Low-rank approximated Kalman filter using Oja's principal component flow for discrete-time linear systems
<|reference_start|>Low-rank approximated Kalman filter using Oja's principal component flow for discrete-time linear systems: The Kalman filter is indispensable for state estimation across diverse fields but faces computational challenges with higher dimensions. Approaches such as Riccati equation approximations aim to alleviate this complexity, yet ensuring properties like bounded errors remains challenging. Yamada and Ohki introduced low-rank Kalman-Bucy filters for continuous-time systems, ensuring bounded errors. This paper proposes a discrete-time counterpart of the low-rank filter and shows its system theoretic properties and conditions for bounded mean square error estimation. Numerical simulations show the effectiveness of the proposed method.<|reference_end|>
@article{tsuzuki2024low-rank,
    title={Low-rank approximated Kalman filter using Oja's principal component flow
  for discrete-time linear systems},
    author={Daiki Tsuzuki, Kentaro Ohki},
    journal={arXiv preprint arXiv:2407.05675},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.05675},
    primaryClass={math.OC cs.SY eess.SY}
}