Open Access

4D Near-Field Source Localization Using Cumulant

EURASIP Journal on Advances in Signal Processing20072007:017820

Received: 20 September 2006

Accepted: 24 March 2007

Published: 23 May 2007


This paper proposes a new cumulant-based algorithm to jointly estimate four-dimensional (4D) source parameters of multiple near-field narrowband sources. Firstly, this approach proposes a new cross-array, and constructs five high-dimensional Toeplitz matrices using the fourth-order cumulants of some properly chosen sensor outputs; secondly, it forms a parallel factor (PARAFAC) model in the cumulant domain using these matrices, and analyzes the unique low-rank decomposition of this model; thirdly, it jointly estimates the frequency, two-dimensional (2D) directions-of-arrival (DOAs), and range of each near-field source from the matrices via the low-rank three-way array (TWA) decomposition. In comparison with some available methods, the proposed algorithm, which efficiently makes use of the array aperture, can localize sources using sensors. In addition, it requires neither pairing parameters nor multidimensional search. Simulation results are presented to validate the performance of the proposed method.


Authors’ Affiliations

Institute of Acoustics, Chinese Academy of Sciences
Graduate School of Chinese Academy of Sciences
National Laboratory of Radar Signal Processing, Xidian University
School of Computer Science and Engineering, Xidian University


