noise process to close the expectations. For the alpha-stable and impulsive noise cases in the AEC simulations, this assumption is typically violated; the manuscript does not show that the derived stability conditions or MSD expression remain predictive when the input has heavy tails, which directly undercuts the broad robustness claim across 'diverse noise environments'.

    Authors: The independence assumption is standard in the adaptive filtering literature and is employed in the foundational analyses of both RGA and TLS algorithms. While it may not hold strictly for heavy-tailed distributions, the local stability conditions derived under this assumption still provide useful guidelines, and the extensive simulations in Section VI (including alpha-stable noise in AEC) empirically confirm stability and performance. We will revise the manuscript to explicitly state the assumption, discuss its limitations for heavy-tailed cases, and note that robustness is supported by simulation evidence rather than solely by the analysis. revision: partial

  2. Referee: [§V] §V (Theoretical Steady-State MSD Derivation): The IDR and OC modifications introduce additional cross-terms in the weight-error recursion that are not explicitly bounded or averaged in the provided steps. Without showing how these terms are handled under the same moment conditions used for the base RGA/TLS analysis, it is unclear whether the closed-form MSD expression accurately matches the simulated curves for the full RTGA-IDROC algorithm.

    Authors: The cross-terms introduced by IDR and OC are averaged using the same moment conditions as the base analysis, with the OC mechanism ensuring that outlier contributions remain bounded. To improve transparency, we will expand the derivation steps and add an appendix that explicitly shows the bounding and averaging of these additional terms under the stated assumptions. revision: yes

  3. Referee: Simulation section (system identification and AEC experiments): The abstract states that simulations validate performance, yet the reported results lack error bars, explicit data-exclusion rules for the OC threshold, and direct overlays of the theoretical MSD curves versus empirical ones under impulsive noise. This prevents verification that the derived MSD supports the observed superiority without circular fitting to the simulation parameters.

    Authors: We agree that these elements would strengthen verifiability. We will revise the simulation section to include error bars from multiple independent runs, explicitly state the data-exclusion rules and modified threshold for the real-valued OC strategy, and add overlays comparing the theoretical MSD expression against empirical curves, particularly for the impulsive and alpha-stable noise cases. revision: yes

Circularity Check

0 steps flagged

Derivation of stability analysis and MSD is self-contained under standard assumptions

full rationale

The paper presents the RTGA-IDROC algorithm as a combination of TLS and RGA strategies, augmented by IDR for convergence speed and OC for complexity control, with an explicit modification to the OC threshold for real-valued signals. The local stability analysis and theoretical steady-state MSD derivation are described as independent steps relying on typical adaptive-filtering modeling assumptions (e.g., independence between regressor and noise, bounded-moment conditions). These do not reduce by construction to fitted parameters, self-citations, or ansatzes imported from the authors' prior work. No equations are shown that equate a 'prediction' directly to a fit or that invoke a uniqueness theorem whose only support is a self-citation chain. Simulations in system identification and AEC provide separate empirical checks. The derivation chain therefore remains non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities beyond the standard modeling assumptions of errors-in-variables and noise statistics already present in the cited TLS and RGA literature.

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