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Introduction

  • Gökhan Gül
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 414)

Abstract

The objective of this book is to develop new robust detection schemes that are able to deal with both outliers as well as modeling errors, improve existing methods, design novel decentralized detection systems, and determine the bounds on the performance losses in minimax (decentralized) decision making as well as in minimax decentralized system design. Robustness has several different meanings in the literature, and in this book robustness is meant to be statistical robustness in the context of imprecise knowledge of the Bayesian prior and the nominal probability distributions. An important consideration is that the developed methods must be application independent, i.e. they should be applicable to any (distributed) robust decision making problem for a set of suitably chosen parameters.

Keywords

Cognitive Radio Fusion Center Robust Test Sequential Probability Ratio Test Fixed Sample Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [AM06]
    S. Aldosari and J. Moura, “Topology of sensor networks in distributed detection,” in Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference on, vol. 5, May 2006, pp. 1061–1064.Google Scholar
  2. [AVJ02]
    S. Appadwedula, V. Veeravalli, and D. Jones, “Robust and locally-optimum decentralized detection with censoring sensors,” in Information Fusion, 2002. Proceedings of the Fifth International Conference on, vol. 1, July 2002, pp. 56–63.Google Scholar
  3. [AVJ08a]
    S. Appadwedula, V. V. Veeravalli, and D. L. Jones, “Decentralized detection with censoring sensors,” IEEE Transactions on Signal Processing, vol. 56, no. 4, pp. 1362–1373, 2008.Google Scholar
  4. [BS07]
    S. Barbarossa and G. Scutari, “Bio-inspired sensor network design,” Signal Processing Magazine, IEEE, vol. 24, no. 3, pp. 26–35, May 2007.Google Scholar
  5. [BKP97]
    R. Blum, S. Kassam, and H. Poor, “Distributed detection with multiple sensors I. advanced topics,” Proceedings of the IEEE, vol. 85, no. 1, pp. 64–79, Jan 1997.Google Scholar
  6. [CS11]
    F. S. Cattivelli and A. H. Sayed, “Distributed detection over adaptive networks using diffusion adaptation,” IEEE Transactions on Signal Processing, vol. 59, no. 5, pp. 1917–1932, May 2011.Google Scholar
  7. [CV03]
    J.-F. Chamberland and V. Veeravalli, “Decentralized detection in sensor networks,” Signal Processing, IEEE Transactions on, vol. 51, no. 2, pp. 407–416, Feb 2003.Google Scholar
  8. [CV07]
    J.-F. Chamberland and V. V. Veeravalli, “Wireless sensors in distributed detection applications,” IEEE Signal Processing Magazine, vol. 24, pp. 16–25, May 2007.Google Scholar
  9. [CP93]
    P.-N. Chen and A. Papamarcou, “New asymptotic results in parallel distributed detection,” Information Theory, IEEE Transactions on, vol. 39, no. 6, pp. 1847–1863, Nov 1993.Google Scholar
  10. [CP95]
    P.-N. Chen and A. Papamarcou, “Error bounds for parallel distributed detection under the neyman-pearson criterion,” Information Theory, IEEE Transactions on, vol. 41, no. 2, pp. 528–533, Mar 1995.Google Scholar
  11. [CJKV04]
    B. Chen, R. Jiang, T. Kasetkasem, and P. Varshney, “Channel aware decision fusion in wireless sensor networks,” Signal Processing, IEEE Transactions on, vol. 52, no. 12, pp. 3454–3458, Dec 2004.Google Scholar
  12. [CTV06]
    B. Chen, L. Tong, and P. Varshney, “Channel-aware distributed detection in wireless sensor networks,” Signal Processing Magazine, IEEE, vol. 23, no. 4, pp. 16–26, July 2006.Google Scholar
  13. [CVB08]
    Q. Cheng, P. Varshney, and C. Belcastro, “Fault detection in dynamic systems via decision fusion,” Aerospace and Electronic Systems, IEEE Transactions on, vol. 44, no. 1, pp. 227–242, January 2008.Google Scholar
  14. [CVMB09]
