A unified square-root approach for the score and Fisher information matrix computation in linear dynamic systems

One of the most frequently encountered problems in practice is to combine a priori knowledge about a physical system with experimental data to provide on-line estimation of an unknown dynamic state and system parameters. The classical way for solving this problem is to use adaptive filtering techniq...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Mathematics and computers in simulation Ročník 119; s. 128 - 141
Hlavní autoři:	Kulikova, M.V., Tsyganova, J.V.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier B.V 01.01.2016
Témata:	Fisher information matrix Gradient-based methods Kalman filtering Maximum likelihood estimation Square-root algorithms Gradient-based methods Maximum likelihood estimation Kalman filtering Square-root algorithms Fisher information matrix
ISSN:	0378-4754, 1872-7166
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Popis
Shrnutí:	One of the most frequently encountered problems in practice is to combine a priori knowledge about a physical system with experimental data to provide on-line estimation of an unknown dynamic state and system parameters. The classical way for solving this problem is to use adaptive filtering techniques. The adaptive schemes for the maximum likelihood estimation based on gradient-based optimization methods are, in general, preferable. They require the likelihood function and its gradient evaluation (score), and might demand the Fisher information matrix (FIM) computation. All techniques for the score and the FIM calculation in linear dynamic systems yield the implementation of the Kalman filter (KF) and its derivatives (with respect to unknown system parameters), which is known to be numerically unstable. An alternative solution can be found among algorithms developed in the KF community for solving ill conditioned problems: the square-root algorithms, the UD-based factorization methods and the fast SR Chandrasekhar–Kailath–Morf–Sidhu techniques. Recently, these advanced KF implementations have been extended on the filter derivatives computation. However there is no systematic way of designing the robust “differentiated” methods. In this paper, we develop a unified square-root methodology of generating the computational techniques for the filter/smoother derivatives evaluation required in gradient-based adaptive schemes for the score and the FIM computation.
ISSN:	0378-4754 1872-7166
DOI:	10.1016/j.matcom.2015.07.007