Sea clutter: Scattering, the K distribution and radar performance

Sea Clutter: Scattering, the K Distribution and Radar Performance

Volumn , Issue , 2006, Pages 1-452

  Ward, Keith D ^a   Tough, Robert J A ^a   Watts, Simon ^b  

^a TW Research Ltd   (United Kingdom)

^b Thales Optics Ltd   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CLUTTER (INFORMATION THEORY); RADAR CLUTTER; REMOTE SENSING; SURFACE WATERS;

AMPLITUDE STATISTICS; K DISTRIBUTION; MARITIME ENVIRONMENT; PERFORMANCE OF SYSTEMS; RADAR PERFORMANCE; RADAR SCATTERING; SEA CLUTTERS; SEA SURFACES;

RADAR;

EID: 84988936891     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1049/PBRA020E     Document Type: Book

References (273)

1. L. J. Cantafio, ‘Space-based radar handbook, Artech House, Boston, 1989.
2. S.J. Austin, D.J.Q. Carter and J.D. McCaughey, ‘ERS-1 spacecraft - active microwave instrumentation: a major achievement’, GEC J. Res., 9(1), 2-12, 1991.
3. S.J. Austin, D.J.Q. Carter and J.D. McCaughey GEC J. Res., http://envisat.esa.int/
4. S. Watts and A.J. Gordon, ‘The Searchwater family of radars’, IEE International Conference, Radar 97, 14-16 October 1997, IEE Publication No. 449, pp. 334-338.
5. A.M. Kinghorn, P.E. Holbourn, M.J. Smith and J.F. Roulston, ‘The Blue Vixen Radar for Sea Harrier FRS.2’, GEC Review, 9(3), p. 131-145, 1994.
6. E. Jakeman and P.N. Pusey, ‘A model for non-Rayleigh sea echo’, IEEE Trans. Antennas Propag., AP-24, 808, 1976.
7. K.D. Ward, ‘Compound representation of high resolution sea clutter’, Electron. Lett., 17(16), 561-563, 1981.
8. K.D. Ward, C.J. Baker and S. Watts, ‘Maritime surveillance radar part 1: Radar scattering from the ocean surface’, Proc. IEE, 137 (part F, No. 2), 51-62, 1990.
9. S. Watts, C.J. Baker and K.D. Ward, ‘Maritime surveillanceradarpart2: Detection performance prediction in sea clutter’, Proc. IEE, 137 (part F, No. 2), 63-72, 1990.
10. C.J. Oliver and S. Quegan, ‘Understanding synthetic aperture radar images’, Artech House, Boston, 1998.
11. E. Jakeman and R.J.A. Tough, ‘Non-Gaussian models for the statistics of scattered waves’, Adv. Phys, 37, 471, 1988.
12. E. Jakeman and R.J.A. Tough, ‘The generalised K distribution: a statistical model for weak scattering’, J. Opt. Soc. Am., A4, 1764, 1987.
13. R.J.A. Tough, D. Blacknell and S. Quegan, ‘A statistical description of polari-metric and interferometric synthetic aperture data’, Proc. Roy. Soc. Series A, 449, 567, 1995.
14. S.O. Rice, ‘Reflection of electromagnetic waves from slightly rough surfaces’, Commun. PureAppl. Math., 4, 351-478, 1951.
15. G.R. Valenzuela, ‘Theories for the interaction of electromagnetic waves and oceanic waves - a review’, Boundary-Layer Meteorol., 13, 61-85, 1978.
16. G.R. Valenzuela IEEE Trans. Antennas propagation (special issue on LGA scattering by the sea surface), AP-46(1), 1998.
17. E. Jakeman and K. Ridley, ‘Modelling fluctuations in scattered waves’, Taylor & Francis, London, 2006.
18. F.E. Nathanson, ‘Radar design principles’, McGraw Hill, New York, 1969.
19. M.W. Long, ‘Radar reflectivity of land and sea’, Artech House, Boston, 1983.
20. M.I. Skolnik, ‘Radar handbook’, McGraw Hill, New York, 1970.
21. S.J. Austin, D.J.Q. Carter and J.D. McCaughey, ‘ERS-1 spacecraft - active microwave instrumentation: a major achievement’, GEC J. Res., 9(1), 2-12, 1991.
22. K.D. Ward, ‘Compound representation of high resolution sea clutter’, Electron. Lett., 17(16), 561-563, 1981.
23. K.D. Ward, C.J. Baker and S. Watts, ‘Maritime surveillance radar part 1: Radar scattering from the ocean surface’, Proc. IEE, 137(part F, No. 2), 51-62, 1990.