    Q. Cheng, P. Varshney, J. Michels, and C. Belcastro, “Distributed fault detection with correlated decision fusion,” Aerospace and Electronic Systems, IEEE Transactions on, vol. 45, no. 4, pp. 1448–1465, Oct 2009.Google Scholar
  15. [Che52]
    H. Chernoff, “A measure of asymptotic efficiency for tests of a hypothesis based on the sums of observations,” Annals of Mathematical Statistics, vol. 23, pp. 409–507, 1952.Google Scholar
  16. [Dab93]
    A. G. Dabak, “A geometry for detection theory,” Ph.D. dissertation, Rice University, May 1993.Google Scholar
  17. [DJ94]
    A. G. Dabak and D. H. Johnson, “Geometrically based robust detection,” in Proceedings of the Conference on Information Sciences and Systems, Johns Hopkins University, Baltimore, MD, May 1994, pp. 73–77.Google Scholar
  18. [Dev83]
    L. Devroye, “On arbitrary slow rates of global convergence in density estimation,” Zeitschrift fr Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 62, no. 4, pp. 475–483, 1983.Google Scholar
  19. [DLG02]
    G. L. Devroye L. and L. G., “A Note on robust hypothesis testing,” IEEE Transactions on Information Theory, vol. 48, no. 7, pp. 2111–2114, 2002.Google Scholar
  20. [Efr04]
    S. Efromovich, “Density estimation for biased data,” Ann. Statist., vol. 32, no. 3, pp. 1137–1161, 06 2004.Google Scholar
  21. [FM07]
    G. Fabeck and R. Mathar, “Tight performance bounds for distributed detection,” in Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on, vol. 3, April 2007, pp. III–1049–III–1052.Google Scholar
  22. [FRHS86]
    P. J. R. Frank R. Hampel, Elvezio M. Ronchetti and W. A. Stahel, Robust Statistics - The Approach Based on Influence Functions. Wiley, 1986.Google Scholar
  23. [Ger87]
    E. Geroniotis, “Robust distributed discrete-time block and sequential detection,” in Proc. 1987 Conf. Inform. Sci. Syst., Johns Hopkins Univ., Baltimore, MD, Mar. 1987, pp. 354–360.Google Scholar
  24. [Ger90]
    E. Geroniotis and Y. A. Chau, “Robust data fusion for multisensor detection systems,” IEEE Trans. Inform. Theory, vol. 36, pp. 1265–1279, Nov 1990.Google Scholar
  25. [GC88]
    E. Geroniotis and Y. A. Chau, “On minimax robust data fusion,” in Proc. 1988 Conf. Inform. Sci. Syst., Princeton Univ., Princeton, NJ, Mar. 1988, pp. 876–881.Google Scholar
  26. [GM75]
    J. D. Gibson and J. L. Melsa, Introduction to nonparametric detection with applications, ser. Mathematics in science and engineering. New York, San Francisco, London: Academic Press, 1975.Google Scholar
  27. [GZ12]
    G. Gül and A. M. Zoubir, “Robust detection and optimization with decentralized parallel sensor networks,” in Proc. IEEE 13th Int. Workshop on Advances in Wireless Communications (SPAWC), Cesme, Turkey, June 2012, pp. 21–24.Google Scholar
  28. [GM91]
    L. Györfi and E. C. V. D. Meulen, “Consistent nonparametric tests of independence,” Nonparametric Functional Estimation and Related Topics, vol. 335, pp. 631–645, 1991.Google Scholar
  29. [HB09]
    M. Hefeeda and M. Bagheri, “Forest fire modeling and early detection using wireless sensor networks.” Ad Hoc & Sensor Wireless Networks, vol. 7, no. 3-4, pp. 169–224, 2009.Google Scholar
  30. [HV89]
    I. Hoballah and P. Varshney, “Distributed Bayesian signal detection,” Information Theory, IEEE Transactions on, vol. 35, no. 5, pp. 995–1000, Sep 1989.Google Scholar
  31. [Hub65]
    P. J. Huber, “A robust version of the probability ratio test,” Ann. Math. Statist., vol. 36, pp. 1753–1758, 1965.Google Scholar
  32. [Hub81]
    P. J. Huber, Robust statistics. Wiley New York, 1981.Google Scholar
  33. [HS68]
    P. J. Huber, “Robust confidence limits,” Z. Wahrcheinlichkeitstheorie verw. Gebiete, vol. 10, pp. 269—278, 1968.Google Scholar
  34. [HS73]
    P. J. Huber and V. Strassen, “Minimax tests and the Neyman-Pearson lemma for capacities,” Ann. Statistics, vol. 1, pp. 251–263, 1973.Google Scholar
