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Peer-reviewedCC BY-NC 4.0International Journal of Adaptive Control and Signal Processing

On the bias distribution of pseudo-linear regression algorithms for recursive identification

  • Bernard Vau
  • Henri Bourlés
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Abstract

This paper presents a detailed analysis of the asymptotic bias distribution of recursive identification schemes based on Pseudo-Linear Regression. As shown in a previous article, the criterion asymptotically minimized is the variance of a non-measurable signal (called the equivalent prediction error) when the system to be identified is in the model set. We prove a similar but slightly weaker (however still relevant) result when the true system does not belong to the model set, provided that the resulting bias remains small, in a sense that is specified in the paper. It is also shown that the open-loop output error algorithm obtained with Pseudo-Linear Regression provides a limit model which has the same bias distribution as the one obtained by the Instrumental Variable algorithm with auxiliary model.

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Cite

BibTeXRIS
BibTeX
@article{vau2026bias,
  title = {{On the bias distribution of pseudo-linear regression algorithms for recursive identification}},
  author = {Bernard Vau and Henri Bourlés},
  journal = {International Journal of Adaptive Control and Signal Processing},
  year = {2026},
  month = oct,
  doi = {10.1002/acs.70155},
  url = {https://hal.science/hal-05768069v1},
  note = {CC BY-NC 4.0},
}
RIS
TY  - JOUR
TI  - On the bias distribution of pseudo-linear regression algorithms for recursive identification
AU  - Bernard Vau
AU  - Henri Bourlés
PY  - 2026
DA  - 2026/10/14
JO  - International Journal of Adaptive Control and Signal Processing
DO  - 10.1002/acs.70155
UR  - https://hal.science/hal-05768069v1
AB  - This paper presents a detailed analysis of the asymptotic bias distribution of recursive identification schemes based on Pseudo-Linear Regression. As shown in a previous article, the criterion asymptotically minimized is the variance of a non-measurable signal (called the equivalent prediction error) when the system to be identified is in the model set. We prove a similar but slightly weaker (however still relevant) result when the true system does not belong to the model set, provided that the resulting bias remains small, in a sense that is specified in the paper. It is also shown that the open-loop output error algorithm obtained with Pseudo-Linear Regression provides a limit model which has the same bias distribution as the one obtained by the Instrumental Variable algorithm with auxiliary model.
SN  - 0890-6327
SN  - 1099-1115
ER  -