24. K.D. Ward, R.J.A. Tough and P.W. Shepherd, ‘Modelling sea clutter: correlation, resolution and non-Gaussian statistics’, IEE Conference Publication 449, Radar 97, pp. 95-99.
25. S. Watts and G. Knight, ‘Performance prediction for scanning radars with correlated returns from K-distributed sea clutter ’, Radar 2004 International Conference on Radar Systems, Toulouse 19-21 October 2004.
26. T. Hair, T. Lee and C.J. Baker, ‘Statistical properties of multifrequency highrange-resolution sea reflections’, Proc. IEE, 138(part F, No. 2), 75-79, 1991.
27. T. Lamont-Smith, K.D. Ward and D. Walker, ‘A comparison of EM scattering results and radar sea clutter’, IEE Radar 2002 International Conference, October 2002, IEE Publication 490, pp. 439-443.
28. I. D. Olin, ‘Characterisation of spiky sea clutter for target detection’, Proceedings of the 1984 IEEE National Radar Conference, 1984, pp. 27-31.
29. G.W. Ewell, M.T. Tuley and W.F. Horne,‘ Temporal and spatial behaviour of high resolution sea clutter spikes’, Proceedings of the 1984 IEEE National Radar Conference, 1984, pp. 100-104.
30. B.O. Werle, ‘Sea backscatter, spikes and wave group observations at low grazing angles’, IEEE 1995 International Radar Conference, Washington DC, May 1995, pp. 187-195.
31. F.L. Posner, ‘Distribution function for temporal measures of sea spike characterization’, International Conference Radar 2004, Toulouse France, October 2004, paper 3B-PHENO-3.
32. F.L. Posner, ‘Spiky sea clutter at high range resolutions and very low grazing angles’, IEEE Trans. AES, 38(1), 58-73, 2002.
33. F.L. Posner and K. Gerlach, ‘Sea spike demographics at high range resolutions and very low grazing angles’, Proceedings of the 2003 IEEE Radar Conference, Huntsville, AL, May 2003, pp. 38-45.
34. C. J. Baker, ‘K-distributed radar sea clutter’, Proc. IEE, 138(part F, No. 2), 89-92, 1991.
35. D. G. Money et al., ‘Sea clutter power spectral lineshape measurements’, Radar 97, 140-16 October 1997, IEE Publication No. 449, pp. 85-89.
36. R.J. Miller and W.N. Dawber, ‘Analysis of spectrum variability in sea clutter’, Radar 2002, 15-17 October 2002, IEE Conference Publication No. 490, pp. 444-448.
37. W.N. Dawber and N.M. Harwood, ‘Comparison of Doppler clutter cancellation techniques for naval multi-function radars’, Radar 2002, 15-17 October 2002, IEE Publication No. 490, pp. 424-428.
38. S. Watts and K. D. Ward, ‘Spatial correlation in K-distributed Sea Clutter’, Proc. IEE Part F, 134(6), 526-532, 1987.
39. R. J. A. Tough, K. D. Ward and P. W. Shepherd, ‘The modelling and exploitation of spatial correlation in spiky sea clutter’, EMRS DTC 2nd Annual Conference, 16-17 June 2005, paper A1.
40. T. Lamont Smith, ‘Radar Imaging of Strain Rate’, IEE Int Radar Conference RADAR97, IEE publication 449, pp. 80-84, 1997.
41. W.J. Pierson and L. Moskowitz, ‘A proposed spectral form for fully developed wind sea based on the similarity theory of SA Kitaigorodskii’, J. Geophys. Res., 69, 5181-5190, 1964.
42. M. I. Skolnik, ‘Radar Handbook’, second edition, McGraw-Hill, 1990.
43. B. Jahne and K.S. Riemer, ‘Two-dimensional wave number spectra of small-scale water surface waves’, J. Geophys. Res., 95, 11531-11546, 1990.
44. T. Elfouhaily, B. Chapron and K. Katsaros, ‘A unified directional spectrum for long and short wind-driven waves’, J. Geophys. Res., 102(C7), 15781-15796, 1997.
45. T. Inoue, ‘On the growth of the spectrum of a wind generated sea according to a modified Miles-Phillips mechanism and its application to wave forecasting”, Report TR-67-5, Geophysics Science Lab., New York University, New York, 1967.
46. K. Hasselmann, ‘Measurements of wind-wave growth and swell during the Joint North Sea Wave Project (JONSWAP)’, Deutch. Hydrogr. Z., 12, 95, 1973.
