Chapter 2
Spatial Spectrum Estimation
Book Editor(s):Simon Haykin,
K. J. Ray Liu,
Simon Haykin
Department of Electrical Engineering, McMaster University, Hamilton, Ontario, Canada
Search for more papers by this authorK. J. Ray Liu
Department of Electrical & Computer Engineering, University of Maryland, College Park, MD, USA
Search for more papers by this authorFirst published: 22 January 2010
Summary
This chapter contains sections titled:
-
Introduction
-
Fundamentals
-
Temporal Spectrum Estimation
-
Spatial Spectrum Estimation
-
Final Remarks
-
References
REFERENCES
- E. A. Robinson, “A historical perspective of spectrum estimation,” Proc. IEEE, vol. 70, pp. 886–907, 1982.
-
A. Schuster, “On the investigation of hidden periodicities with application to a supposed 26-day period of meteorological phenomena,” Terrestr. Magnet., vol. 3, pp. 13–41, 1898.
10.1029/TM003i001p00013 Google Scholar
- J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput., vol. 19, pp. 297–301, 1965.
- J. P. Burg, “A new analysis technique for time series data,” in NATO Advanced Study Institute on Signal Processing with Emphasis on Underwater Acoustics, Enschede, Netherlands, 1968.
- J. P. Burg, “Maximum entropy spectral analysis”, PhD dissertation, Stanford University, 1975.
- J. Capon, “High-resolution frequency-wavenumber spectrum analysis,” Proc. IEEE , vol. 57, no. 8, pp. 1408–1418, 1969.
- H. Hotelling, “Analysis of a complex of statistical variables with principal components,” J. Ed. Psychol., vol. 24, pp. 417–441, 498–520, 1933.
- T. Koopmans, Linear Regression Analysis of Economic Time Series, De Erven F. Bohn N. V.: Harlem, 1937.
- V. F. Pisarenko, “The retrieval of harmonics from a covariance function,” Geophys. J. R. Astron. Soc., vol. 33, pp. 347–366, 1973.
- G. Bienvenu and L. Kopp, “Adaptivity to bakground noise spatial coherence for high resolution passive methods,” in the Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 1980, pp. 307–310.
- R. O. Schmidt, “A signal subspace approach to multiple emitter location and spectral estimation,” PhD dissertation, Stanford University, 1981.
- L. Marple, Digital Spectral Analysis with Applications, Englewood Cliffs, NJ: 1997.
- P. Stoica and R. Moses, Spectral Analysis of Signals, Upper Saddle River, NJ: Pearson Prentice Hall, 2005.
-
H. L. Van Trees, Optimum Array Processing, Wiley, 2002.
10.1002/0471221104 Google Scholar
- H. Krim and M. Viberg, “Two decades of array signal processing,” IEEE Signal Process. Mag., vol. 4, pp. 67–94, 1996.
- B. D. Van Veen and K. M. Buckley, “Beamforming: A versatile approach to spatial filtering,” IEEE Signal Process. Mag., vol. 2, pp. 4–24, 1988.
- M. B. Priestley, Spectral Analysis and Time Series, New York: Academic 1981.
- S. M. Kay, Modern Spectral Estimation, Englewood Cliffs, NJ: Prentice Hall, 1988.
- R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra from the Point of View of Communications Engineering, New York: Dover, 1958.
- D. J. Thomson, “Spectrum estimation and harmonic analysis,” Proc. IEEE , vol. 72, no. 9, pp. 1055–1096, 1982.
- C. T. Mullis and L. L. Scharf, “Quadratic estimators of the power spectrum,” in Advances in Spectrum Analysis and Array Processing, S. Haykin (Ed.), Englewood Cliffs, NJ: Prentice Hall, 1991, pp. 395–402.
-
D. B. Percival and A. T. Walden, Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques, Cambridge: Cambridge University Press, 1993.
10.1017/CBO9780511622762 Google Scholar
- K. Reidel and A. Sidorenko, “Minimum bias multiple taper spectral estimation,” IEEE Trans. Signal Process., vol. 43, no. 1, pp. 188–195, 1989.
- D. J. Thomson, “Jackknifing multitaper spectrum estimates,” IEEE Signal Process. Mag., vol. 24, no. 4, pp. 20–30, 2007.