  35. [IT94]
    W. Irving and J. Tsitsiklis, “Some properties of optimal thresholds in decentralized detection,” Automatic Control, IEEE Transactions on, vol. 39, no. 4, pp. 835–838, Apr 1994.Google Scholar
  36. [IVD11]
    S. Iyengar, P. Varshney, and T. Damarla, “A parametric copula-based framework for hypothesis testing using heterogeneous data,” Signal Processing, IEEE Transactions on, vol. 59, no. 5, pp. 2308–2319, May 2011.Google Scholar
  37. [KAM08]
    S. Kar, S. Aldosari, and J. Moura, “Topology for distributed inference on graphs,” Signal Processing, IEEE Transactions on, vol. 56, no. 6, pp. 2609–2613, June 2008.Google Scholar
  38. [Kay98]
    S. M. Kay, Fundamentals of Statistical Signal Processing, Vol. 2: Detection Theory. Prentice Hall PTR, Jan. 1998.Google Scholar
  39. [Kha05]
    K. D. Kharin, A., “Robust sequential testing of hypothesis on discrete probability distributions,” Austrian Journal of Statistics, vol. 34, no. 2, pp. 153–162, 2005.Google Scholar
  40. [Leh86]
    E. Lehmann, Testing statistical hypotheses, ser. Wiley series in probability and mathematical statistics: Probability and mathematical statistics. Wiley, 1986.Google Scholar
  41. [Lev08]
    B. C. Levy, Principles of Signal Detection and Parameter Estimation, 1st ed. Springer Publishing Company, Incorporated, 2008.Google Scholar
  42. [Lev09]
    B. C. Levy, “Robust hypothesis testing with a relative entropy tolerance,” IEEE Transactions on Information Theory, vol. 55, no. 1, pp. 413–421, 2009.Google Scholar
  43. [LWI11]
    L. Lu, H.-C. Wu, and S. Iyengar, “A novel robust detection algorithm for spectrum sensing,” Selected Areas in Communications, IEEE Journal on, vol. 29, no. 2, pp. 305–315, February 2011.Google Scholar
  44. [MV97]
    A. McKellips and S. Verdu, “Worst case additive noise for binary-input channels and zero-threshold detection under constraints of power and divergence,” Information Theory, IEEE Transactions on, vol. 43, no. 4, pp. 1256–1264, Jul 1997.Google Scholar
  45. [MV06]
    A. L. McKellips and S. Verdu, “Maximin performance of binary-input channels with uncertain noise distributions,” IEEE Trans. Inf. Theor., vol. 44, no. 3, pp. 947–972, Sep. 2006.Google Scholar
  46. [PBS08]
    L. Pescosolido, S. Barbarossa, and G. Scutari, “Radar sensor networks with distributed detection capabilities,” in Radar Conference, 2008. RADAR ’08. IEEE, May 2008, pp. 1–6.Google Scholar
  47. [PKP06]
    J. Predd, S. Kulkarni, and H. Poor, “Distributed learning in wireless sensor networks,” Signal Processing Magazine, IEEE, vol. 23, no. 4, pp. 56–69, July 2006.Google Scholar
  48. [Qua85]
    P. X. Quang, “Robust sequential testing,” Annals of Statistics, vol. 13, no. 2, pp. 638–649, 1985.Google Scholar
  49. [SE99]
    S. Schneider and L. Excoffier, “Estimation of past demographic parameters from the distribution of pairwise differences when the mutation rates vary among sites: application to human mitochondrial dna,” Genetics, vol. 152, no. 3, pp. 1079–1089, Jul 1999.Google Scholar
  50. [SVR11]
    A. Sundaresan, P. Varshney, and N. Rao, “Copula-based fusion of correlated decisions,” Aerospace and Electronic Systems, IEEE Transactions on, vol. 47, no. 1, pp. 454–471, January 2011.Google Scholar
  51. [Sur14]
    F. Y. Suratman, “Spectrum sensing in cognitive radio: Bootstrap and sequential detection approaches,” Ph.D. dissertation, TU Darmstadt, Darmstadt, February 2014.Google Scholar
  52. [SZ11]
    F. Suratman and A. Zoubir, “Collaborative spectrum sensing in cognitive radio using hard decision combining with quality information,” in Statistical Signal Processing Workshop (SSP), 2011 IEEE, June 2011, pp. 377–380.Google Scholar
  53. [SCZ10]
