Grid Size Selection for Nonlinear Least-Squares Optimization in Spectral Estimation and Array Processing

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

6 Citations (Scopus)
158 Downloads (Pure)

Abstract

In many spectral estimation and array processing problems, the process
of finding estimates of model parameters often involves the optimisation
of a cost function containing multiple peaks and dips. Such
non-convex problems are hard to solve using traditional optimisation
algorithms developed for convex problems, and computationally intensive
grid searches are therefore often used instead. In this paper,
we establish an analytical connection between the grid size and the
parametrisation of the cost function so that the grid size can be selected
as coarsely as possible to lower the computation time. Additionally,
we show via three common examples how the grid size depends
on parameters such as the number of data points or the number
of sensors in DOA estimation. We also demonstrate that the computation
time can potentially be lowered by several orders of magnitude
by combining a coarse grid search with a local refinement step.
Original languageEnglish
Title of host publicationSignal Processing Conference (EUSIPCO), 2016 24th European
PublisherIEEE
Publication dateAug 2016
Pages1653-1657
ISBN (Electronic)978-0-9928-6265-7
DOIs
Publication statusPublished - Aug 2016
Event European Signal Processing Conference - Hotel Hilton Budapest, Budapest, Hungary
Duration: 29 Aug 20162 Sep 2016
http://www.eusipco2016.org/

Conference

Conference European Signal Processing Conference
LocationHotel Hilton Budapest
CountryHungary
CityBudapest
Period29/08/201602/09/2016
Internet address
SeriesProceedings of the European Signal Processing Conference (EUSIPCO)
ISSN2076-1465

Fingerprint

Array processing
Cost functions
Sensors

Keywords

  • optimisation
  • DOA estimation
  • fundamental frequency estimation
  • periodogram

Cite this

Nielsen, J. K., Jensen, T. L., Jensen, J. R., Christensen, M. G., & Jensen, S. H. (2016). Grid Size Selection for Nonlinear Least-Squares Optimization in Spectral Estimation and Array Processing. In Signal Processing Conference (EUSIPCO), 2016 24th European (pp. 1653-1657). IEEE. Proceedings of the European Signal Processing Conference (EUSIPCO) https://doi.org/10.1109/EUSIPCO.2016.7760529
Nielsen, Jesper Kjær ; Jensen, Tobias Lindstrøm ; Jensen, Jesper Rindom ; Christensen, Mads Græsbøll ; Jensen, Søren Holdt. / Grid Size Selection for Nonlinear Least-Squares Optimization in Spectral Estimation and Array Processing. Signal Processing Conference (EUSIPCO), 2016 24th European. IEEE, 2016. pp. 1653-1657 (Proceedings of the European Signal Processing Conference (EUSIPCO)).
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abstract = "In many spectral estimation and array processing problems, the processof finding estimates of model parameters often involves the optimisationof a cost function containing multiple peaks and dips. Suchnon-convex problems are hard to solve using traditional optimisationalgorithms developed for convex problems, and computationally intensivegrid searches are therefore often used instead. In this paper,we establish an analytical connection between the grid size and theparametrisation of the cost function so that the grid size can be selectedas coarsely as possible to lower the computation time. Additionally,we show via three common examples how the grid size dependson parameters such as the number of data points or the numberof sensors in DOA estimation. We also demonstrate that the computationtime can potentially be lowered by several orders of magnitudeby combining a coarse grid search with a local refinement step.",
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Nielsen, JK, Jensen, TL, Jensen, JR, Christensen, MG & Jensen, SH 2016, Grid Size Selection for Nonlinear Least-Squares Optimization in Spectral Estimation and Array Processing. in Signal Processing Conference (EUSIPCO), 2016 24th European. IEEE, Proceedings of the European Signal Processing Conference (EUSIPCO), pp. 1653-1657, European Signal Processing Conference, Budapest, Hungary, 29/08/2016. https://doi.org/10.1109/EUSIPCO.2016.7760529

Grid Size Selection for Nonlinear Least-Squares Optimization in Spectral Estimation and Array Processing. / Nielsen, Jesper Kjær; Jensen, Tobias Lindstrøm; Jensen, Jesper Rindom; Christensen, Mads Græsbøll; Jensen, Søren Holdt.

Signal Processing Conference (EUSIPCO), 2016 24th European. IEEE, 2016. p. 1653-1657 (Proceedings of the European Signal Processing Conference (EUSIPCO)).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

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Nielsen JK, Jensen TL, Jensen JR, Christensen MG, Jensen SH. Grid Size Selection for Nonlinear Least-Squares Optimization in Spectral Estimation and Array Processing. In Signal Processing Conference (EUSIPCO), 2016 24th European. IEEE. 2016. p. 1653-1657. (Proceedings of the European Signal Processing Conference (EUSIPCO)). https://doi.org/10.1109/EUSIPCO.2016.7760529