- P. Stoica and Y. Selén, “Model order selection,” IEEE Signal Process. Mag., vol. 21, no. 4, pp. 36–47, 2004.
- H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Automat. Control, vol. AC-19, no. 4, pp. 716–723, 1974.
- J. Rissanen, “Modeling by shortest data description,” Automatica, vol. 14, pp. 465–471, 1978.
- J. F. Böehme, “Array processing,” in Advances in Spectrum Analysis and Array Processing, S. Haykin (Ed.), Prentice Hall, 1991, pp. 97–63.
- J. Benesty, J. Chen, and Y. Huang, “A generalized MVDR spectrum,” IEEE Signal Process. Lett., vol. 12, no. 12, pp. 827–830, 2005.
- A. Drosopoulos and S. Haykin, “Adaptive radar parameter estimation with Thomson's multiple window method,” in Adaptive Radar Detection and Estimation, S. Haykin and A. Steinhardt, (Eds.), New York: Wiley, 1991.
- T.-C. Liu and D. Van Veen, “Multiple window based minimum variance spectrum estimation for multidimensional random fields,” IEEE Trans. Signal Process., vol. 40, no. 3, pp. 578–589, 1992.
- M. Viberg and A. L. Swindlehurst, “A Bayesian approach to auto-calibration for parametric array signal processing,” IEEE Trans. Signal Process., vol. 42, no. 12, pp. 3073–3083, 1989.
- P. Stoica, R. Moses, B. Friedlander, and T. Söderström, “Maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements,” IEEE Trans. Acoust. Speech Signal Process., vol. 37, no. 3, pp. 378–392, 1989.
- I. Ziskind and M. Wax, “Maximum likelihood localization of multiple sources by alternating projection,” IEEE Trans. Signal Process., vol. 36, no. 10, pp. 1553–1560, 1988.
-
B. Ottersten, M. Viberg, P. Stoica, and A. Nehorai, “Exact and large sample ML techniques for parameter estimation from sensor array data,” in Radar Array Processing, S. Haykin, J. Litva, and T. J. Shepherd (Eds.), Springer-Verlag, 1993, pp. 99–151.
10.1007/978-3-642-77347-1_4 Google Scholar
- B. Ottersten, M. Viberg, and T. Kailath, “Analysis of subspace fitting and ML techniques for parameter estimation from sensor array data,” IEEE Trans. Signal Process., vol. 40, no. 3, pp. 590–600, 2002.
- G. Bienvenu, “Influence of the spatial coherence of the bakground in high resolution passive methods,” in the Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 1979, pp. 306–309.
- A. J. Barabell, “Improving the resolution performance of eigenstructure-based direction-finding algorithms,” in the Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 1983, pp. 336–339.
- W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Markov Chain Monte Carlo in Practice, New York: Chapman & Hall, 1996.
- J.-R. Larocque and J. P. Reilly, “Reversible jump MCMC for joint detection and estimation of sources in colored noise,” IEEE Trans. Signal Process., vol. 50, no. 2, pp. 231–240, 2002.
- G. Schwartz, “Estimating the dimension of a model,” Ann. Statist., vol. 6, pp. 461–464, 1978.
- M. Wax and T. Kailath, “Detection of signals by information theoretic criteria,” IEEE Trans. Acoust. Speech Signal Process., vol. 33, no. 2, pp. 387–392, 1985.
- M. Kaveh, H. Wang, and H. Hung, “On the theoretical performance of a class of estimators of the number of narrowband sources,” IEEE Trans. Acoust. Speech, Signal Process., vol. 35, no. 19, pp. 1350–1352, 1987.
- K. M. Wong, Q.-T. Zhang, J. Reilly, and P. Yip, “On information theoretic criteria for determining the number of signals in high resolution array processing,” IEEE Trans. Acoust. Speech Signal Process., vol. 38, no. 11, pp. 1959–1971, 1990.
- A. P. Liavas and P. A Regalia, “On the behavior of information theoretic criteria for model order selection,” IEEE Trans. Signal Process., vol. 49, no. 8, pp. 1689–1695, 2001.
- P. J. Green, “Reversible jump Markov chain Monte Carlo computation and Bayesian model determination,” Biometrika, vol. 4, pp. 711–732, 1995.
