Complex Factor Analysis and Extensions Article Swipe
Ahmad Mouri Sardarabadi
,
A. van Veen
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1109/tsp.2017.2780047
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1109/tsp.2017.2780047
Many subspace-based array signal processing algorithms assume that the noise is spatially white. In this case, the noise covariance matrix is a multiple of the identity and the eigenvectors of the data covariance matrix are not affected by it. If the noise covariance is an unknown arbitrary diagonal (e.g., for an uncalibrated array), the eigenvalue decomposition leads to incorrect subspace estimates and it has to be replaced by a more general “factor analysis” decomposition (FA), which then reveals all relevant information. We consider this data model and several extensions where the noise covariance matrix has a more general structure, such as banded, sparse, block diagonal, and cases, where we have multiple data covariance matrices that share the same noise covariance matrix. Starting from a nonlinear weighted least squares formulation, we propose new estimation algorithms for both classical FA and its extensions. The optimization is based on Gauss–Newton gradient descent. Generally, this leads to an iteration involving the inversion of a very large matrix. Using the structure of the problem, we show how this can be reduced to the inversion of a matrix with dimension equal to the number of unknown noise covariance parameters. This results in new algorithms that have faster numerical convergence and lower complexity compared to several maximum-likelihood based algorithms that could be considered state of the art. The new algorithms scale well to large dimensions and can replace eigenvalue decompositions in many applications even if the noise can be assumed to be white.
Related Topics
Concepts
Mathematics
Covariance matrix
Estimation of covariance matrices
Eigendecomposition of a matrix
Covariance
Algorithm
Diagonal matrix
Eigenvalues and eigenvectors
Identity matrix
Covariance intersection
Applied mathematics
Mathematical optimization
Diagonal
Statistics
Quantum mechanics
Physics
Geometry
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1109/tsp.2017.2780047
- OA Status
- green
- Cited By
- 12
- References
- 55
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2773200628
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W2773200628Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1109/tsp.2017.2780047Digital Object Identifier
- Title
-
Complex Factor Analysis and ExtensionsWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2017Year of publication
- Publication date
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2017-12-04Full publication date if available
- Authors
-
Ahmad Mouri Sardarabadi, A. van VeenList of authors in order
- Landing page
-
https://doi.org/10.1109/tsp.2017.2780047Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://resolver.tudelft.nl/uuid:13293f3d-0380-4416-950d-613661b76a1dDirect OA link when available
- Concepts
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Mathematics, Covariance matrix, Estimation of covariance matrices, Eigendecomposition of a matrix, Covariance, Algorithm, Diagonal matrix, Eigenvalues and eigenvectors, Identity matrix, Covariance intersection, Applied mathematics, Mathematical optimization, Diagonal, Statistics, Quantum mechanics, Physics, GeometryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
12Total citation count in OpenAlex
- Citations by year (recent)
-
2024: 3, 2023: 1, 2021: 1, 2020: 1, 2019: 3Per-year citation counts (last 5 years)
- References (count)
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55Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| primary_location.source.host_organization_lineage_names | Institute of Electrical and Electronics Engineers |
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| primary_location.raw_source_name | IEEE Transactions on Signal Processing |
| primary_location.landing_page_url | https://doi.org/10.1109/tsp.2017.2780047 |
| publication_date | 2017-12-04 |
| publication_year | 2017 |
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