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Covariance Analysis of Subspace Identification Methods

Research Project

Project/Area Number 15K06146
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Control engineering/System engineering
Research InstitutionThe University of Tokushima

Principal Investigator

IKEDA Kenji  徳島大学, 大学院社会産業理工学研究部(理工学域), 准教授 (80232180)

Project Period (FY) 2015-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords部分空間同定法 / 一致推定値 / イノベーションモデル / 分散解析 / 半正定値計画問題 / gap (開き) / カルマンフィルタ / gap / 開き
Outline of Final Research Achievements

Magnitude of the estimation error of the system matrices in subspace identification methods are considered. First, an explicit formulation of the estimation error in PO-MOESP methods are derived. This enables us to evaluate the covariance of the estimate. However, Kalman gain and the covariance of the innovations process are required for the covariance of of the estimate. As far as the author's knowledge, there are no consistent estimates of them. The problem of estimating them is formulated by using linear matrix inequality and the consistent estimates are obtained.

Academic Significance and Societal Importance of the Research Achievements

部分空間の間の開き(gap)という概念を用いてシステム行列の推定誤差の公式を求めた。これにより、PO-MOESP法はシステム行列の一致推定値を与えることを示した。また、カルマンゲインとイノベーション過程の共分散行列を求める問題を半正定値計画問題として定式化できることを示した。これにより、データ長に比例した計算量でイノベーションモデルの一致推定値を得ることが可能となった。また、システム行列の推定値の共分散行列も計算できるため、様々な解析に応用可能である。

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (22 results)

All 2019 2018 2017 2016 2015

All Journal Article (1 results) (of which Peer Reviewed: 1 results,  Open Access: 1 results) Presentation (21 results) (of which Int'l Joint Research: 10 results)

  • [Journal Article] Closed-loop subspace identification taking initial state into account2018

    • Author(s)
      Hideyuki Tanaka and Kenji Ikeda
    • Journal Title

      IFAC-PapersOnLine

      Volume: 51 Issue: 15 Pages: 604-609

    • DOI

      10.1016/j.ifacol.2018.09.229

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] 不可到達な確率系をもつ安定限界なシステムの同定2019

    • Author(s)
      池田建司,田中秀幸
    • Organizer
      第6回 制御部門マルチシンポジウム
    • Related Report
      2018 Annual Research Report
  • [Presentation] On the Uniqueness of Spectral Densiti Function in an SDP Problem for the Estimation of Innovations Model2018

    • Author(s)
      Kenji Ikeda, Hideyuki Tanaka
    • Organizer
      SICE Annual Conference 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A closed-loop subspace identification algorithm based on finite-interval realization2018

    • Author(s)
      Hideyuki Tanaka, Kenji Ikeda
    • Organizer
      SICE Annual Conference 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 初期状態を考慮した部分空間同定法のためのもう一つの半正定値計画問題2018

    • Author(s)
      池田建司,田中秀幸
    • Organizer
      第61回自動制御連合講演会
    • Related Report
      2018 Annual Research Report
  • [Presentation] イノベーションモデルの一致推定のための解法の局所収束性2017

    • Author(s)
      池田建司
    • Organizer
      第4回制御部門マルチシンポジウム
    • Place of Presentation
      岡山大学 (岡山市)
    • Year and Date
      2017-03-06
    • Related Report
      2016 Research-status Report
  • [Presentation] Identification of Linear Stochastic Systems Taking Initial State into Account2017

    • Author(s)
      Hideyuki Tanaka and Kenji Ikeda
    • Organizer
      SICE Annual Conference 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] An LMI Problem for Consistent Estimate of Innovations Model2017

    • Author(s)
      Kenji Ikeda
    • Organizer
      SICE Annual Conference 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] An SDP Formulation for Consistent Estimate of Innovations Model2017

    • Author(s)
      Kenji Ikeda and Hideyuki Tanaka
    • Organizer
      The 2017 Asian Control Conference
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 変数変換を用いたイノベーションモデル推定問題の定式化2017

