Cramér-Rao Bounds for Underdetermined Source Localization

Although Cramér-Rao Bounds (CRB) for direction-of-arrival (DOA) estimation have been extensively studied for decades, existing results are mainly applicable when there are fewer sources than sensors. In contrast, this letter considers an underdetermined signal model (more sources than sensors) and...

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Bibliographic Details
Published in:IEEE signal processing letters Vol. 23; no. 7; pp. 919 - 923
Main Authors: Koochakzadeh, Ali, Pal, Piya
Format: Journal Article
Language:English
Published: IEEE 01.07.2016
Subjects:
Antenna arrays
Array signal processing
Coprime arrays
Cramér–Rao bound (CRB)
direction-of-arrival (DOA) estimation
Direction-of-arrival estimation
Estimation
Geometry
nested arrays
Sensor arrays
singular Fisher information
direction-of-arrival (DOA) estimation
Coprime arrays
Cramér–Rao bound (CRB)
nested arrays
singular Fisher information
ISSN:1070-9908, 1558-2361
Online Access:Get full text
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Summary:Although Cramér-Rao Bounds (CRB) for direction-of-arrival (DOA) estimation have been extensively studied for decades, existing results are mainly applicable when there are fewer sources than sensors. In contrast, this letter considers an underdetermined signal model (more sources than sensors) and investigates conditions under which CRB exist. Necessary and sufficient conditions are derived for the associated Fisher information matrix to be nonsingular, which in turn, leads to closed-form expressions for the CRBs for underdetermined DOA estimation. These conditions highlight crucial roles played by the array geometry, as well as the correlation between source signals. The CRB for different array geometries are numerically compared both in the overdetermined and underdetermined settings.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2016.2569504