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arxiv: 2510.04839 · v2 · submitted 2025-10-06 · 💻 cs.RO

TAG-K: Tail-Averaged Greedy Kaczmarz for Computationally Efficient and Performant Online Inertial Parameter Estimation

Shuo Sha , Anupam Bhakta , Zhenyuan Jiang , Kevin Qiu , Ishaan Mahajan , Gabriel Bravo-Palacios , Brian Plancher This is my paper

Pith reviewed 2026-05-18 09:25 UTC · model grok-4.3

classification 💻 cs.RO
keywords inertial parameter estimationKaczmarz methodgreedy row selectiontail averagingonline estimationrobotic controlquadrotor trackingembedded systems
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The pith

TAG-K extends the Kaczmarz method with greedy selection and tail averaging for faster online inertial parameter estimation in robots.

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

The paper presents TAG-K as a lightweight variant of the Kaczmarz method for accurate online estimation of inertial parameters. Traditional methods often cannot track sudden changes or demand too much computation for embedded hardware. TAG-K selects informative rows greedily to speed convergence and applies tail averaging to stabilize results against noise and inconsistent data. This combination preserves the simple per-step cost of basic Kaczmarz while improving adaptation speed and accuracy. The approach matters for robots that must update to new payloads or wear in real time without high compute demands.

Core claim

TAG-K is a lightweight extension of the Kaczmarz method that combines greedy randomized row selection for rapid convergence with tail averaging for robustness under noise and inconsistency. This design enables fast, stable parameter adaptation while retaining the low per-iteration complexity inherent to the Kaczmarz framework.

What carries the argument

The TAG-K update that performs greedy randomized row selection followed by tail averaging of recent iterates to produce each new inertial parameter estimate.

If this is right

  • Delivers 1.5x-1.9x faster solve times on laptop-class CPUs.
  • Delivers 4.8x-20.7x faster solve times on embedded microcontrollers.
  • Improves robustness to measurement noise compared with standard recursive least squares and Kalman filters.
  • Reduces estimation error by 25 percent in the tested scenarios.
  • Yields nearly 2x better end-to-end tracking performance in quadrotor flight tasks.

Where Pith is reading between the lines

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

  • The same selection-plus-averaging pattern could transfer to other online regression tasks that run on microcontrollers.
  • Higher update rates become feasible in tight control loops because each iteration stays cheap.
  • The noise-handling benefit may extend to robots with lower-quality sensors than those used in the quadrotor tests.

Load-bearing premise

The linear regression model for inertial parameters remains valid and the robot motion supplies enough persistent excitation for the updates to converge despite noise.

What would settle it

A controlled test on a quadrotor where excitation drops below the level needed for identifiability while sensor noise is present, checking whether estimation error rises sharply or tracking performance collapses.

Figures

Figures reproduced from arXiv: 2510.04839 by Anupam Bhakta, Brian Plancher, Gabriel Bravo-Palacios, Ishaan Mahajan, Kevin Qiu, Shuo Sha, Zhenyuan Jiang.

Figure 1
Figure 1. Figure 1: Closed-loop online estimation with fast control and [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Upper Left: Example single trial of a quadrotor tracking a figure-8 reference trajectory (dotted line) with unknown payload add/drop events (gray rings). Lower Left: Prediction error timeseries comparing TAG-K with baseline estimators averages over 2,000 trials per estimator. Grey shaded regions denote payload add/drop events, highlighting TAG-K’s rapid and consistent re-convergence after disturbances. Low… view at source ↗
Figure 3
Figure 3. Figure 3: Ablation studies across algorithmic variants demonstrate the performance derived from our algorithmic design. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

Accurate online inertial parameter estimation is essential for adaptive robotic control, enabling real-time adjustment to payload changes, environmental interactions, and system wear. Traditional methods often struggle to track abrupt parameter shifts or incur high computational costs, limiting their effectiveness in dynamic environments and for computationally constrained robotic systems. We introduce TAG-K, a lightweight extension of the Kaczmarz method that combines greedy randomized row selection for rapid convergence with tail averaging for robustness under noise and inconsistency. This design enables fast, stable parameter adaptation while retaining the low per-iteration complexity inherent to the Kaczmarz framework. We evaluate TAG-K in synthetic benchmarks and quadrotor tracking tasks against RLS, KF, and other Kaczmarz variants. TAG-K achieves 1.5x-1.9x faster solve times on laptop-class CPUs and 4.8x-20.7x faster solve times on embedded microcontrollers. More importantly, these speedups are paired with improved robustness to measurement noise and a 25% reduction in estimation error, leading to nearly 2x better end-to-end tracking performance. Website, documentation, and code available at: https://a2r-lab.org/TAG-K/.

