Skip to main content

Exact and Large Sample Maximum Likelihood Techniques for Parameter Estimation and Detection in Array Processing

  • Chapter
Radar Array Processing

Part of the book series: Springer Series in Information Sciences ((SSINF,volume 25))

Abstract

Sensor array signal processing deals with the problem of extracting information from a collection of measurements obtained from sensors distributed in space. The number of signals present is assumed to be finite, and each signal is parameterized by a finite number of parameters. Based on measurements of the array output, the objective is to estimate the signals and their parameters. This research area has attracted considerable interest for several years. A vast number of algorithms has appeared in the literature for estimating unknown signal parameters from the measured output of a sensor array.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S.P. Applebaum: Adaptive arrays. Technical Report SPL TR 66–1, Syracuse University Research Corporation (1966)

    Google Scholar 

  2. B. Widrow, P.E. Mantey, L.J. Griffiths, B.B. Goode: Adaptive antenna systems. Proc. IEEE 55, 2143–2159(1967)

    Article  Google Scholar 

  3. F.C. Schweppe: Sensor array data processing for multiple signal sources. IEEE Trans. IT-14, 294–305 (1968)

    MathSciNet  Google Scholar 

  4. V.H. MacDonald, P.M. Schultheiss: Optimum passive bearing estimation in a spatially incoherent noise environment. J. Acoust. Soc. Am., 46(1), 37–43 (1969)

    Article  Google Scholar 

  5. J. Capon: High resolution frequency wave number spectrum analysis. Proc. IEEE 57, 1408–1418 (1969)

    Article  Google Scholar 

  6. R.A. Monzingo, T.W. Miller: Introduction to Adaptive Arrays (Wiley, New York 1980)

    Google Scholar 

  7. S. Haykin (ed): Array Signal Processing (Prentice-Hall, Englewood Cliffs, NJ 1985)

    MATH  Google Scholar 

  8. B.D. Van Veen, K.M. Buckley: Beamforming: A versatile approach to spatial filtering. IEEE ASSP Mag. pp. 4–24 (April 1988)

    Google Scholar 

  9. J.P. Burg: Maximum entropy spectral analysis, in Proc 37th Annual Int. SEG Meeting, Oklahoma City, OK (1967)

    Google Scholar 

  10. D.W. Tufts, R. Kumaresan: Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihood. Proc. IEEE 70, 975ö989 (1982)

    Article  Google Scholar 

  11. R. Kumaresan, D.W. Tufts: Estimating the angles of arrival of multiple plane waves. IEEE Trans. AES-19, 134–139 (1983)

    Google Scholar 

  12. R.O. Schmidt: Multiple emitter location and signal parameter estimation, in Proc. RADC Spectrum Estimation Workshop, Rome, NY (1979) pp. 243–258

    Google Scholar 

  13. G. Bienvenu, L. Kopp: Principle de la goniometrie passive adaptive, in Proc. 7’eme Colloque GRESIT, Nice, France (1979) pp. 106/1–10

    Google Scholar 

  14. G. Bienvenu, L. Kopp: Adaptivity to background noise spatial coherence for high resolution passive methods, in Proc. IEEE ICASSP, Denver, CO (1980) pp. 307–310

    Google Scholar 

  15. N.L. Owsley: Data adaptive orthonormalization, in Proc. ICASSP 78, Tulsa, OK (1978) pp. 109–112

    Google Scholar 

  16. V.F. Pisarenko: The retrieval of harmonics from a covariance function. Geophys. J. R. Astron. Soc. 33, 347–366 (1973)

    MATH  Google Scholar 

  17. G. Bienvenu, L. Kopp: Optimality of high resolution array processing, IEEE Trans. ASSP-31, 1235–1248 (1983)

    Article  Google Scholar 

  18. A. Paulraj, R. Roy, T. Kailath: A subspace rotation approach to signal parameter estimation. Proc. IEEE 74, 1044–1045 (1986)

    Article  Google Scholar 

  19. S.Y. Kumg, CK. Lo, R. Foka: A Toeplitz approximation approach to coherent source direction finding, in, Proc. ICASSP 86, Tokyo (1986)

    Google Scholar 

  20. S.J. Orfanidis: A reduced MUSIC algorithm, in Proc. IEEE ASSP 3rd Workshop Spectrum Est. Modeling, Boston, MA (1986) pp. 165–167

    Google Scholar 

  21. W.J. Bangs: Array processing with generalized beamformers. Ph.D. Thesis, Yale University (1971)

    Google Scholar 

  22. M. Wax: Detection and estimation of superimposed signals. Ph.D. Thesis, Stanford University (1985)

    Google Scholar 

  23. J.F. Böhme: Estimation of source parameters by maximum likelihood and non-linear regression, in Proc ICASSP 84, San Diego, CA (1984) pp. 7.3.1–4

