Optimal Designs for Steady-state Kalman filters

Please always quote using this URN: urn:nbn:de:0297-zib-52808
  • We consider a stationary discrete-time linear process that can be observed by a finite number of sensors. The experimental design for the observations consists of an allocation of available resources to these sensors. We formalize the problem of selecting a design that maximizes the information matrix of the steady-state of the Kalman filter, with respect to a standard optimality criterion, such as $D-$ or $A-$optimality. This problem generalizes the optimal experimental design problem for a linear regression model with a finite design space and uncorrelated errors. Finally, we show that under natural assumptions, a steady-state optimal design can be computed by semidefinite programming.

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Author:Guillaume Sagnol, Radoslav Harman
Document Type:ZIB-Report
Tag:Kalman Filter; Optimal Design; Semidefinite programming
MSC-Classification:93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX)
Date of first Publication:2014/10/15
Series (Serial Number):ZIB-Report (14-39)