RLS Framework with Segmentation of the Forgetting Profile and Low Rank Updates Article Swipe
This report describes a new regularization approach based on segmentation of the forgetting profile 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 divided in three segments, where the speed of estimation is ensured by the first segment, which employs rapid exponential forgetting of recent data.The second segment features a decline in the profile and marks the transition to the third segment, characterized by slow exponential forgetting to reduce the condition number of the information matrix using more distant data. 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. Recursive and computationally efficient algorithm with low rank updates based on new matrix inversion lemma for moving window associated with this regularization approach is developed. 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.
Related Topics
Concepts
Forgetting
Algorithm
Estimator
Segmentation
Redundancy (engineering)
Regularization (linguistics)
Lemma (botany)
A priori and a posteriori
Computer science
Offset (computer science)
Rank (graph theory)
Mathematics
Sliding window protocol
Matrix (chemical analysis)
Artificial intelligence
Pattern recognition (psychology)
Low-rank approximation
Image segmentation
Inversion (geology)
Exponential function
Estimation theory
Mathematical optimization
Reduction (mathematics)
Mean squared error
Metadata
- Type
- preprint
- Landing Page
- https://doi.org/10.48550/arxiv.2511.15273
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7106265839
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W7106265839Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2511.15273Digital Object Identifier
- Title
-
RLS Framework with Segmentation of the Forgetting Profile and Low Rank UpdatesWork title
- Type
-
preprintOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
-
2025-11-19Full publication date if available
- Authors
-
Stotsky, AlexanderList of authors in order
- Landing page
-
https://doi.org/10.48550/arxiv.2511.15273Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.48550/arxiv.2511.15273Direct OA link when available
- Concepts
-
Forgetting, Algorithm, Estimator, Segmentation, Redundancy (engineering), Regularization (linguistics), Lemma (botany), A priori and a posteriori, Computer science, Offset (computer science), Rank (graph theory), Mathematics, Sliding window protocol, Matrix (chemical analysis), Artificial intelligence, Pattern recognition (psychology), Low-rank approximation, Image segmentation, Inversion (geology), Exponential function, Estimation theory, Mathematical optimization, Reduction (mathematics), Mean squared errorTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
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