State estimation for multiple clocks under anomalies using ℓ1-norm optimization

Masato Hirano, Kazumune Hashimoto, Fumimaru Nakagawa, Tetsuya Ido, Yuko Hanado, Shuichi Adachi

Research output: Contribution to journalArticle

Abstract

We investigate an estimation strategy for multiple clock systems, which is in particular resilient against clock anomalies. The clock anomalies, including frequency or phase jumps, can potentially degrade the estimation performance for multiple clock systems. While the conventional Kalman filter is known as one of the powerful methods for the estimation problem of multiple clock systems, we will show that it is vulnerable to the effects of clock anomalies. In this paper, we overcome this issue by employing an alternative approach to the Kalman filter, which is based on solving the ℓ1-norm optimization problem. The estimation method employs a multiple clock model that includes only phase states. Nevertheless, the approach is shown to have more resilience against clock anomalies than the Kalman filter, because the deviation of the state from the apriori estimate is evaluated based on the ℓ1-norm instead of the ℓ2-norm. Moreover, the approach is shown to be competitive with many reset algorithms, since it does neighter require special stability assumptions about the reference clock, nor require any threshold for detecting the anomalies. The usefulness of the proposed method is validated through several numerical examples using actual clock data.

Original languageEnglish
Article number025006
JournalMetrologia
Volume56
Issue number2
DOIs
Publication statusPublished - 2019 Mar 1

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State estimation
Clocks
Kalman filters

Keywords

  • clock anomalies
  • Kalman filter
  • multiple clocks system
  • ℓ-norm optimization

ASJC Scopus subject areas

  • Engineering(all)

Cite this

State estimation for multiple clocks under anomalies using ℓ1-norm optimization. / Hirano, Masato; Hashimoto, Kazumune; Nakagawa, Fumimaru; Ido, Tetsuya; Hanado, Yuko; Adachi, Shuichi.

In: Metrologia, Vol. 56, No. 2, 025006, 01.03.2019.

Research output: Contribution to journalArticle

Hirano, Masato ; Hashimoto, Kazumune ; Nakagawa, Fumimaru ; Ido, Tetsuya ; Hanado, Yuko ; Adachi, Shuichi. / State estimation for multiple clocks under anomalies using ℓ1-norm optimization. In: Metrologia. 2019 ; Vol. 56, No. 2.
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