Cramér–Rao lower bound in nonlinear filtering problems under noises and measurement errors dependent on estimated parameters

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• 作者：O. A. Stepanov ; V. A. Vasil’ev
• 刊名：Automation and Remote Control
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：77
• 期：1
• 页码：81-105
• 全文大小：641 KB
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• 作者单位：O. A. Stepanov (1) (2)
  V. A. Vasil’ev (1)
  
  1. State Research Center of the Russian Federation JSC Concern CSRI Elektropribor, St. Petersburg, Russia
  2. ITMO University, St. Petersburg, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Systems Theory and Control
  Automation and Robotics
  Mechanical Engineering
  Computer-Aided Engineering and Design
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1608-3032

文摘

This paper derives recurrent expressions for the maximum attainable estimation accuracy calculated using the Cramér–Rao inequality (Cramér–Rao lower bound) in the discretetime nonlinear filtering problem under conditions when generating noises in the state vector and measurement error equations depend on estimated parameters and the state vector incorporates a constant subvector. We establish a connection to similar expressions in the case of no such dependence. An example illustrates application of the obtained algorithms to lowerbound accuracy calculation in a parameter estimation problem often arising in navigation data processing within a model described by the sum of a Wiener sequence and discrete-time white noise of an unknown variance. Original Russian Text © O.A. Stepanov, V.A. Vasil’ev, 2016, published in Avtomatika i Telemekhanika, 2016, No. 1, pp. 104–133.This paper was recommended for publication by A.P. Kurdyukov, a member of the Editorial Board