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

2 major / 2 minor

Summary. The paper proposes TAG-K, a lightweight extension of the Kaczmarz method for online inertial parameter estimation that integrates greedy randomized row selection for rapid convergence with tail averaging for robustness to noise and inconsistency. It claims 1.5x-1.9x faster solve times on CPUs and 4.8x-20.7x on microcontrollers, plus a 25% reduction in estimation error and nearly 2x better end-to-end tracking performance versus RLS, KF, and other Kaczmarz variants, evaluated on synthetic benchmarks and quadrotor tracking tasks.

Significance. If the empirical results hold under fuller validation, the work offers a computationally efficient alternative for real-time adaptive control on resource-constrained platforms, addressing a practical gap in handling dynamic payloads and noise. The low per-iteration complexity and reported speedups on embedded hardware are strengths that could enable broader deployment of online estimation in robotics.

major comments (2)
  1. [Abstract and Evaluation] Abstract and §4 (Evaluation): The central motivation is fast adaptation to abrupt parameter shifts, yet no post-change convergence times, adaptation latency metrics, or forgetting-factor equivalents are reported for the quadrotor payload-jump experiments. Tail averaging inherently smooths iterates, so it is unclear whether the claimed robustness gains preserve the tracking agility needed to support the abstract's performance claims.
  2. [Evaluation] §4 and results tables: The reported speedups and 25% error reduction lack accompanying statistical tests, trial counts, or variance measures. Without these, the evidence for consistent superiority over baselines remains moderate and does not fully substantiate the load-bearing performance assertions.
minor comments (2)
  1. [Method] Ensure all algorithmic parameters (e.g., tail length, greedy selection probability) are explicitly defined with default values in the method section for reproducibility.
  2. [Figures] Figure captions for timing and error plots should include axis scales, units, and the exact number of Monte Carlo runs used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the major comments point by point below and will incorporate revisions to strengthen the manuscript where appropriate.

read point-by-point responses

  1. Referee: [Abstract and Evaluation] Abstract and §4 (Evaluation): The central motivation is fast adaptation to abrupt parameter shifts, yet no post-change convergence times, adaptation latency metrics, or forgetting-factor equivalents are reported for the quadrotor payload-jump experiments. Tail averaging inherently smooths iterates, so it is unclear whether the claimed robustness gains preserve the tracking agility needed to support the abstract's performance claims.

    Authors: The quadrotor payload-jump experiments were designed to evaluate adaptation to abrupt shifts, with the reported nearly 2x improvement in end-to-end tracking performance serving as evidence that TAG-K retains sufficient agility. The combination of greedy row selection and tail averaging is intended to balance rapid convergence with noise robustness without excessive smoothing. That said, we agree that explicit post-change convergence times, adaptation latency metrics, and direct comparisons to forgetting-factor equivalents in RLS/KF would provide clearer quantification. In the revised manuscript we will add these metrics to §4. revision: yes

  2. Referee: [Evaluation] §4 and results tables: The reported speedups and 25% error reduction lack accompanying statistical tests, trial counts, or variance measures. Without these, the evidence for consistent superiority over baselines remains moderate and does not fully substantiate the load-bearing performance assertions.

    Authors: We acknowledge that the current results presentation would be strengthened by explicit statistical support. The evaluations were performed over multiple independent trials on both synthetic and hardware platforms, but trial counts, variance, and formal statistical tests were not reported in the tables. In the revision we will add the number of trials, standard deviations or inter-quartile ranges, and appropriate statistical comparisons (e.g., paired t-tests or Wilcoxon signed-rank tests) to substantiate the speedups and error reductions. revision: yes

Circularity Check

0 steps flagged

No circularity in algorithmic proposal or empirical claims

full rationale

The paper presents TAG-K as a lightweight algorithmic extension of the Kaczmarz method that adds greedy randomized row selection and tail averaging for online inertial parameter estimation. All performance claims (solve-time speedups, noise robustness, 25% error reduction, and tracking improvements) are established through direct empirical comparison against RLS, KF, and other Kaczmarz variants on synthetic benchmarks and quadrotor experiments. No derivation, equation, or first-principles result is shown to reduce to a fitted quantity or prior self-citation by construction; the central contribution is an independent algorithmic design whose validity rests on external experimental benchmarks rather than internal redefinition or self-referential justification.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are stated. The method inherits standard assumptions of linear regression models for inertial parameters and the convergence properties of Kaczmarz-type solvers.

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