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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
S.P. Applebaum: Adaptive arrays. Technical Report SPL TR 66–1, Syracuse University Research Corporation (1966)
B. Widrow, P.E. Mantey, L.J. Griffiths, B.B. Goode: Adaptive antenna systems. Proc. IEEE 55, 2143–2159(1967)
F.C. Schweppe: Sensor array data processing for multiple signal sources. IEEE Trans. IT-14, 294–305 (1968)
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)
J. Capon: High resolution frequency wave number spectrum analysis. Proc. IEEE 57, 1408–1418 (1969)
R.A. Monzingo, T.W. Miller: Introduction to Adaptive Arrays (Wiley, New York 1980)
S. Haykin (ed): Array Signal Processing (Prentice-Hall, Englewood Cliffs, NJ 1985)
B.D. Van Veen, K.M. Buckley: Beamforming: A versatile approach to spatial filtering. IEEE ASSP Mag. pp. 4–24 (April 1988)
J.P. Burg: Maximum entropy spectral analysis, in Proc 37th Annual Int. SEG Meeting, Oklahoma City, OK (1967)
D.W. Tufts, R. Kumaresan: Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihood. Proc. IEEE 70, 975ö989 (1982)
R. Kumaresan, D.W. Tufts: Estimating the angles of arrival of multiple plane waves. IEEE Trans. AES-19, 134–139 (1983)
R.O. Schmidt: Multiple emitter location and signal parameter estimation, in Proc. RADC Spectrum Estimation Workshop, Rome, NY (1979) pp. 243–258
G. Bienvenu, L. Kopp: Principle de la goniometrie passive adaptive, in Proc. 7’eme Colloque GRESIT, Nice, France (1979) pp. 106/1–10
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
N.L. Owsley: Data adaptive orthonormalization, in Proc. ICASSP 78, Tulsa, OK (1978) pp. 109–112
V.F. Pisarenko: The retrieval of harmonics from a covariance function. Geophys. J. R. Astron. Soc. 33, 347–366 (1973)
G. Bienvenu, L. Kopp: Optimality of high resolution array processing, IEEE Trans. ASSP-31, 1235–1248 (1983)
A. Paulraj, R. Roy, T. Kailath: A subspace rotation approach to signal parameter estimation. Proc. IEEE 74, 1044–1045 (1986)
S.Y. Kumg, CK. Lo, R. Foka: A Toeplitz approximation approach to coherent source direction finding, in, Proc. ICASSP 86, Tokyo (1986)
S.J. Orfanidis: A reduced MUSIC algorithm, in Proc. IEEE ASSP 3rd Workshop Spectrum Est. Modeling, Boston, MA (1986) pp. 165–167
W.J. Bangs: Array processing with generalized beamformers. Ph.D. Thesis, Yale University (1971)
M. Wax: Detection and estimation of superimposed signals. Ph.D. Thesis, Stanford University (1985)
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
J.F. Böhme: Estimation of spectral parameters of correlated signals in wavefields. Signal Processing 10, 329–337 (1986)
P. Stoica, A. Nehorai: MUSIC, maximum likelihood and Cramér-Rao bound, in Proc. ICASSP 88 New York (1988) pp. 2296–2299
B. Ottersten, L. Ljung: Asymptotic results for sensor array processing, in Proc. ICASSP 89, Glasgow, Scotland (1989) pp. 2266–2269
B. Ottersten, M. Viberg: Analysis of subspace fitting based methods for sensor array processing, in Proc. ICASSP 89, Glasgow, Scotland (1989) pp. 2807–2810
R.O. Schmidt: A signal subspace approach to multiple emitter location and spectral estimation. Ph.D. Thesis, Stanford University (1981)
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
P. Stoica, A. Nehorai: MUSIC, maximum likelihood and Cramér-Rao bound. IEEE Trans. AssP-37, 720–741 (1989)
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)
P. Stoica, A. Nehorai: Performance study of conditional and unconditional direction-of-arnval estimation. IEEE Trans. ASSP-38, 1783–1795 (1990)
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
DJ. Jeffries, D.R. Farrier: Asymptotic results for eigenvector methods. IEE Proc. F 132, 589–594 (1985)
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)
B. Porat, B. Friedlander: Analysis of the asymptotic relative efficiency of the MUSIC algorithm. IEEE Trans. ASSP-36, 532–544 (1988)
B.D. Rao, K.V.S. Hari: Performance analysis of root-music. IEEE Trans. ASSP-37,1939–1949 (1989)
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)
P. Stoica, A. Nehorai: MUSIC, maximum likelihood, and Cramér-Rao bound: Further results and comparisons. IEEE Trans. ASSP-38, 2140–2150 (1990)
P. Stoica, A. Nehorai: Performance comparison of subspace rotation and MUSIC methods for direction estimation. IEEE Trans. SP-39, 446–453 (1991)
P. Stoica, K. Sharman: A novel eigenanalysis method for direction estimation. IEE Proc. part F, 19–26 (1990)
P. Stoica, K. Sharman: Maximum likelihood methods for direction-of-arrival estimation. IEEE Trans. ASSP-38, 1132–1143 (1990)
D. Staren Algorithms for polynomial-based signal processing. Ph.D. Thesis, Yale University (1990)
M. Viberg, B. Ottersten: Sensor array processing based on subspace fitting. IEEE Trans. SP-39, 1110–1121 (1991)
B. Ottersten, M. Viberg, T. Kailath: Performance analysis of the total least squares ESPRIT algorithm. IEEE Trans. SP-39, 1122–1135 (1991)