    Google Scholar 

  24. J.F. Böhme: Estimation of spectral parameters of correlated signals in wavefields. Signal Processing 10, 329–337 (1986)

    Article  Google Scholar 

  25. P. Stoica, A. Nehorai: MUSIC, maximum likelihood and Cramér-Rao bound, in Proc. ICASSP 88 New York (1988) pp. 2296–2299

    Google Scholar 

  26. B. Ottersten, L. Ljung: Asymptotic results for sensor array processing, in Proc. ICASSP 89, Glasgow, Scotland (1989) pp. 2266–2269

    Google Scholar 

  27. B. Ottersten, M. Viberg: Analysis of subspace fitting based methods for sensor array processing, in Proc. ICASSP 89, Glasgow, Scotland (1989) pp. 2807–2810

    Google Scholar 

  28. R.O. Schmidt: A signal subspace approach to multiple emitter location and spectral estimation. Ph.D. Thesis, Stanford University (1981)

    Google Scholar 

  29. B. Ottersten, B. Wahlberg, M. Viberg, T. Kailath: Stochastic maximum likelihood estimation in sensor arrays by weighted subspace fitting, in Proc. 23rd Asilomar Conf. Sig., Syst., Comput, Monterey, CA (1989) pp. 599–603

    Google Scholar 

  30. P. Stoica, A. Nehorai: MUSIC, maximum likelihood and Cramér-Rao bound. IEEE Trans. AssP-37, 720–741 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  31. H. Clergeot, S. Tressens, A. Ouamri: Performance of high resolution frequencies estimation methods compared to the Cramér-Rao bounds. IEEE Trans. ASSP 37, 1703–1720 (1989)

    Article  MATH  Google Scholar 

  32. P. Stoica, A. Nehorai: Performance study of conditional and unconditional direction-of-arnval estimation. IEEE Trans. ASSP-38, 1783–1795 (1990)

    Article  MATH  Google Scholar 

  33. K. Sharman, T.S. Durrani, M. Wax, T. Kailath: Asymptotic performance of eigenstructure spectral analysis methods, in Proc. ICASSP 84, San Diego, CA (1984) pp. 45.5.1–4

    Google Scholar 

  34. DJ. Jeffries, D.R. Farrier: Asymptotic results for eigenvector methods. IEE Proc. F 132, 589–594 (1985)

    Google Scholar 

  35. M. Kaveh, A.J. Barabell: The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise. IEEE Trans. ASSP-34, 331–341 (1986)

    Article  Google Scholar 

  36. B. Porat, B. Friedlander: Analysis of the asymptotic relative efficiency of the MUSIC algorithm. IEEE Trans. ASSP-36, 532–544 (1988)

    Article  MATH  Google Scholar 

  37. B.D. Rao, K.V.S. Hari: Performance analysis of root-music. IEEE Trans. ASSP-37,1939–1949 (1989)

    Article  Google Scholar 

  38. B.D. Rao, K.V.S. Hari: Performance analysis of ESPRIT and TAM in determining the direction of arrival of plane waves in noise. IEEE Trans. ASSP-37, 1990–1995 (1989)

    Article  Google Scholar 

  39. P. Stoica, A. Nehorai: MUSIC, maximum likelihood, and Cramér-Rao bound: Further results and comparisons. IEEE Trans. ASSP-38, 2140–2150 (1990)

    Article  Google Scholar 

  40. P. Stoica, A. Nehorai: Performance comparison of subspace rotation and MUSIC methods for direction estimation. IEEE Trans. SP-39, 446–453 (1991)

    Article  MATH  Google Scholar 

  41. P. Stoica, K. Sharman: A novel eigenanalysis method for direction estimation. IEE Proc. part F, 19–26 (1990)

    Google Scholar 

  42. P. Stoica, K. Sharman: Maximum likelihood methods for direction-of-arrival estimation. IEEE Trans. ASSP-38, 1132–1143 (1990)

    Article  MATH  Google Scholar 

  43. D. Staren Algorithms for polynomial-based signal processing. Ph.D. Thesis, Yale University (1990)

    Google Scholar 

  44. M. Viberg, B. Ottersten: Sensor array processing based on subspace fitting. IEEE Trans. SP-39, 1110–1121 (1991)

    Article  MATH  Google Scholar 

  45. B. Ottersten, M. Viberg, T. Kailath: Performance analysis of the total least squares ESPRIT algorithm. IEEE Trans. SP-39, 1122–1135 (1991)