    F. Suratman, Y. Chakhchoukh, and A. Zoubir, “Locally optimum detection in heavy-tailed noise for spectrum sensing in cognitive radio,” in Cognitive Information Processing (CIP), 2010 2nd International Workshop on, June 2010, pp. 134–139.Google Scholar
  54. [STZ13]
    F. Suratman, A. Tetz, and A. Zoubir, “Collaborative spectrum sensing using sequential detections: Soft decision vs. hard decision,” in Information and Communication Technology (ICoICT), 2013 International Conference of, March 2013, pp. 1–6.Google Scholar
  55. [TTW08]
    W. P. Tay, J. Tsitsiklis, and M. Win, “On the impact of node failures and unreliable communications in dense sensor networks,” Signal Processing, IEEE Transactions on, vol. 56, no. 6, pp. 2535–2546, June 2008.Google Scholar
  56. [TVB87]
    S. Thomopoulos, R. Viswanathan, and D. Bougoulias, “Optimal decision fusion in multiple sensor systems,” Aerospace and Electronic Systems, IEEE Transactions on, vol. AES-23, no. 5, pp. 644–653, Sept 1987.Google Scholar
  57. [Tsi93]
    J. N. Tsitsiklis, “Decentralized detection,” in In Advances in Statistical Signal Processing. JAI Press, 1993, pp. 297–344.Google Scholar
  58. [Var96]
    P. K. Varshney, Distributed detection and data fusion, 1st ed. Secaucus, NJ, USA: Springer-Verlag New York, Inc., 1996.Google Scholar
  59. [VBP93]
    V. V.  Veeravalli, T. Basar, and H. Poor, “Decentralized sequential detection with a fusion center performing the sequential test,” Information Theory, IEEE Transactions on, vol. 39, no. 2, pp. 433–442, Mar 1993.Google Scholar
  60. [VBP94]
    V. V. Veeravalli, T. Basar, and H. V. Poor, “Decentralized sequential detection with sensors performing sequential tests,” MCSS, vol. 7, no. 4, pp. 292–305, 1994.Google Scholar
  61. [VP94]
    V. V. Veeravalli, T. Basar and H. V. Poor, “Minimax robust decentralized detection,” IEEE Trans. Inform. Theory, vol. 40, pp. 35–40, Jan 1994.Google Scholar
  62. [VV97]
    R. Viswanathan and P. Varshney, “Distributed detection with multiple sensors I. fundamentals,” Proceedings of the IEEE, vol. 85, no. 1, pp. 54–63, Jan 1997.Google Scholar
  63. [WSB00]
    P. Willett, P. Swaszek, and R. Blum, “The good, bad and ugly: distributed detection of a known signal in dependent gaussian noise,” Signal Processing, IEEE Transactions on, vol. 48, no. 12, pp. 3266–3279, Dec 2000.Google Scholar
  64. [WCS13]
    I. Winkelmann, P. F. Campos, J. Strugnell, Y. Cherel, P. J. Smith, T. Kubodera, L. Allcock, M.-L. Kampmann, H. Schroeder, A. Guerra, M. Norman, J. Finn, D. Ingrao, M. Clarke, and M. T. P. Gilbert, “Mitochondrial genome diversity and population structure of the giant squid architeuthis: genetics sheds new light on one of the most enigmatic marine species,” Proceedings of the Royal Society of London B: Biological Sciences, vol. 280, no. 1759, 2013.Google Scholar
  65. [XBL05]
    L. Xiao, S. Boyd, and S. Lall, “A scheme for robust distributed sensor fusion based on average consensus,” in Information Processing in Sensor Networks, 2005. IPSN 2005. Fourth International Symposium on, April 2005, pp. 63–70.Google Scholar
  66. [Yin14]
    F. Yin, “Robust wireless localization in harsh mixed line-of-sight/non-line-of-sight environments,” Ph.D. dissertation, TU Darmstadt, August 2014.Google Scholar
  67. [ZW94]
    S. M. Zabin and G. A. Wright, “Nonparametric density estimation and detection in impulsive interference channels. II. detectors,” IEEE Transactions on Communications, vol. 42, no. 234, pp. 1698–1711, 1994.Google Scholar
  68. [ZVW00]
    Q. Zhang, P. K. Varshney, and R. D. Wesel, “Optimal distributed binary hypothesis testing with independent identical sensors,” in Department of Computer Engineering and Informatics, University of Patras, 2000, pp. 1–7.Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut für Nachrichtentechnik, Fachbereich Elektro- und Informationstechnik (ETIT)Technische Universität DarmstadtDarmstadtGermany

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