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An Alternative Derivation of the Kalman Filter Using the Quasi-likelihood Method

Journal Article


Abstract


  • The Kalman filter gives a recursive procedure for estimating state vectors. The recursive procedure is determined by a matrix, so-called gain matrix, where the gain matrix is varied based on the system to which the Kalman filter is applied. Traditionally the gain matrix is derived through the maximum likelihood approach when the probability structure of underlying system is known. As an alternative approach, the quasi-likelihood method is considered in this paper. This method is used to derive the gain matrix without the full knowledge of the probability structure of the underlying system. Two models are considered in this paper, the simple state space model and the model with correlated between measurement and transition equation disturbances. The purposes of this paper are (i) to show a simple way to derive the gain matrix; (ii) to give an alternative approach for obtaining optimal estimation of state vector when underlying system is relatively complex.

Publication Date


  • 2007

Citation


  • Lin, Y. (2007). An Alternative Derivation of the Kalman Filter Using the Quasi-likelihood Method. Journal of Statistical Planning and Inference, 137 (5), 1627-1633.

Scopus Eid


  • 2-s2.0-33846122254

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2878

Number Of Pages


  • 6

Start Page


  • 1627

End Page


  • 1633

Volume


  • 137

Issue


  • 5

Abstract


  • The Kalman filter gives a recursive procedure for estimating state vectors. The recursive procedure is determined by a matrix, so-called gain matrix, where the gain matrix is varied based on the system to which the Kalman filter is applied. Traditionally the gain matrix is derived through the maximum likelihood approach when the probability structure of underlying system is known. As an alternative approach, the quasi-likelihood method is considered in this paper. This method is used to derive the gain matrix without the full knowledge of the probability structure of the underlying system. Two models are considered in this paper, the simple state space model and the model with correlated between measurement and transition equation disturbances. The purposes of this paper are (i) to show a simple way to derive the gain matrix; (ii) to give an alternative approach for obtaining optimal estimation of state vector when underlying system is relatively complex.

Publication Date


  • 2007

Citation


  • Lin, Y. (2007). An Alternative Derivation of the Kalman Filter Using the Quasi-likelihood Method. Journal of Statistical Planning and Inference, 137 (5), 1627-1633.

Scopus Eid


  • 2-s2.0-33846122254

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2878

Number Of Pages


  • 6

Start Page


  • 1627

End Page


  • 1633

Volume


  • 137

Issue


  • 5