Research Papers

Cramer–Rao Bound Development for Linear Time Periodic Systems

[+] Author and Article Information
Chris S. Schulz

Department of Aeronautics and Astronautics, Air Force Institute of Technology, WPAFB, OH 45433-7765christopher.schulz@darpa.mil

Donald L. Kunz

Department of Aeronautics and Astronautics, Air Force Institute of Technology, WPAFB, OH 45433-7765donald.kunz@afit.edu

Norman M. Wereley

Department of Aerospace Engineering, University of Maryland, College Park, MD 20742wereley@eng.umd.edu

J. Dyn. Sys., Meas., Control 133(1), 011001 (Nov 23, 2010) (10 pages) doi:10.1115/1.4002104 History: Received June 19, 2008; Revised June 16, 2010; Published November 23, 2010; Online November 23, 2010

System identification techniques are often used to determine the parameters required to define a model of a linear time invariant (LTI) system. The Cramer–Rao bound can be used to validate those parameters in order to ensure that the system model is an accurate representation of the system. Unfortunately, the Cramer–Rao bound is only valid for LTI systems and is not valid for linear time periodic (LTP) systems such as a helicopter rotor in forward flight. This paper describes an extension of the Cramer–Rao bound to LTP systems and demonstrates the methodology for a simple LTP system.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Comparison of parameter estimates for LTI and LTP systems (10)

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Figure 2

Example of Cramer–Rao bounds for parameter estimates (11)

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Figure 3

Example of a simple LTP system represented by a modulating gain (15)

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Figure 4

Multiharmonic response of a LTP system (16)

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Figure 5

Rigid rotor blade flapping moments (17)

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Figure 6

Cramer–Rao bounds for all frequency and noise values

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Figure 7

Blade flap frequency response for the fundamental frequency band input (10)

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Figure 8

Cramer–Rao bounds for 100 runs at all frequencies (Sv=4)



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