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
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
M. Wax, I. Ziskind: On unique localization of multiple sources by passive sensor arrays. IEEE Trans. ASSP-37, 996–1000 (1989)
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)
K.V. Mardia, J.T. Kent, J.M. Bibby: Multivariate Analysis (Academic, London 1979)
T.W. Anderson: An Introduction to Multivariate Statistical Analysis, 2nd edn. (Wiley, New York 1984)
N.R. Goodman: Statistical analysis based on a certain multivariate, complex gaussian distribution (an introduction). Ann. Math. Stat. 34, 152–176 (1963)
A.G. Jaffer: Maximum likelihood direction finding of stochastic sources: A separable solution, in Proc. ICASSP 88, New York (1988) pp. 2893–2896
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)
S.D. Silvey: Statistical Inference (Penguin, London 1970)
E.L. Lehmann: Theory of Point Estimation (Wiley, New York 1983)
A.J. Weiss, E. Weinstein: Lower bounds in parameter estimation- Summary of results, in Proc. ICASSP 86, Tokyo, Japan (1986) pp. 569–572
A. Graham: Kronecker Products and Matrix Calculus with Applications (ElHs Horwood, Chichester, UK 1981)
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)
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)
T. Söderström, P. Stoica: System Identification (Prentice-Hall, International, London, UK 1989)
R.H. Roy: ESPRIT, estimation of signal parameters via rotational invariance techniques. Ph.D. Thesis, Stanford University (1987)
J.A. Cadzow: A high resolution direction-of-arrival algorithm for narrow-band coherent and incoherent sources. IEEE Trans. ASSP-36, 965–979 (1988)
M. Viberg, B. Ottersten, T. Kailath: Detection and estimation in sensor arrays using weighted subspace fitting. IEEE Trans. ASSP-39, 2436–2449 (1991)
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)
M. Feder, E. Weinstein: Parameter estimation of superimposed signals using the EM algorithm. IEEE Trans. ASSP-36, 477–489 (1988)
M.I. Miller, D.R. Fuhrmann: Maximum-likelihood narrow-band direction finding and the EM algorithm., IEEE Trans. ASSP-38, 1560–1577 (1990)
I. Ziskind, M. Wax: Maximum likelihood localization of multiple sources by alternating projection. IEEE Trans. ASSP-36, 1553–1560 (1988)
Y. Bresler, A. Macovski: Exact maximum likelihood parameter estimation of superimposed exponential signals in noise. IEEE Trans. ASSP-34, 1081–1089 (1986)
K. Sharman: Maximum likelihood estimation by simulated annealing, in Proc. ICASSP 88, New York (1988) pp. 2741–2744
D. Goryn, M. Kaveh: Neural networks for narrowband and wideband direction finding, in Proc. ICASSP 88, New York (1988) pp. 2164–2167
K. Sharman, G.D. McClurkin: Genetic algorithms for maximum likelihood parameter estimation, in Proc. ICASSP 89, Glasgow, Scotland (1989) pp. 2716–2719
M. Wax, T. Kailath: Optimal localization of multiple sources by passive arrays. IEEE Trans. ASSP-31, 1210–1218 (1983)
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
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)
P.E. Gill, W. Murray, M.H. Wright: Practical Optimization (Academic, London 1981)
J.E. Dennis, R.B. Schnabel: Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice Hall, Englewood Cliffs, NJ 1983)
P.E. Gill, G.H. Golub, W. Murray, M.A. Saunders: Methods for modifying matrix factorizations. Math. Comp. 28, 505–535 (1974)
M. Wax, T. Kailath: Detection of signals by information theoretic criteria. IEEE Trans. ASSP-33, 387–392 (1985)
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)
G.H. Golub, C.F. Van Loan: Matrix Computations, 2nd edn. (Johns Hopkins University Press, Baltimore, MD 1989)
G. Xu, T. Kailath: Fast signal subspace decomposition without eigendecomposition, in Proc. 24th Asilomar Conf. Sig., Syst., Comput., Monterey, CA (1990)
I. Karasalo: Estimating the covariance matrix by signal subspace averaging. IEEE Trans. ASSP-34, 8–12 (1986)
R. Schreiber: Implementation of adaptive array algorithms. IEEE Trans. ASSP-34,1038–1045 (1986)
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
A.H. Abdallah, Y.H. Hu: Parallel VLSI computing array implementation for signal subspace updating algorithm. IEEE Trans. ASSP-37, 742–748 (1989)
R. Roy, T. Kailath: ESPRIT-Estimation of signal parameters via rotational invariance techniques. IEEE Trans. ASSP-37, 984–995 (1989)
J. Rissanen: Modeling by shortest data description. Automatica 14, 465–471 (1978)
M. Wax, I. Ziskind: Detection of the number of coherent signals by the MDL principle. IEEE Trans. ASSP-37 1190–1196 (1989)
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)
T.W. Anderson: Asymptotic theory for principal component analysis. Ann. Math. Statist. 34, 122–148 (1963)
R.P. Gupta: Asymptotic theory for principal component analysis in the complex case. J. Indian Stat. Assoc. 3, 97–106 (1965)
Editor information
Editors and Affiliations
Rights 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