    Article  MATH  Google Scholar 

  46. Y. Bresler: Maximum likelihood estimation of Hnearly structured covariance with application to antenna array processing, in Proc. 4th ASSP Workshop on Spectrum Estimation and Modeling, Minneapolis, MN (1988) pp. 172–175

    Google Scholar 

  47. B. Ottersten, R. Roy, T. Kailath: Signal waveform estimation in sensor array processing, in Proc. 23rd Asilomar Conf. Sig., Syst., Comput., Pacific Grove, CA (1989) pp. 787–791

    Google Scholar 

  48. M. Wax, I. Ziskind: On unique localization of multiple sources by passive sensor arrays. IEEE Trans. ASSP-37, 996–1000 (1989)

    Article  Google Scholar 

  49. A. Nehorai, D. Starer, P. Stoica: Direction-of-arrival estimation in applications with multipath and few snapshots. Circuits, Syst., Signal Proc. 10, 327–342 (1991)

    MATH  Google Scholar 

  50. K.V. Mardia, J.T. Kent, J.M. Bibby: Multivariate Analysis (Academic, London 1979)

    MATH  Google Scholar 

  51. T.W. Anderson: An Introduction to Multivariate Statistical Analysis, 2nd edn. (Wiley, New York 1984)

    MATH  Google Scholar 

  52. N.R. Goodman: Statistical analysis based on a certain multivariate, complex gaussian distribution (an introduction). Ann. Math. Stat. 34, 152–176 (1963)

    Article  MATH  Google Scholar 

  53. A.G. Jaffer: Maximum likelihood direction finding of stochastic sources: A separable solution, in Proc. ICASSP 88, New York (1988) pp. 2893–2896

    Google Scholar 

  54. G. Golub, V. Pereyra: The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. SIAM J. Numer. Anal. 10, 413–432 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  55. S.D. Silvey: Statistical Inference (Penguin, London 1970)

    MATH  Google Scholar 

  56. E.L. Lehmann: Theory of Point Estimation (Wiley, New York 1983)

    MATH  Google Scholar 

  57. A.J. Weiss, E. Weinstein: Lower bounds in parameter estimation- Summary of results, in Proc. ICASSP 86, Tokyo, Japan (1986) pp. 569–572

    Google Scholar 

  58. A. Graham: Kronecker Products and Matrix Calculus with Applications (ElHs Horwood, Chichester, UK 1981)

    MATH  Google Scholar 

  59. A.J. Weiss, B. Friedlander: On the Cramér-Rao bound for direction finding of correlated signals. Technical Report, Signal Processing Technology, Ltd., Palo Alto, CA (1990)

    Google Scholar 

  60. B. Ottersten, M. Viberg, T. Kailath: Analysis of Subspace Fitting and ML Techniques for Parameter Estimation from Sensor Array Data. IEEE Trans. SP-40, 590–600 (1992)

    Article  MATH  Google Scholar 

  61. T. Söderström, P. Stoica: System Identification (Prentice-Hall, International, London, UK 1989)

    MATH  Google Scholar 

  62. R.H. Roy: ESPRIT, estimation of signal parameters via rotational invariance techniques. Ph.D. Thesis, Stanford University (1987)

    Google Scholar 

  63. J.A. Cadzow: A high resolution direction-of-arrival algorithm for narrow-band coherent and incoherent sources. IEEE Trans. ASSP-36, 965–979 (1988)

    Article  MATH  Google Scholar 

  64. M. Viberg, B. Ottersten, T. Kailath: Detection and estimation in sensor arrays using weighted subspace fitting. IEEE Trans. ASSP-39, 2436–2449 (1991)

    Google Scholar 

  65. T.J. Shan, M. Wax, T. Kailath: On spatial smoothing for direction-of-arrival estimation of coherent signals. IEEE Trans. ASSP-33, 806–811 (1985)

    Article  Google Scholar 

  66. M. Feder, E. Weinstein: Parameter estimation of superimposed signals using the EM algorithm. IEEE Trans. ASSP-36, 477–489 (1988)

    Article  MATH  Google Scholar 

  67. M.I. Miller, D.R. Fuhrmann: Maximum-likelihood narrow-band direction finding and the EM algorithm., IEEE Trans. ASSP-38, 1560–1577 (1990)

    Article  MATH  Google Scholar 

  68. I. Ziskind, M. Wax: Maximum likelihood localization of multiple sources by alternating projection. IEEE Trans. ASSP-36, 1553–1560 (1988)

    Article  MATH  Google Scholar 

  69. Y. Bresler, A. Macovski: Exact maximum likelihood parameter estimation of superimposed exponential signals in noise. IEEE Trans. ASSP-34, 1081–1089 (1986)

