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

2025-10-06

AI Summary

Traditional online inertia parameter estimation methods—such as Recursive Least Squares (RLS) and Kalman Filtering (KF)—exhibit poor tracking performance under abrupt dynamical changes and impose high computational overhead, rendering them unsuitable for resource-constrained robotic platforms. To address these limitations, this paper proposes a lightweight, highly robust iterative online estimation algorithm grounded in the Kaczmarz framework. Our method innovatively integrates greedy randomized row selection with a tail-averaging mechanism, achieving rapid convergence and strong noise resilience while maintaining low per-iteration complexity—O(n). Evaluated on synthetic data and real-world quadrotor flight experiments, the proposed approach accelerates computation by 1.5–20.7× over RLS and KF, reduces estimation error by 25%, and nearly doubles end-to-end tracking accuracy. These improvements significantly enhance real-time performance and stability in dynamic environments.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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 such as Recursive Least Squares (RLS) and the Kalman Filter (KF) often struggle to track abrupt parameter shifts or incur high computational costs, limiting their effectiveness in dynamic environments and for computationally constrained robotic systems. As such, 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 resilience to measurement noise and a 25% reduction in estimation error, leading to nearly 2x better end-to-end tracking performance.

Problem

• Online inertial parameter estimation for adaptive robotic control
• Overcoming computational limitations of traditional estimation methods
• Achieving fast stable parameter adaptation in dynamic environments

Innovation

• Greedy randomized row selection for rapid convergence
• Tail averaging for robustness under noise
• Low per-iteration complexity Kaczmarz framework