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.
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| 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 |
