Student or educator? Sign up with your school email and get 6 months of Pro free.
Cited by 2,820

The DOI matches its Crossref record.

MUSIC, maximum likelihood, and Cramer-Rao bound

Stoica, P., Nehorai, Arye·1989·IEEE Transactions on Acoustics, Speech, and Signal Processing

Abstract

The performance of the MUSIC and ML methods is studied, and their statistical efficiency is analyzed. The Cramer-Rao bound (CRB) for the estimation problems is derived, and some useful properties of the CRB covariance matrix are established. The relationship between the MUSIC and ML estimators is investigated as well. A numerical study is reported of the statistical efficiency of the MUSIC estimator for the problem of finding the directions of two plane waves using a uniform linear array. An exact description of the results is included.>

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1109/29.17564

Cites

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

No references could be resolved yet.

Research works printed but not linked: 43

  1. janssen, 1987, On the expectation of the product of four matrix-valued Gaussian random variables
  2. 10.1109/9.1319 · doi:10.1109/9.1319
  3. 10.1109/TASSP.1985.1164649 · DOI
  4. 10.1109/ICASSP.1988.197217 · DOI
  5. soderstrom, 1988, System Identification
  6. 10.1214/aoms/1177704248 · DOI · Paper page
  7. 10.1109/TASSP.1986.1164815 · DOI · Paper page
  8. beex, 1986, Signal Processing III Theories and Applications, 1001
  9. 1986, IEEE Trans Acoust Speech Signal Processing, assp 34, 633
  10. 10.1109/29.7543 · DOI · Paper page
  11. 10.1109/29.1552 · DOI · Paper page
  12. kumaresan, 1985, High resolution bearing estimation without cigendecomposition, Proc IEEE Int Conf Acoust Speech Signal Processing, 576, 10.1109/ICASSP.1985.1168370 · doi:10.1109/icassp.1985.1168370
  13. bangs, 1971, Array Processing with Generalized Beamformers
  14. 10.1109/TASSP.1986.1164843 · DOI · Paper page
  15. 10.1109/TASSP.1986.1164949 · DOI · Paper page
  16. 10.1109/PROC.1982.12428 · DOI · Paper page
  17. parthasarathy, 1985, maximum-likelihood estimation of parameters of exponentially damped sinusoids, Proceedings of the IEEE, 73, 1528, 10.1109/PROC.1985.13328 · doi:10.1109/proc.1985.13328
  18. orfanidis, 1986, A reduced MUSIC algorithm, Proc 3rd ASSP Workshop on Spectrum Estimation and Modeling, 165
  19. 10.1109/TAES.1983.309427 · DOI · Paper page
  20. xu, 1986, Single vector approaches to eigenstructure analysis for harmonic retrieval, Proc IEEE Int Conf Acoust Speech Signal Processing, 173
  21. 10.1109/ICASSP.1986.1169189 · doi:10.1109/icassp.1986.1169189
  22. 10.1109/TASSP.1986.1164943 · doi:10.1109/tassp.1986.1164943
  23. 1989, Proc IEEE Int Conf Acoust Speech Signal Processing
  24. anderson, 1984, An Introduction to Multivariate Statistical Analysis
  25. 10.1109/TASSP.1985.1164557 · DOI · Paper page
  26. kendall, 1961, The Advanced Theory of Statistics
  27. 10.1109/TASSP.1983.1164185 · DOI · Paper page
  28. sharman, 1986, A comparative study of modern eigenstructure methods for bearing estimation?A new high performance approach, Proc 25th IEEE Conf Dec Contr, 1737
  29. stoica, 1987, On reparameterization of loss function used in estimation and the invariance principle
  30. 10.1109/ICASSP.1984.1172704 · doi:10.1109/icassp.1984.1172704
  31. 10.1049/ip-f-1.1985.0110 · doi:10.1049/ip-f-1.1985.0110
  32. 10.1109/ICASSP.1980.1171029 · doi:10.1109/icassp.1980.1171029
  33. 10.1109/TASSP.1985.1164725 · DOI
  34. 10.1109/TAP.1986.1143830 · DOI · Paper page
  35. 10.1109/TASSP.1986.1164944 · doi:10.1109/tassp.1986.1164944
  36. tuteur, 1986, The covariance difference method in signal detection, Proc 3rd ASSP Workshop on Spectrum Estimation and Modeling, 120
  37. 10.1109/TASSP.1986.1164957 · DOI
  38. 10.1109/SPECT.1988.206199 · doi:10.1109/spect.1988.206199
  39. 10.1109/TIT.1974.1055282 · DOI · Paper page
  40. hung, 1987, On the statistical sufficiency of the coherently averaged covariance matrix for the estimation of the parameters of wideband sources, Proc IEEE Int Conf Acoust Speech Signal Processing, 33
  41. 10.1109/TASSP.1986.1164935 · DOI · Paper page
  42. 10.1109/29.21705 · doi:10.1109/29.21705
  43. rife, 1976, Multiple tone parameter estimation from discrete-time observations, Bell Syst Tech J, 55, 1389, 10.1002/j.1538-7305.1976.tb02941.x · doi:10.1002/j.1538-7305.1976.tb02941.x

Cited by

See all 2,820

Metadata

Authors
Stoica, P., & Nehorai, A.
Venue
IEEE Transactions on Acoustics, Speech, and Signal Processing
Published
1989-05
Volume
37
Issue
5
Pages
720-741
ISSN
0096-3518 (ISSN-L)
OpenAlex
W2149755721
Cited by
2,820
References
0
FWCI
61.03
Type
journal article
Language
en
Open access
closed

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: MUSIC, maximum likelihood, and Cramer-Rao bound. https://app.cochat.ai/papers/10.1109/29.17564
The paper
Stoica, P., & Nehorai, A. (1989). MUSIC, maximum likelihood, and Cramer-Rao bound. IEEE Transactions on Acoustics, Speech, and Signal Processing. https://doi.org/10.1109/29.17564

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.