47. B. LeMehaute, ‘An introduction to hydrodynamics and water waves’, SpringerVerlag, New York, 1976.
48. R. K. Price, ‘The breaking of water waves’, J. Geophys. Res., 76, 1576-1581, 1971.
49. M.S. Longuet-Higgins, ‘On the overturning of gravity waves’, Proc. Roy. Soc., A376, 377-400, 1981.
50. D. Xu, P.A. Hwang and J. Wu, ‘Breaking of wind generated waves’, J. Phys. Oceanogr., 16,2172-2178, 1986.
51. M.A. Srokosz, ‘On the probability of wave breaking in deep water’, J. Phys. Oceanogr., 16, 382-385, 1986.
52. M. Clements and U. Yurtsever, ‘The Breaking Area model for LGA radar sea clutter’, Dynamics Technology Inc, DTW-9234-97009, 1997.
53. J.W. Dold, ‘An efficient surface-integral algorithm applied to unsteady gravity waves’, J. Comp. Phys., 103, 90-115, 1992.
54. P. Wang, Y. Yao and M.P. Tulin, ‘An efficient numerical tank for non-linear water waves, based on the multi-subdomain approach with BEM’, Int. J. Num. Math. Fluids, 20, 1315-1336, 1995.
55. J. A. Stratton, ‘Electromagnetic theory’, Section 8.14, McGraw Hill, New York, 1945.
56. B. Hughes, ‘The effect of internal waves on surface wind waves: 2. Theoretical Analysis’, JGR, 83(C1), 455-465, 1978.
57. O.M. Phillips, ‘The dynamics of the upper ocean’, Cambridge University Press, New York, 1966.
58. D. Holliday, G. St-Cyr and N.E. Woods, ‘Comparison of a new radar ocean imaging model with SARSEX internal wave image data’, Int. J. Remote Sensing, 8(9), 1423-1430, 1987.
59. W. Alpers and I. Hennings, ‘A theory of the imaging mechanism of underwater bottom topography by real and synthetic aperture radar ’, J. Geophys. Res., 89(C6), 10529-10546, 1984.
60. D. Holliday, G. St-Cyr and N.E. Woods, ‘A radar ocean imaging model for small to moderate incidence angles’, Int. J. Remote Sensing, 7(12), 1809-1834, 1986.
61. S.O. Rice, ‘Reflections of electromagnetic waves from slightly rough surfaces’, Commun. PureAppl. Math., 4, 351-378, 1951.
62. W.H. Peake, ‘Theory of radar return from terrain’, IRENat. Conv.Rec., 7,27-41, 1959.
63. J.W. Wright, ‘A new model for sea clutter’, IEEE Trans. AP, 16, 217-223, 1968.
64. D. Holliday, ‘Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory’, IEEE Trans. Antennas Propagat., AP-35, 120-122, 1987.
65. G.R. Valenzuela, ‘Theories for the interaction of electromagnetic waves and oceanic waves-areview’, Boundary-LayerMeteorol., 13, 61-85, 1978.
66. D.R. Thompson, ‘Calculation of radar backscatter modulation from internal waves’, J. Geophys. Res., 93(C10), 12371-12380, 1988.
67. M.M. Horst, F. B. Dyer and M. T. Tuley, ‘Radar Sea Clutter model’, International IEEE AP/S URSI symposium, 1978.
68. D. Holliday, L.L. DeRaad, Jr. and G. J. St.-Cyr, ‘Forward-backward: a new method for computing low grazing angle scattering’, IEEE Trans. Antennas Propagat., 44, 722-729, 1996.
69. W.T. Shaw and A.J. Dougan, ‘Green’s function refinement as an approach to radar back-scatter: general theory and applications to LGA scattering’, IEEE Trans. Antenna Propagat., 46, 57, 1998.
70. M. Katzin, ‘On the mechanisms ofradar sea clutter’, Proc. IRE, 45,44-54, 1957.
71. L. B. Wetzel, ‘Electromagnetic scattering from the sea at low grazing angles’, Vol. 2, in Surface Waves and Fluxes, G.L. Geernaert and W. J. Plant (Eds.), Kluwer Academic Publishers, pp. 109-171, 1990.
72. A. Voronovich, ‘Small slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces’, Waves Random Media, 4, 337, 1994.
73. T. Lamont-Smith, ‘An empirical model for EM scattering from steeping wave profiles derived from numerical computation’, IEEE Trans. Geosci. Remote Sens, 41(6), 1447-1454, 2003.
74. J. Fuchs and M.P. Tulin, ‘Laboratory measurements of the joint dependence of radar frequency and water wavelength on sea spike returns’, IGARSS ’99 Conference Proceedings, Seattle, 1999.
75. J. Fuchs, T. Lamont-Smith, and M.P. Tulin, ‘Laboratory Measurements of LGA’ Doppler Spectral components and their physical saivces unveiled’ Proc IGARSS 98, Seattle 1998, 2276-2278.
76. T. Lamont-Smith, A.M. Jackson, P.W. Shepherd and R.D. Hill, ‘Low grazing angle radar imaging experiments over the South Falls sandbank’, Int. J. Remote Sensing, 26(5), 937-966, 2005.
77. W. Feller, ‘Introduction to probability theory and its applications’, Vol. 2, Chap. 8, John Wiley & Sons, New York, 1971.
78. S. O. Rice, ‘Mathematical analysis of random noise’, Bell Syst. Tech. J., 23, 282, 1944.
79. S. O. Rice, ‘Mathematical analysis of random noise’, Bell Syst. Tech. J., 25, 46, 1945.
80. K.D. Ward, ‘Compound representation of high resolution sea clutter’, Electron. Lett., 17,561-65, 1981.
81. G. V. Trunk, ‘Radar properties of non-Rayleigh sea clutter’, IEEE Trans. AES-8, 196-204, 1972.
82. G. R. Valenzuela and M.B. Lang, ‘On the statistics of sea clutter’, NRL Report 7349, 1971.
83. J.M. Blythe et al., ‘The CFE clutter model, with application to automatic detection’, The Marconi Rev., 32, 185-206, 1969.
84. K.D. Ward, C.J. Baker and S. Watts, ‘Maritime surveillance radar part 1: Radar scattering from the ocean surface’, Proc. IEE, 137(part F, No. 2), 51-62, 1990.
85. E. Conte, A. De Maio and C. Galdi, ‘Statistical validation of the compound-Gaussian model on clutter data from IPIX radar’, Radar 2004 International Conference on Radar Systems, Toulouse, 18-22 October 2004.
86. E. Jakeman, ‘On the statistics of K distributed noise’, J. Phys. A 13, 31-48, 1980.
87. E. Jakeman and R.J.A. Tough, ‘Generalised K distribution: A statistical model for weak scattering’, J. Opt. Soc. AM., 4, 1764, 1987.
88. S. Watts, ‘Radar detection prediction for targets in both K-distributed sea clutter and thermal noise’, IEEE Trans. AES-23(2), 40-45, 1987.
89. T. Lamont-Smith, ‘Translation to the normal distribution for radar clutter’, IEE Proc. Radar, Sonar Navig., 147(1), 17-22, 2000.
90. T.R. Field and R.J.A. Tough, ‘Dynamical models for weak scattering’, J. Math. Phys., 46,013302, 2005.
91. D. Middleton ‘Canonical and non-canonical non-Gaussian noise models of class A interference’, IEEE Trans. Electromag. Compat., EMC-25, 76-106, 1983.
92. D. Middleton, ‘New physical-statistical methods and models for clutter and reverberation: The KA distribution and related probability structures’, IEEE J. Oceanic Eng., 24(3), 261-284, 1999.
93. K.D. Ward and R.J. Tough, ‘Radar detection performance in sea clutter with discrete spikes’, International Conference Radar 2002, IEE Publication 490, 15-17 October 2002, pp. 253-257.
94. M. Clements and U. Yurtsever, ‘The breaking area model for low grazing angle sea clutter’, Dynamics Technology Inc., Arlington, VA, 1997.
95. R.J. Adler, ‘The geometry of random fields’, John Wiley & Sons, New York, 1981.
96. G. N. Watson ‘A treatise on the theory of Bessel functions’, Section 13.51, University Press, Cambridge, 1966.
97. E. Jakeman and P. N. Pusey, ‘A model for non-Rayleigh sea echo’, IEEE Trans. Antennas Propag., AP-24, 808, 1976.
98. S. Watts and A. G. Stove, ‘Non-coherent integration strategies in scanning radar for the detection of targets in sea clutter and noise’, International Radar Conference Radar 2004, Toulouse, 19-21 October 2004.
99. S. Watts, K.D. Ward and R.J.A. Tough, ‘The physics and modelling of discrete spikes in radar sea clutter’, IEEE International Radar Conference Radar 2005, Washington, May 2005.
100. G. V. Trunk and S. F. George, ‘Detection of targets in non-Gaussian sea clutter’, IEEE Trans AES-6, 620-628, 1970.
101. F.A. Fay, J. Clarke and R. S. Peters, ‘Weibull distribution applications to sea clutter’, IEE Conf Publ. 155, 1012, 1977.
102. T. Bucciarelli, P. Lombardo, C.J. Oliver and M. Perrotta, ‘A compound Weibull model for SAR texture analysis’, Proc. IGARRS, 1, 181-183, 1997.
103. D. Walker, ‘Experimentally motivated model for low grazing angle radar Doppler spectra ofthe sea surface’, IEE Proc. Radar, Sonar Navig., 147(3), 114-120,2000.
104. D. Walker, ‘Doppler modelling of radar sea clutter’, IEE Proc. Radar, Sonar Navig., 148(2), 73-80, 2001.
105. P.H.Y. Lee, J.D. Barter, B.M. Lake and H.R. Thompson, ‘Lineshape analysis of breaking wave Doppler spectra’, IEE Proc. Radar, Sonar Navig., 145(2), 135-139, 1998.
106. J. Fuchs, D. Regas, T. Waseda, S. Welch and M. Tulin, Correlation of hydrodynamic features with radar backscatter from breaking waves, IEEE Trans. Geosci. Remote Sens., 37(5), 2442-2460, 1999
107. P.H.Y. Lee et al., ‘Power spectral lineshapes of microwave radiation scattered from sea surfaces at low grazing angles’, IEE Proc. Radar, Sonar Navig., 142(5), 252-258, 1995.
108. R.J. Miller, ‘Variability in spectra of low-grazing angle sea clutter returns’, NATO/RTO Publications, Proceedings of SET Symposium on Low Grazing Angle Clutter: Its Characterisation, Measurement and Application, April 2000.
109. A.J. Hughes, E. Jakeman, C.J. Oliver and E.R. Pike, ‘Photon-correlation spectroscopy: dependence of linewidth error on normalization, clip level, detector area, sample time and count rate’, J. Phys. A: Math. Gen, 6, 1327, 1973.
110. S. Chandrasekhar, ‘Stochastic problems in physics and astronomy’, Rev. Mod. Phys., 15, 1-89, 1943.
111. G.H. Golub and C.F. Van Loan, ‘Matrix computations’, Johns Hopkins University Press, Baltimore, MD, 1989.
112. W.F. Coffey, Y.P. Kalmykov and J.T. Waldon, ‘The Langevin equation, with applications to stochastic problems in physics, chemistry and engineering’, World Scientific, Singapore, 2004.
113. C.J. Oliver and R.J.A. Tough, ‘On the simulation of correlated K-distributed random clutter’, Optica Acta, 33, 223-250, 1986.
114. D. Blacknell, A. Blake, P. Lombardo and C. J. Oliver, ‘A comparison of simulation techniques for correlated gamma and K distributed images for SAR applications’, Proceedings of the IGARSS 1994, Pasadena CA, 8-12 August 1994.
115. K.D. Ward, R.J.A. Tough and P.W. Shepherd, ‘Modeling sea clutter: correlation, resolution and non-Gaussian statistics’, Proceedings of the RADAR 97, IEE publication 449, Edinburgh UK, 14-16 October 1997.
116. R.J.A. Tough and K.D. Ward, ‘Thecorrelationpropertiesofgammaandothernon-Gaussain processes generated by memoryless nonlinear transformation’, J. Phys. D., 32, 3075-3084, 1999.
117. S. Wolfram, ‘The Mathematica book’, University Press, Cambridge, 1996.
118. G. Li and K.-B. Yu, ‘Modelling and simulation of coherent Weibull clutter’, IEE Proc. F., 136(1), 2-12, 1989.
119. B.C. Armstrong and H.D. Griffiths, ‘Modelling spatially correlated K-distributed clutter’, Electron. Lett., 27, 1355-1356, 1991.
120. W.W Peterson, T.G. Birdsall and W.C. Fox, ‘The theory of signal detectability’, Section 2.7, IRE Trans. Inform. Theory, PGIT-6, 204-221, 1956.
121. E.S. Pearson, ‘The Neyman-Pearson story: 1926-34’, in F.N. David (Ed.), ‘Research papers in Statistics’, John Wiley & Sons, London, 1966.
122. H.L. van Trees, ‘Detection, Estimation and Modulation Theory, Part 1’, John Wiley & Sons, New York, 1968.
123. D. Middleton, ‘Statistical Communication Theory’, McGraw Hill, New York, 1960.
124. M.I. Skolnik, ‘Introduction to Radar Systems’, Section 9.6, McGraw Hill, New York, 1962.
125. M.G. Kendall, ‘The Advanced Theory of Statistics’, Vol. 2, Chaps. 17-20, Griffin, London, 1946.
126. M.G. Kendall, ‘The Advanced Theory of Statistics’, Vol. 1, Chap. 10, Griffin, London, 1943.
127. E. T. Copson, ‘Introduction to the Theory of Functions of a Complex Variable’, Section 10.62, Clarendon Press, Oxford, 1970.
128. R.V. Hogg and A.T. Craig, ‘Introduction to Mathematical Statistics’, Section 4.6, Collier Macmillan, London, 1978.
129. W.H Press, S.A. Teukolsky, W.T. VetterlingandB.P. Flannery, ‘ Numerical recipes in FORTRAN; The art of scientific computing.’, 2nd Edn., University Press, Cambridge, 1992.
130. C.J. Oliver, ‘Optimum texture estimators or SAR clutter’, J. Phys. D, 26, 1824-1835, 1994.
131. D. Blacknell and R.J.A. Tough, ‘Parameter estimation for the K distribution based on [zlog(z)]’, IEE Proc. Radar, Sonar, Navig., 148, 309-312, 2001.
132. E.T. Copson, ‘An introduction to the theory offunctions of a complex variable’, Clarendon Press, Oxford, 1970.
133. L.M. Novak, M.C. Burl and W.W. Irving, ‘Optimal polarimetric processing for enhanced target detection’, IEEE Trans. Aerospace Electr. Syst., 29, 234-244, 1993.
134. D. Blacknell and R.J.A. Tough, ‘Clutter discrimination in polarimetric and inter-ferometric synthetic aperture radar imagery’, J.Phys. D, Appl. Phys., 30, 551-566, 1997.
135. M.G. Kendall, ‘Advanced theory of statistics: Vol.1’ Sects. 14.12-14.14, ‘Advanced theory of statistics: vol.2’, Sects. 28.4-28.10, Charles Griffin, London, 1943, 1946.
136. J. Wishart, ‘The generalised product-moment distribution in samples from a normal multi variate population’, Biometrica, 20, 32-43, 1928.
137. N.R. Goodman, ‘Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction)’, Ann. Math. Stat., 34, 152-177, 1963.
138. R.M. Goldstein and H.A. Zebker, ‘Interferometric radar map of ocean currents’, Nature, 328, 707-709, 1987.
139. F.T. Ulaby and C. Elachi, ‘Radar polarimetry for geoscience applications’, Artech House, New York, 1990.
140. R.J.A. Tough, D. Blacknell, and S. Quegan, ‘A statistical description of polarimetric and interferometric synthetic aperture radar data’, Proc. Roy. Soc., A449, 567-589, 1995.
141. B.C. Barber, ‘The non-isotropic random walk’ and ‘The phase statistics of a multi channel radar interferometer’, Waves Random Media, 3, 243-256 and 257-266, 1993.
142. J.S. Lee, A.R. Miller, and K.W. Hoppel, ‘Statistics ofphase difference and product magnitude of multi-look processed Gaussian signals’, Waves Random Media, 4, 307-317, 1994.
143. D.O. North, ‘An analysis of factors which determine signal/noise discrimination in pulsed-carrier systems’, RCA Technical Report, PTR-6C, 1943.
144. S.O. Rice, ‘Mathematical analysis of random noise’, Bell Syst. Tech. J., 23, 282-332, 1944 and, 24, 46-156, 1945.
145. M.S. Longuet-Higgins, ‘Statistical analysis of a random moving surface’, Phil. Trans. Roy. Soc., A249, 321-388, 1957.
146. J.P. Oakley, ‘Statistical properties of local extrema in two-dimensional Gaussian random fields’, IEEE Trans. Sig. Proc., 46, 130-140, 1998.
147. R.D. Hill, R.J.A. Tough, and K.D. Ward, ‘The distribution of the global maximum of a Gaussian random field and the performance of matched filter detectors’, IEE Proc. Vis. Image Signal Process, 147, 297-903, 2000.
148. R.J. Adler, ‘The geometry of random fields’, John Wiley, New York, 1981.
149. R. D. Hill, R.J.A. Tough, and K.D. Ward, ‘The false alarm curve for the envelope of a Gaussian random field’, Electron. Lett., 37(4), 258-259, 2002.
150. B. Picinbono, ‘Spherically invariant and compound Gaussian stochastic processes’, IEEE Trans. Information Theory, 77-79, 1970.
151. E. Conte and M. Longo, ‘Characterisation of radar clutter as a spherically invariant random process’, IEE Proceedings-F, 134(2), pp. 191-197, April 1987.
152. R.D. Hill, ‘Along-track interferometric SAR measurements of the South Falls sandbank’, submitted for publication.
153. M.I. Skolnik, ‘Radar handbook’, McGraw-Hill, second edition, 1990.
154. 0 sea clutter model’, Royal Radar Establishment, 1974 (unpublished).
155. F.E. Nathanson, ‘Radar design principles’, McGraw-Hill, New York, 1969.
156. J.C. Daley, J.T. Ransome, J.A. Burkett and J.R. Duncan, ‘Sea clutter measurements on four frequencies’, Naval Research Lab report 6806, 1968.
157. M. Horst, F. Dyer and M. Tuley, ‘Radar sea clutter model’, International IEEE AP/S URSI Symposium (IEEE Antennas and Propagation), 1978.
158. T.P. Leonard, I. Antipov and K.D. Ward, ‘A comparison of radar sea clutter models’, Proceedings of the Radar 2002, IEE International Radar Conference, 2002.
159. S. Watts, ‘Radar detection prediction for targets in both K-distributed sea clutter and thermal noise’, IEEE AES-23, No.2, pp. 40-45, January 1987.
160. P. Swerling, ‘Probability of detection for fluctuating targets’, IRE Trans IT-6, pp. 269-308, 1960.
161. J.L. Marcum, ‘A statistical theory of target detection by pulsed radar’, IRE Trans IT-6, pp. 59-144, 1960.
162. P. Swerling, ‘Probability ofdetection for some additional fluctuating target cases’, IEEE AES-33, No. 2, 698-709, April 1997.
163. D. Shnidman, ‘Radar detection probabilities and their calculation’, IEEE AES-31, No. 3, pp. 928-950, July 1995.
164. S. Watts, ‘Radar detection performance in sea clutter using the compound K-distribution model’, IEE Proc. Part F, 7, pp. 613-620, 1985.
165. S. Watts and D.C. Wicks, ‘Empirical models for detection prediction in K-distributed radar sea clutter’, Proceedings of the IEEE 1990 International Radar Conference, pp. 189-194, 1990.
166. S. Watts, ‘Radar performance in K-distributed sea clutter’, SET Panel Symposium on ‘Low grazing angle clutter: its characterisation, measurement and application’, Laurel, Maryland, USA, 25-27 April 2000.
167. D. Shnidman, ‘Expanded swerling target models’, IEEE AES-39, No. 3, pp. 1059-1068, 2003.
168. S. Watts and A. G. Stove, ‘Non-coherent integration strategies in scanning radar for the detection of targets in sea clutter and noise’, Proceedings of the International Radar Conference Radar 2004, Toulouse 19-21 October 2004, paper 10P-SP-229.
169. K.D. Ward, R.J.A. Tough and P.W. Shepherd, ‘Modelling sea clutter: correlation, resolution and non-Gaussian statistics’, IEE Conference Publ. 449, Radar 97, pp. 95-99, 1997.
170. J.A. Scheer and J.L. Kurtz, ‘Coherent radar performance estimation’, Artech House, Boston, 1993.
171. C.J. Oliver and S. Quegan, ‘Understanding synthetic aperture radar images’, Artech House, Boston, 1995.
172. W.R. Wallace, ‘The use of track-before-detect in pulse-Doppler radar’, Radar 2002, IEE Conference Publication 490, October 2002, pp. 315-319.
173. M.W. Long, ‘Radar reflectivity of land and sea’, Artech House, New York, 1983.
174. M.M. Finn and R.S. Johnson, ‘Adaptive detection mode with threshold control as a function of spatially sampled clutter-level estimates’, RCA Review, 30,414-465, 1968.
175. V.Y.F. Li and K.M. Miller, ‘Target detection in radar: Current status and future possibilities’, J. Navigat., 50(2), 303-313, 1997.
176. I.S. Gradshteyn and I.W. Ryzhik, ‘Table of integrals, series, and products’, Academic Press, 4th edition, 1965 (Equation 8.350 p. 940).
177. D. Shnidman, ‘Radar detection probabilities and their calculation’, IEEE AES-31(3), 928-950, 1995.
178. V.G. Hansen and J.H. Sawyers, ‘Detectability loss due to ‘Greatest Of’ selection in a cell-averaging CFAR’, IEEE Trans. AES, 16(1), 115-118, 1980.
179. H. Rohling, ‘Radar CFAR thresholding in clutter and multiple target situations’, IEEE Trans. AES, AES-19(4), 608-621, 1983.
180. S. Watts, ‘Radar detection prediction in sea clutter using the compound K-distribution model’, Proc. IEE, 132 (Part F, No. 7), 613-620, 1985.
181. S. Watts, ‘Cell-averaging CFAR gain in spatially correlated K distributed sea clutter’, IEE Proc. Radar, Sonar, Navig., 143(5), 321-327, 1996.
182. H. Darwish and D.C. Cooper, ‘The log-lattice detector for radar targets in sea clutter’, IEE Colloquium on ‘Discrimination and identification methods in radar and sonar systems’, Digest No. 1986/69, paper 9, 6 May 1986.
183. S. Watts, ‘Improved cell-averaging CFAR for maritime surveillance radar’, UK Patent 2191052, 1981.
184. S. Haykin and X.B. Li, ‘Detection of signals in chaos’, Proc. IEEE, 83, 95-122, 1995.
185. S. Haykin and S. Puthusserypady, ‘Chaotic dynamics of sea clutter: an experimental study’, Proceedings of the IEE Conference on Radar, 1997, pp. 75-79.
