## Abstract

Signal detection systems frequently must operate in environments that are difficult to characterize with precise statistical models, and thus it is of interest to develop signal detection procedures that are robust against (i.e., insensitive to) deviations in the statistical behavior of signals and noise. During the past two decades there has been considerable work on the problem of designing such procedures, and in this chapter we present a survey of some of the principal developments in this area.

## Keywords

Signal Detection Matched Filter Nominal Signal Noise Density Noise Sequence
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.

## Preview

Unable to display preview. Download preview PDF.

## References

- [1]P.J. Huber, A robust version of the probability ratio test,
*Ann. Math. Statist.*, Vol. 36, pp. 1753–1758, 1965.MathSciNetzbMATHCrossRefGoogle Scholar - [2]S.A. Kassam, Robust hypothesis testing for bounded classes of probability densities,
*IEEE Trans. Inform. Theory*, Vol IT–27, pp. 242–247, 1981.Google Scholar - [3]P.J. Huber, Robust confidence limits, Z. Wahr. verw. Geb., Vol. 10, pp. 269–278, 1968.zbMATHCrossRefGoogle Scholar
- [4]K.S. Vastola and H.V. Poor, On the p-point uncertainty class,
*IEEE Trans. Inform. Theory*, Vol. IT-29, pp. 316–327, 1984.Google Scholar - [5]H. Rieder, Least favorable pairs for special capacities,
*Ann. Statist.*, Vol. 5, pp. 909–921, 1977.MathSciNetzbMATHCrossRefGoogle Scholar - [6]P.J. Huber and V. Strassen, Minimax tests and the Neyman-Pearson lemma for capacities,
*Ann. Statist.*, Vol. 1, pp. 251–263, 1973.MathSciNetzbMATHCrossRefGoogle Scholar - [7]N.M. Khalfina and L.A. Khalfin, On a robust version of the likelihood ratio test,
*SIAM Th. Prob. Appl.*, Vol. 20, pp. 199–202, 1975.zbMATHCrossRefGoogle Scholar - [8]T. Bednarski, On solutions of minimax test problems for special capacities,
*Z. Wahr. verw. Geb.*, Vol. 58, pp. 397–405, 1981.MathSciNetzbMATHCrossRefGoogle Scholar - [9]V.P. Kuznetsov, Stable rules for discriminating hypotheses, Prob. Inform. Trans., Vol. 18, pp. 41–51, 1982.zbMATHGoogle Scholar
- [10]P.J. Huber, Robust estimation of a location parameter, Ann. Math. Statist., Vol. 35, pp. 73–101, 1964.MathSciNetzbMATHCrossRefGoogle Scholar
- [11]P.J. Huber, Robust Statistics, New York, NY: Wiley, 1981.zbMATHCrossRefGoogle Scholar
- [12]R.D. Martin and S.C. Schwartz, Robust detection of a known signal in nearly Gaussian noise,
*IEEE Trans. Inform. Theory*, Vol. IT–17, pp. 50–56, 1971.Google Scholar - [13]S.A. Kassam and J.B. Thomas, Asymptotically robust quantization for detection,
*IEEE Trans. Inform. Theory*, Vol. IT–22, pp. 22–26, 1976.Google Scholar - [14]H.V. Poor and J.B. Thomas, Asymptotically robust quantization for detection,
*IEEE Trans. Inform. Theory*, Vol. IT–24, pp. 222–229, 1978.Google Scholar - [15]A.H. El-Sawy and V.D. VandeLinde, Robust detection of known signals,
*IEEE Trans. Inform. Theory*, Vol. IT–23, pp. 722–727, 1977.Google Scholar - [16]A.H. El-Sawy and V.D. VandeLinde, Robust sequential detection of signals in noise, IEEE Trans. Inform. Theory, Vol. IT–25, pp. 346–353, 1979.Google Scholar
- [17]P.A. Kelly, Robust estimation and detection of signals with arbitrary parameters,
*Proc. 21st Annual Allerton Conf Comm., Contr., Comp*. pp. 602–609, 1983.Google Scholar - [18]A.H. El-Sawy, Detection of signals with unknown phase,
*Proc. 17 th Annual Allerton Conf. Comm., Contr., and Comp.*, pp. 152–165, 1979.Google Scholar - [19]H.V. Poor, Signal detection in weakly dependent noise - Part II: Robust detection,
*IEEE Trans. Inform. Theory*, Vol. IT–28, pp. 744–752, 1982.Google Scholar - [20]G.V. Moustakides and J.B. Thomas, Min-max detection of weak signals in
*ø*-mixing noise, IEEE Trans. Inform. Theory, Vol. IT–30, pp. 529–537, 1984.Google Scholar - [21]S.A. Kassam, G. Moustakides and J.G. Shin, Robust detection of known signals in asymmetric noise,
*IEEE Trans. Inform. Theory*, Vol. IT–28, pp. 84–91, 1982.Google Scholar - [22]R.D. Martin, Robust estimation of signal parameters with dependent data,
*Proc. 21st IEEE Conf. Dec. Contr.*, pp. 433–436, 1982.Google Scholar - [23]W.L. Root, Stability in signal detection problems, in
*Proc. Symp. Appl. Math.*, Vol. 16, Providence, RI: American Math. Society, 1964.Google Scholar - [24]F.R. Hampel, A general qualitative definition of robustness,
*Ann. Math. Statist.*, Vol. 42, pp. 1887–1896, 1971.MathSciNetzbMATHCrossRefGoogle Scholar - [25]W.A. Gardner, A unifying view of second-order measures of quality for signal classification,
*IEEE Trans. Comm.*, Vol. COM–28, pp. 807–815, 1980.Google Scholar - [26]L.H. Zetterberg, Signal detection under noise interference in a game situation,
*IEEE Trans. Inform. Theory*, Vol. IT–8, pp. 47–57, 1962.Google Scholar - [27]V.P. Kutznetsov, Synthesis of linear detectors when the signal is inexactly given and the properties of the normal noise are incompletely known,
*Radio Eng. Electron. Phys.*, (English Transl.), Vol. 19, pp. 65–73, 1974.Google Scholar - [28]V.P. Kuznetsov, Stable detection when the signal and spectrum of normal noise are inaccurately known,
*Telecomm. Radio Eng.*, (English Transl.), Vol. 30–31, pp. 58–64, 1976.Google Scholar - [29]S.A. Kassam, T.L. Lim and L.J. Cimini, Two dimensional filters for signal processing under modeling uncertainty,
*IEEE Trans. Geosci. Elec.*, Vol. GE–18, pp. 331–336, 1980.Google Scholar - [30]C.T. Chen and S.A. Kassam, Robust multi-input matched filters, Proc. 19th Annual Allerton Conf. on Comm., Contr., Comp., pp. 586–595, 1981.Google Scholar
- [31]R.Sh. Aleyner, Synthesis of stable linear dectectors for an inaccurately known signal,
*Radio Eng. Electron. Phys*. (English Transl.), Vol. 22, pp. 142–145, 1977Google Scholar - [32]M.V. Burnashev, On the minimax detection of an inaccurately known signal in a white Gaussian noise background,
*Theor. Prob. Appl*, Vol. 24, pp. 107–119, 1979.MathSciNetzbMATHCrossRefGoogle Scholar - [33]S. Verdu and H.V. Poor, Minimax robust discrete-time matched filters,
*IEEE Trans. Comm.*, Vol. COM–31, pp. 208–215, 1983.Google Scholar - [34]S. Verdu and H.V. Poor, Signal selection for robust matched filtering,
*IEEE Trans. Comm.*, Vol. COM–31, pp. 667–670, 1983.Google Scholar - [35]H.V. Poor, Robust matched filters,
*IEEE Trans. Inform. Theory*, Vol. IT–29, pp. 677–687, 1983.Google Scholar - [36]S. Verdu and H.V. Poor, On minimax robustness: A general approach and applications,
*IEEE Trans. Inform. Theory*, Vol. IT–30, pp. 328–340, 1984.Google Scholar - [37]D. Slepian, Indistinguishable signals,
*Proc. IEEE*, Vol. 64, pp. 292–300, 1976.MathSciNetCrossRefGoogle Scholar - [38]C.R. Baker, Optimum quadratic detection of a random vector in Gaussian noise,
*IEEE Trans. Comm.*, Vol. COM–14, pp. 802–805, 1966.Google Scholar - [39]H.V. Poor, Robust decision design using a distance criterion,
*IEEE Trans. Inform. Theory*, Vol. IT–26, pp. 575–587, 1980.Google Scholar - [40]C.J. Masreliez and R.D. Martin, Robust Bayesian estimation for the linear model and robustifying the Kalman filter,
*IEEE Trans. Auto. Contr.*, Vol. AC–22, pp. 361–371, 1977.Google Scholar - [41]41]S.A. Kassam and T.L. Lim, Robust Wiener filters,
*J. Franklin Inst.*, Vol. 304, pp. 171–185, 1977.zbMATHCrossRefGoogle Scholar - 42]K.S. Vastola and H.V. Poor, Robust Wiener-Kolmogorov theory,
*IEEE Trans. Inform. Theory*, Vol. IT–30, pp. 316–327, 1984.Google Scholar - 43]S.A. Kassam and H.V. Poor, Robust techniques for signal processing: A survey,
*Proc. IEEE*, Vol. 73, March 1985.Google Scholar

## Copyright information

© Springer-Verlag New York Inc. 1986