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

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.
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Details

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
DOI
StatePublished - Aug 2016
Publication categoryResearch
Peer-reviewedYes
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
LandHungary
ByBudapest
Periode29/08/201602/09/2016
Internetadresse
SeriesProceedings of the European Signal Processing Conference (EUSIPCO)
ISSN2076-1465

    Research areas

  • optimisation, DOA estimation, fundamental frequency estimation, periodogram

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