Standard LSParameter Estimators Ensure Finite Convergence Time for Linear Regression Equations Under an Interval Excitation Assumption
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913887155126272 |
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| author | Ortega, Romeo Romero, Jose Guadalupe Aranovskiy, Stanislav Tao, Gang |
| author_facet | Ortega, Romeo Romero, Jose Guadalupe Aranovskiy, Stanislav Tao, Gang |
| contents | In this brief note we recall the little-known fact that, for linear regression equations (LRE) with intervally excited (IE) regressors, standard Least Square (LS) parameter estimators ensure finite convergence time (FCT) of the estimated parameters. The convergence time being equal to the time length needed to comply with the IE assumption. As is well-known, IE is necessary and sufficient for the identifiability of the LRE-hence, it is the weakest assumption for the on-or off-line solution of the parameter estimation problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08211 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Standard LSParameter Estimators Ensure Finite Convergence Time for Linear Regression Equations Under an Interval Excitation Assumption Ortega, Romeo Romero, Jose Guadalupe Aranovskiy, Stanislav Tao, Gang Systems and Control Statistics Theory In this brief note we recall the little-known fact that, for linear regression equations (LRE) with intervally excited (IE) regressors, standard Least Square (LS) parameter estimators ensure finite convergence time (FCT) of the estimated parameters. The convergence time being equal to the time length needed to comply with the IE assumption. As is well-known, IE is necessary and sufficient for the identifiability of the LRE-hence, it is the weakest assumption for the on-or off-line solution of the parameter estimation problem. |
| title | Standard LSParameter Estimators Ensure Finite Convergence Time for Linear Regression Equations Under an Interval Excitation Assumption |
| topic | Systems and Control Statistics Theory |
| url | https://arxiv.org/abs/2506.08211 |