Optimal Designs for Steady-state Kalman filters

  • 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.
Metadaten
Author:Guillaume Sagnol, Radoslav Harman
Editor:Ansgar Steland, Ewaryst Rafajłowicz, Krzysztof Szajowski
Document Type:In Proceedings
Parent Title (English):Stochastic Models, Statistics and Their Applications
Volume:122
First Page:149
Last Page:157
Series:Springer Proceedings in Mathematics & Statistics
Publisher:Springer
Year of first publication:2015
Preprint:urn:nbn:de:0297-zib-52808
DOI:https://doi.org/10.1007/978-3-319-13881-7_17