  1. Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Upper Saddle River, NJ, USA; 1993.MATHGoogle Scholar
  2. Schmidt RO: Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation 1986,34(3):276-280. 10.1109/TAP.1986.1143830View ArticleGoogle Scholar
  3. Roy R, Kailath T: ESPRIT—estimation of signal parameters via rotational invariance techniques. IEEE Transactions on Acoustics, Speech, and Signal Processing 1989,37(7):984-995. 10.1109/29.32276View ArticleMATHGoogle Scholar
  4. Krim H, Viberg M: Two decades of array signal processing research: the parametric approach. IEEE Signal Processing Magazine 1996,13(4):67-94. 10.1109/79.526899View ArticleGoogle Scholar
  5. Swindlehurst AL, Kailath T: Passive direction-of-arrival and range estimation for near-field sources. Proceedings of the 4th Annual ASSP Workshop on Spectrum Estimation and Modeling, August 1988, Minneapolis, Minn, USA 123-128.View ArticleGoogle Scholar
  6. Huang Y-D, Barkat M: Near-field multiple source localization by passive sensor array. IEEE Transactions on Antennas and Propagation 1991,39(7):968-975. 10.1109/8.86917View ArticleGoogle Scholar
  7. Jeffers R, Bell KL, Van Trees HL: Broadband passive range estimation using MUSIC. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '02), May 2002, Orlando, Fla, USA 3: 2921-2924.Google Scholar
  8. Weiss AJ, Friedlander B: Range and bearing estimation using polynomial rooting. IEEE Journal of Oceanic Engineering 1993,18(2):130-137. 10.1109/48.219532View ArticleGoogle Scholar
  9. Starer D, Nehorai A: Passive localization on near-field sources by path following. IEEE Transactions on Signal Processing 1994,42(3):677-680. 10.1109/78.277864View ArticleGoogle Scholar
  10. Grosicki E, Abed-Meraim K, Hua Y: A weighted linear prediction method for near-field source localization. IEEE Transactions on Signal Processing 2005,53(10, part 1):3651-3660.MathSciNetView ArticleGoogle Scholar
  11. Abed-Meraim K, Hua Y, Belouchrani A: Second-order near-field source localization: algorithm and performance analysis. Proceedings of the 30th Asilomar Conference on Signals, Systems, and Computers, November 1996, Pacific Grove, Calif, USA 1: 723-727.View ArticleGoogle Scholar
  12. Challa RN, Shamsunder S: High-order subspace based algorithms for passive localization of near-field sources. Proceedings of the 29th Asilomar Conference on Signals, Systems, and Computers, October 1995, Pacific Grove, Calif, USA 2: 777-781.View ArticleGoogle Scholar
  13. Yuen N, Friedlander B: Performance analysis of higher order ESPRIT for localization of near-field sources. IEEE Transactions on Signal Processing 1998,46(3):709-719. 10.1109/78.661337View ArticleGoogle Scholar
  14. Chen J-F, Zhu X-L, Zhang X-D: A new algorithm for joint range-DOA-frequency estimation of near-field sources. EURASIP Journal on Applied Signal Processing 2004,2004(3):386-392. 10.1155/S1110865704310152MathSciNetView ArticleMATHGoogle Scholar
  15. Wu Y, Ma L, Hou C, Zhang G, Li J: Subspace-based method for joint range and DOA estimation of multiple near-field sources. Signal Processing 2006,86(8):2129-2133. 10.1016/j.sigpro.2006.01.015View ArticleMATHGoogle Scholar
  16. Kabaoglu N, Cirpan HA, Cekli E, Paker S: Maximum likelihood 3-D near-field source localization using the EM algorithm. Proceedings of the 8th IEEE International Symposium on Computers and Communication (ISCC '03), June-July 2003, Kiris-Kemer, Turkey 1: 492-497.Google Scholar
  17. Hung H-S, Chang S-H, Wu C-H: 3-D MUSIC with polynomial rooting for near-field source localization. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '96), May 1996, Atlanta, Ga, USA 6: 3065-3068.Google Scholar
  18. Abed-Meraim K, Hua Y: 3-D near field source localization using second order statistics. Proceedings of the 31st Asilomar Conference on Signals, Systems, and Computers, November 1997, Pacific Grove, Calif, USA 2: 1307-1311.Google Scholar
  19. Cattell RB: "Parallel proportional profiles" and other principles for determining the choice of factors by rotation. Psychometrika 1944,9(4):267-283. 10.1007/BF02288739View ArticleGoogle Scholar
  20. Carroll JD, Chang J: Analysis of individual differences in multidimensional scaling via an n-way generalization of "Eckart-Young" decomposition. Psychometrika 1970,35(3):283-319. 10.1007/BF02310791View ArticleMATHGoogle Scholar
  21. Harshman RA: Foundations of the PARAFAC procedure: models and conditions for an "explanatory" multi-modal factor analysis. UCLA Working Papers in Phonetics 1970, 16: 1-84.Google Scholar
  22. Smilde A, Bro R, Geladi P: Multi-Way Analysis with Applications in the Chemical Sciences. John Wiley & Sons, Chichester, UK; 2004.View ArticleGoogle Scholar
  23. Kruskal JB: Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear Algebra and Its Applications 1977,18(2):95-138. 10.1016/0024-3795(77)90069-6MathSciNetView ArticleMATHGoogle Scholar
  24. Kruskal JB: Rank decomposition, and uniqueness for 3-way and n-way arrays. In Multiway Data Analysis. Edited by: Coppi R, Bolasco S. North-Holland, Amsterdam, The Netherlands; 1988:7-18.Google Scholar
  25. Jiang T, Sidiropoulos ND: Kruskal's permutation lemma and the identification of CANDECOMP/PARAFAC and bilinear models with constant modulus constraints. IEEE Transactions on Signal Processing 2004,52(9):2625-2636. 10.1109/TSP.2004.832022MathSciNetView ArticleGoogle Scholar
  26. Sidiropoulos ND, Giannakis GB, Bro R: Blind PARAFAC receivers for DS-CDMA systems. IEEE Transactions on Signal Processing 2000,48(3):810-823. 10.1109/78.824675View ArticleGoogle Scholar
  27. Leurgans SE, Ross RT, Abel RB: A decomposition for three-way arrays. SIAM Journal on Matrix Analysis and Applications 1993,14(4):1064-1083. 10.1137/0614071MathSciNetView ArticleMATHGoogle Scholar
  28. Sanchez E, Kowalski BR: Tensorial resolution: a direct trilinear decomposition. Journal of Chemometrics 1990,4(1):29-45. 10.1002/cem.1180040105View ArticleGoogle Scholar
  29. De Lathauwer L: A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization. SIAM Journal on Matrix Analysis and Applications 2006,28(3):642-666. 10.1137/040608830MathSciNetView ArticleMATHGoogle Scholar
  30. Sidiropoulos ND, Bro R, Giannakis GB: Parallel factor analysis in sensor array processing. IEEE Transactions on Signal Processing 2000,48(8):2377-2388. 10.1109/78.852018View ArticleGoogle Scholar
  31. Rong Y, Vorobyov SA, Gershman AB, Sidiropoulos ND: Blind spatial signature estimation via time-varying user power loading and parallel factor analysis. IEEE Transactions on Signal Processing 2005,53(5):1697-1710.MathSciNetView ArticleGoogle Scholar
  32. Mendel JM: Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications. Proceedings of the IEEE 1991,79(3):278-305. 10.1109/5.75086View ArticleGoogle Scholar
  33. Bro R, Sidiropoulos ND, Giannakis GB: A fast least squares algorithm for separating trilinear mixtures. Proceedings of the 1st International Workshop on Independent Component Analysis and Blind Signal Separation, January 1999, Aussois, France 289-294.Google Scholar
  34. Sidiropoulos ND: COMFAC: Matlab code for LS fitting of the complex PARAFAC model in 3-D. 1998. Scholar
  35. Bro R: PARAFAC: tutorial and applications. Chemometrics and Intelligent Laboratory Systems 1997,38(2):149-171. 10.1016/S0169-7439(97)00032-4View ArticleGoogle Scholar
  36. Bro R, Sidiropoulos ND: Least squares algorithms under unimodality and non-negativity constraints. Journal of Chemometrics 1998,12(4):223-247. 10.1002/(SICI)1099-128X(199807/08)12:4<223::AID-CEM511>3.0.CO;2-2View ArticleGoogle Scholar
  37. Vorobyov SA, Rong Y, Sidiropoulos ND, Gershman AB: Robust iterative fitting of multilinear models. IEEE Transactions on Signal Processing 2005,53(8):2678-2689.MathSciNetView ArticleGoogle Scholar
  38. De Lathauwer L, De Moor B, Vandewalle J: Computation of the canonical decomposition by means of a simultaneous generalized schur decomposition. SIAM Journal on Matrix Analysis and Applications 2004,26(2):295-327. 10.1137/S089547980139786XMathSciNetView ArticleMATHGoogle Scholar
  39. Tomasi G: Practical and computational aspects in chemometric data analysis, Ph.D. thesis. Department of Food Science, Faculty of Life Sciences, University of Copenhagen, Frederiksberg, Denmark; 2006. Scholar
  40. Tucker LR: The extension of factor analysis to three-dimensional matrices. In Contributions to Mathematical Psychology. Edited by: Gulliksen H, Frederiksen N. Holt, Rinehart & Winston, New York, NY, USA; 1964:109-127.Google Scholar
  41. Tucker LR: Some mathematical notes on three-mode factor analysis. Psychometrika 1966,31(3):279-311. 10.1007/BF02289464MathSciNetView ArticleGoogle Scholar


© Junli Liang et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.