Recursive Least Squares

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Recursive least squares (RLS) estimates the parameters of a linear model incrementally, using each new observation without repeatedly solving the problem from scratch. It is used in adaptive filtering, sensor calibration, system identification, and tracking, where conditions or system dynamics may change over time. Common approaches adjust how new data is weighted and use regularization, covariance control, or block-diagonal approximations to improve adaptation, stability, or computational efficiency. A central challenge is balancing rapid tracking of change against reliable estimates when data are noisy, weakly informative, or costly to process.

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A Regularized Block Diagonal RLS Algorithm for Acoustic Echo Cancellation
Aug 21, 2026Ruibin Hou, Chenggang Zhang, Yufeng DiaoRecursive Least Squares
The College of Computer Science and Technology, Inner Mongolia Minzu University, Tongliao, 028000, Inner Mongolia, China.
The Condition-Number Barrier in Sparse Least Squares
Aug 3, 2026Honghao Lin, Vahab Mirrokni, David P. WoodruffRecursive Least Squares Sparse Recovery
Google Research, Carnegie Mellon University / Texas A&M University. · Google Research. · Google Research and Carnegie Mellon University.
From field-scale to large-scale spectral libraries: Tabular foundation models in soil spectroscopy
Aug 1, 2026Viacheslav Barkov, Jonas Schmidinger, Robin Gebbers +1Tabular Foundation Models Recursive Least Squares
Osnabrück University, Joint Lab Artificial Intelligence and Data Science, Osnabrück, Germany · Leibniz Institute for Agricultural Engineering and Bioeconomy (ATB), Department of Agromechatronics, Potsdam, Germany · German Research Center for Artificial Intelligence (DFKI), Cooperative and Autonomous Systems (CAS), Osnabrück, Germany
Dense Soft Weighting for Radar Ego-Velocity Estimation
Jul 29, 2026Atar Babgei, Chenyu Zhao, Michael Breza +1Recursive Least Squares Millimeter-Wave Radar
Imperial College London
Near-Optimal Learning of Gaussian Sobolev Operators
Jul 8, 2026Ben Adcock, Michael Griebel, Gregor MaierRecursive Least Squares Operator Learning
Department of Mathematics, Simon Fraser University, Burnaby BC, Canada · Institute for Numerical Simulation, University of Bonn, Bonn, Germany · Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Sankt Augustin, Germany
Covariance-Regulated Recursive Koopman Learning for Nonlinear Systems with Uncertain Time-Varying Dynamics
Jun 13, 2026Weibin Gu, Chen Yang, Lu Shi +1Online System Identification Recursive Least Squares
1Tsinghua University, PR China · 2China University of Petroleum-Beijing at Karamay, PR China · 3Xinchen Qihang Inc., PR China
Attitude-Aided Linear Calibration of Triaxial Accelerometers
Jun 4, 2026Yongqiang Yu, Tian Huang, Yipeng YangRecursive Least Squares Model Calibration
1Independent researcher · 2Harbin Institute of Technology
PLS in the Mirror of Self-Attention
May 27, 2026Jiangsheng, YouRecursive Least Squares Self-Attention
Jason
Online Nonstochastic Prediction: Logarithmic Regret via Predictive Online Least Squares
May 6, 2026Chih-Fan Pai, Yang ZhengRecursive Least Squares Regret Minimization
Department of Electrical and Computer Engineering, UC San Diego
Real-Time Non-Contact Force Compensation for Wrist-Mounted Force/Torque Sensors in Haptic-Enabled Robotic Surgery Training
Apr 26, 2026Walid Shaker, Mustafa Suphi ErdenRecursive Least Squares Haptic Feedback
School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK

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A Regularized Block Diagonal RLS Algorithm for Acoustic Echo Cancellation

Ruibin Hou, Chenggang Zhang, Yufeng Diao

The College of Computer Science and Technology, Inner Mongolia Minzu University, Tongliao, 028000, Inner Mongolia, China.

Recursive Least Squares

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While the recursive least square (RLS) algorithm is widely used in adaptive filtering applications like acoustic echo cancellation (AEC) due to its fast convergence rate, its high computational complexity severely limit its practical deployment for long filters. In this paper, a regularized block-diagonal RLS (RBD-RLS) algorithm is proposed to address these challenges. By approximating the inverse covariance matrix as a block-diagonal structure, RBD-RLS simplifies the update process into independent parallel computations of sub-blocks, effectively reducing the computational complexity. Additionally, Tikhonov regularization is applied to each sub-blocks for enhance numerical stability. A series of experimental results demonstrate that RBD-RLS maintains good convergence while significantly reducing computational complexity. Moreover, it still exhibits relative robustness in real-world scenarios.