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PreprintCC BY 4.0arXiv

On the Oja-Flow-Based Low-Rank Approximation of Kalman-Bucy Filters for Linear Time-Varying Systems

  • Kentaro Ohki
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Abstract

This paper studies a low-rank Kalman-Bucy filtering framework for linear time-varying systems through the tracking analysis of Oja's principal component flow. Under structured assumptions on the eigenspaces and their time variation, we show that the Oja flow can remain in a neighborhood of the time-varying dominant subspace by tuning a parameter of the flow, rather than tracking it exactly. These restrictive assumptions identify a tractable class of linear time-varying systems and provide a theoretical basis for low-rank filtering, as illustrated by a numerical experiment.

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Cite

BibTeXRIS
BibTeX
@misc{ohki2026ojaflowbased,
  title = {{On the Oja-Flow-Based Low-Rank Approximation of Kalman-Bucy Filters for Linear Time-Varying Systems}},
  author = {Kentaro Ohki},
  howpublished = {arXiv},
  year = {2026},
  month = jul,
  doi = {10.48550/arxiv.2607.29034},
  eprint = {2607.29034},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.29034},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the Oja-Flow-Based Low-Rank Approximation of Kalman-Bucy Filters for Linear Time-Varying Systems
AU  - Kentaro Ohki
PY  - 2026
DA  - 2026/07/31
PB  - arXiv
DO  - 10.48550/arxiv.2607.29034
UR  - https://arxiv.org/abs/2607.29034
AB  - This paper studies a low-rank Kalman-Bucy filtering framework for linear time-varying systems through the tracking analysis of Oja's principal component flow. Under structured assumptions on the eigenspaces and their time variation, we show that the Oja flow can remain in a neighborhood of the time-varying dominant subspace by tuning a parameter of the flow, rather than tracking it exactly. These restrictive assumptions identify a tractable class of linear time-varying systems and provide a theoretical basis for low-rank filtering, as illustrated by a numerical experiment.
ER  -