    Article  Google Scholar 

  70. K. Sharman: Maximum likelihood estimation by simulated annealing, in Proc. ICASSP 88, New York (1988) pp. 2741–2744

    Google Scholar 

  71. D. Goryn, M. Kaveh: Neural networks for narrowband and wideband direction finding, in Proc. ICASSP 88, New York (1988) pp. 2164–2167

    Google Scholar 

  72. K. Sharman, G.D. McClurkin: Genetic algorithms for maximum likelihood parameter estimation, in Proc. ICASSP 89, Glasgow, Scotland (1989) pp. 2716–2719

    Google Scholar 

  73. M. Wax, T. Kailath: Optimal localization of multiple sources by passive arrays. IEEE Trans. ASSP-31, 1210–1218 (1983)

    Article  MathSciNet  Google Scholar 

  74. J.F. Böhme, D. Kraus: On least-squares methods for direction of arrival estimation in the presence of unknown noise fields, in Proc. ICASSP 88, New York (1988) pp. 2833–2836

    Google Scholar 

  75. D. Starer, A. Nehorai: Newton algorithms for conditional and unconditional maximum likelihood estimation of the parameters of exponential signals in noise. IEEE Trans. SP-40 (1992)

    Google Scholar 

  76. P.E. Gill, W. Murray, M.H. Wright: Practical Optimization (Academic, London 1981)

    MATH  Google Scholar 

  77. J.E. Dennis, R.B. Schnabel: Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice Hall, Englewood Cliffs, NJ 1983)

    MATH  Google Scholar 

  78. P.E. Gill, G.H. Golub, W. Murray, M.A. Saunders: Methods for modifying matrix factorizations. Math. Comp. 28, 505–535 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  79. M. Wax, T. Kailath: Detection of signals by information theoretic criteria. IEEE Trans. ASSP-33, 387–392 (1985)

    Article  MathSciNet  Google Scholar 

  80. L.C. Zhao, P.R. Krishnaiah, Z.D. Bai: On detection of the number of signals in presence of white noise. J. Multivar. Anal. 20:1, 1–25 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  81. G.H. Golub, C.F. Van Loan: Matrix Computations, 2nd edn. (Johns Hopkins University Press, Baltimore, MD 1989)

    MATH  Google Scholar 

  82. G. Xu, T. Kailath: Fast signal subspace decomposition without eigendecomposition, in Proc. 24th Asilomar Conf. Sig., Syst., Comput., Monterey, CA (1990)

    Google Scholar 

  83. I. Karasalo: Estimating the covariance matrix by signal subspace averaging. IEEE Trans. ASSP-34, 8–12 (1986)

    Article  MathSciNet  Google Scholar 

  84. R. Schreiber: Implementation of adaptive array algorithms. IEEE Trans. ASSP-34,1038–1045 (1986)

    Article  MATH  Google Scholar 

  85. P. Comon: Fast updating of a low-rank approximation to a varying hermitean matrix, in Proc. 23rd Asilomar Conf. Sig., Syst., Comput, Monterey, CA (1989) pp. 358–362

    Google Scholar 

  86. A.H. Abdallah, Y.H. Hu: Parallel VLSI computing array implementation for signal subspace updating algorithm. IEEE Trans. ASSP-37, 742–748 (1989)

    Article  Google Scholar 

  87. R. Roy, T. Kailath: ESPRIT-Estimation of signal parameters via rotational invariance techniques. IEEE Trans. ASSP-37, 984–995 (1989)

    Article  Google Scholar 

  88. J. Rissanen: Modeling by shortest data description. Automatica 14, 465–471 (1978)

    Article  MATH  Google Scholar 

  89. M. Wax, I. Ziskind: Detection of the number of coherent signals by the MDL principle. IEEE Trans. ASSP-37 1190–1196 (1989)

    Article  Google Scholar 

  90. P. Stoica, R.L. Moses, B. Friedlander, T. Söderström: Maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements. IEEE Trans. ASSP-37, 378ö392 (1989)

    Article  Google Scholar 

  91. T.W. Anderson: Asymptotic theory for principal component analysis. Ann. Math. Statist. 34, 122–148 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  92. R.P. Gupta: Asymptotic theory for principal component analysis in the complex case. J. Indian Stat. Assoc. 3, 97–106 (1965)

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ottersten, B., Viberg, M., Stoica, P., Nehorai, A. (1993). Exact and Large Sample Maximum Likelihood Techniques for Parameter Estimation and Detection in Array Processing. In: Haykin, S., Litva, J., Shepherd, T.J. (eds) Radar Array Processing. Springer Series in Information Sciences, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77347-1_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-77347-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-77349-5

  • Online ISBN: 978-3-642-77347-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics