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Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering

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  • Xiu Kan
  • Huisheng Shu
  • Yan Che

Abstract

The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameter 𠜃 ∶ 𠑑 𠑋 𠑡 = ( 𠜃 𠛼 ( 𠑡 ) + 𠛽 ( 𠑡 ) 𠑋 𠑡 ) 𠑑 𠑡 + 𠜎 ( 𠑡 ) 𠑑 𠑊 𠑡 . Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameter θ based on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.

Suggested Citation

  • Xiu Kan & Huisheng Shu & Yan Che, 2012. "Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-15, September.
    • Handle: RePEc:hin:jnlmpe:342705
    DOI: 10.1155/2012/342705
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