The week's pick
Random Articles
Reseach Article
Accelerating with Low Rank Updates: RLS Framework for Segmentation of the Forgetting Profile
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 187 - Number 54 |
| Year of Publication: 2025 |
| Authors: Alexander Stotsky |
10.5120/ijca2025925940
|
Alexander Stotsky . Accelerating with Low Rank Updates: RLS Framework for Segmentation of the Forgetting Profile. International Journal of Computer Applications. 187, 54 ( Nov 2025), 1-5. DOI=10.5120/ijca2025925940
Abstract
This paper introduces a novel regularization method that leverages segmentation of the forgetting profile for more robust modeling of data aging in sliding window least squares estimation. Each segment is designed to enforce specific desirable properties of the estimator such as rapidity, desired condition number of the information matrix, accuracy, numerical stability, etc. The forgetting profile is structured in three segments, where the first segment enables rapid estimation via fast exponential forgetting of recent data. The second segment features a decline in the profile and marks the transition to the third segment, which is characterized by slow exponential forgetting aimed at reducing the condition number of the information matrix using earlier measurements within the moving window. Condition number reduction mitigates error propagation, thereby enhancing accuracy and stability. This approach facilitates the incorporation of a priori information regarding signal characteristics (i.e., the expected behavior of the signal) into the estimator. The main contribution of this paper is the framework for development of a new family of recursive, computationally efficient algorithms with low rank updates, based on a novel matrix inversion lemma for moving windows and tailored to this regularization approach. New algorithms significantly improve the approximation accuracy of low resolution daily temperature measurements obtained at the Stockholm Old Astronomical Observatory, thereby enhancing the reliability of temperature predictions.
References
- Fomin V., Fradkov A. & Yakubovich V. (1981). Adaptive control of the dynamic plants. Nauka, Moscow, in Russian.
- Ljung, L. & Söderström T. (1983). Theory and practice of recursive identification. The MIT press series in signal processing, optimization, and control. https://mitpress.mit.edu/9780262620581/ theory-and-practice-of-recursive-identification/
- Stotsky A.(2023). Recursive estimation in the moving window: efficient detection of the distortions in the grids with desired accuracy. Journal of Advances in Applied and Computational Mathematics, 9, 181-191. https://doi.org/10. 15377/2409-5761.2022.09.14
- Stotsky A. (2024). Kaczmarz projection algorithms with rank two gain update. Journal of Signal Processing Systems, 96(4-5), 327-332. https://doi.org/10.1007/ s11265-024-01915-w
- Stotsky A. (2025). Recursive least squares estimation with rank two updates. Automatika, 66 (4), 619-624 . https:// doi.org/10.1080/00051144.2025.2517431
- Pillonetto G., Dinuzzo F., Chen T., De Nicolao G., & Ljung, L. (2014). Kernel methods in system identification, machine learning and function estimation: A survey. Automatica, 50(3),657-682. https://doi.org/10.1016/j. automatica.2014.01.001.
- Lai B. & Bernstein D. (2024). Generalized forgetting recursive least squares: stability and robustness guarantees. IEEE Transactions on Automatic Control, 69(11), 7646 - 7661. https://doi.org/10.1109/TAC.2024.3394351
- Maouche, K. and Slock, D. (1995). Performance analysis and FTF version of the generalized sliding window recursive least-squares (GSWRLS) algorithm. In: Proceedings of the Asilomar Conference on Signals, Systems and Computers, Vol. 1, Pacific Grove, USA, November 1995, pp.685–689. https://ieeexplore.ieee.org/document/540637
- Papaodysseus C., Koukoutsis E. , Halkias C. & Roussopoulos G. (1998). A parallelizable recursive least squares algorithm for adaptive filtering with very good tracking properties. International Journal of Computer Mathematics, 67(3-4), 275-292. https://doi.org/10.1080/00207169808804665
- Bernstein D.S. (2018). Scalar, vector, and matrix mathematics: Theory, facts, and formulas. Revised and expanded ed. Princeton: Princeton University Press. https://doi.org/ 10.2307/j.ctvc7729t
- Zhang Q. (2000). Some implementation aspects of sliding window least squares algorithms. In: Proceedings of the 12th IFAC Symposium on System Identification (SYSID 2000), Santa Barbara, California, USA, 21–23 June 2000, pp.763–768. https://doi.org/10.1016/S1474-6670(17)39844-0
- Moberg A. (2019). Stockholm Historical Weather Observations — Daily mean air temperatures since 1756. Dataset version 1. Bolin Centre Database, https://bolin.su.se/ data/stockholm-historical-temps-daily.
- Stotsky A. (2025). Detection and control of credit card fraud attacks in sliding window with exponential forgetting. International Journal of Computer Applications (0975 - 8887), 186(74),9–15. https://doi.org/10.5120/ ijca2025924619
- Stotsky A. (2022). Recursive versus nonrecursive Richardson algorithms: systematic overview, unified frameworks and application to electric grid power quality monitoring, Automatika, 63(2),328-337. https://doi.org/10.1080/ 00051144.2022.2039989
Index Terms
Keywords