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

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 depe...

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Bibliographic Details
Published in:Automation and remote control 2016, Vol.77 (1), p.81-105
Main Authors: Stepanov, O. A., Vasil’ev, V. A.
Format: Article
Language:English
Subjects:
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Computer-Aided Engineering (CAD
Control
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Robotics
Systems Theory
Topical Issue
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Summary: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.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117916010057