    • Author(s)
      池田 建司, 田中 秀幸
    • Organizer
      第60回自動制御連合講演会
    • Related Report
      2017 Research-status Report
  • [Presentation] 半正定値計画問題により初期状態を考慮した確率部分空間同定法2017

    • Author(s)
      田中 秀幸, 池田 建司
    • Organizer
      第60回自動制御連合講演会
    • Related Report
      2017 Research-status Report
  • [Presentation] イノベーションモデル推定のためのSDP問題における可同定性について2017

    • Author(s)
      池田 建司, 田中 秀幸
    • Organizer
      第5回 制御部門マルチシンポジウム
    • Related Report
      2017 Research-status Report
  • [Presentation] Cholesky Factor を用いたKalmanゲインの推定手法の収束性について2016

    • Author(s)
      池田建司
    • Organizer
      第59回自動制御連合講演会
    • Place of Presentation
      北九州国際会議場 (北九州市)
    • Year and Date
      2016-11-10
    • Related Report
      2016 Research-status Report
  • [Presentation] Consistent Estimates of Kalman Gain and the Covariance of the Innovations Process2016

    • Author(s)
      Kenji Ikeda
    • Organizer
      SICE Annual Conference 2017
    • Place of Presentation
      つくば国際会議場 (つくば市)
    • Year and Date
      2016-09-20
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Consistent Estimate of Innovations Model2016

    • Author(s)
      Kenji Ikeda
    • Organizer
      12th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing
    • Place of Presentation
      Eindhoven (The Netherlands)
    • Year and Date
      2016-06-29
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Cholesky 分解を用いた Kalman ゲインの一致推定2016

    • Author(s)
      池田建司
    • Organizer
      第60回システム制御情報学会研究発表講演会
    • Place of Presentation
      京都テルサ (京都市)
    • Year and Date
      2016-05-25
    • Related Report
      2016 Research-status Report
  • [Presentation] カルマンゲインの一致推定値の数値的解法2016

    • Author(s)
      池田 建司
    • Organizer
      第3回制御部門マルチシンポジウム
    • Place of Presentation
      南山大学名古屋キャンパス (愛知県・名古屋市)
    • Year and Date
      2016-03-07
    • Related Report
      2015 Research-status Report
  • [Presentation] Frequency Domain Uncertainty in PO-MOESP Method2015

    • Author(s)
      Kenji Ikeda
    • Organizer
      The 47th ISCIE International Symposium on Stochastic Systems Theory and Its Applications
    • Place of Presentation
      Honolulu (U.S.A.)
    • Year and Date
      2015-12-05
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] イノベーション過程の共分散行列の一致推定値2015

    • Author(s)
      池田 建司
    • Organizer
      第58回自動制御連合講演会
    • Place of Presentation
      神戸大学 (兵庫県・神戸市)
    • Year and Date
      2015-11-14
    • Related Report
      2015 Research-status Report
  • [Presentation] Consistent Estimate of Kalman Gain in Subspace Identification Method2015

    • Author(s)
      Kenji Ikeda
    • Organizer
      The 2015 IEEE Control Systems Society; Multiconference on Systems and Control
    • Place of Presentation
      Sydney (Australia)
    • Year and Date
      2015-09-21
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Estimation Error Analysis of System Matrices in Some Subspace Identification Methods2015

    • Author(s)
      enji Ikeda and Hiroshi Oku
    • Organizer
      10th Asian Control Conference,
    • Place of Presentation
      Kota Kinabalu (Malaysia)
    • Year and Date
      2015-05-31
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] 閉ループ環境における部分空間同定法の誤差解析2015

    • Author(s)
      池田 建司
    • Organizer
      第59回システム制御情報学会研究発表講演会
    • Place of Presentation
      中央電気倶楽部 (大阪府・大阪市)
    • Year and Date
      2015-05-20
    • Related Report
      2015 Research-status Report

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Published: 2015-04-16   Modified: 2020-03-30  

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