186. M.R. Cowper, B. Mulgrew and C.P. Unsworth, ‘Investigation into the use on non-linear predictor networks to improve performance of maritime surveillance radar detectors’, IEE Proc. -Radar, Sonar Navig., 148(3), 103-111,2001.
187. C.P. Unsworth, M.R. Cowper, S. McLaughlin and B. Mulgrew, ‘Re-examining the nature of radar sea clutter’, IEE Proc.-Radar, Sonar Navig., 149(3), 105-114, 2002.
188. G.B. Goldstein, ‘False alarm regulation in log-normal and Weibull clutter’, IEEE Trans., AES-9(1), 84-92, 1973.
189. V.G. Hansen and B.A. Olsen, ‘Non-parametric radar extraction using a generalised sign test’, IEEE Trans., AES-7(5), 942-950, 1971.
190. G.M. Dillard and C.E. Antoniak, ‘A practical distribution-free detection procedure for multiple range-bin radar’, IEEE Trans., AES-6(5), 629-635, 1970.
191. D. Blacknell and R.J.A. Tough, ‘Parameter estimation for the K distribution based on [zlog(z)]’ IEEProc. Radar, Sonar, Navig., 148, 309-312, 2001.
192. th TTCP Workshop on Defence Applications of Signal Processing, DASP 05, Utah, 17 March-1 April 2005.
193. W. Dawber and J. Branson, ‘Use of site specific radar modelling to improve CFAR performance in the littoral’, IEEE International Radar Conference Radar 2005, Washington, DC, 9-12 May 2005, pp. 161-166.
194. R.J.A. Tough, K.D. Ward and P.W. Shepherd, ‘The modelling and exploitation of spatial correlation in spiky sea clutter’, EMRS DTC 2nd Annual Conference, 16-17 June 2005, paper A1.
195. E.J. Hughes and M. Lewis, ‘An intelligent agent-based track-before-detect system applied to a range and velocity ambiguous radar’, EMRS DTC 1st Annual Conference, May 2004, paper A4.
196. M. McDonald and S. Lycett, ‘A comparison of fast scan versus slow scan radars’, International Radar Conference Radar 2004, Toulouse 19-21 October 2004, paper 10P-RCMT-255.
197. S. Watts and A.G. Stove, ‘Non-coherent integration strategies in scanning radar for the detection of targets in sea clutter and noise’, International Radar Conference Radar 2004, Toulouse 19-21 October 2004, paper 10P-SP-229.
198. S. Watts, ‘Performance measures for airborne maritime surveillance radars’, IEE Colloquium on specifying and measuring performance of modern radar systems, 6 March 1998.
199. S. Watts, H.D. Griffiths, J.R. Holloway, A.M. Kinghorn, D.G. Money, D.J. Price, A.M. Whitehead, A.R. Moore, M.A. Wood and D.J. Bannister, The specification and measurement of radar performance, IEE International Conference Radar 2002, 14-17 October 2002, IEE Publication No. 490, pp. 542-546.
200. S. Watts, H.D. Griffiths, J.R. Holloway, A.M. Kinghorn, D.G. Money, D.J. Price, A.M. Whitehead, A.R. Moore, M.A. Wood and D.J. Bannister, The specification and measurement of radar performance - future research challenges, J. Defence Sci., 8(2), 2003, 83-91.
201. S. Watts, ‘Radar detection prediction in sea clutter using the compound K-distribution model’, Proc. IEE, 132(F, 7), 613-620, 1985.
202. S. Watts and A. J. Gordon, The Searchwater family of radars, Proceedings of the IEE International Conference Radar 97, 14-16 October 1997, IEE Publication No. 449, pp 334-338.
203. S. Watts, ‘Method and apparatus for estimating the detection range of a radar’, UK Patent 2297213 (17 Jan 1996); USA Patent 5703592; France Patent 9600418.
204. S. Watts, Specification and measurement of performance for airborne maritime surveillance radars, International Conference, Radar 99, Brest, 17-21 May, 1999, Session 2.6.
205. S. Watts and G. Knight, Performance prediction for scanning radars with correlated returns from K-distributed sea clutter, International Radar Conference Radar 2004, Toulouse 19-21 October 2004.
206. K.D. Ward, R.J.A. Tough and P.W. Shepherd, Modelling sea clutter: correlation, resolution and non-Gaussian statistics, IEE Conference Publication 449, Radar 97, pp. 95-99.
207. S. Watts, Duration of radar false alarms in band-limited Gaussian noise, IEE Proc. Radar, Sonar, Navig., 146(6), 273-277, 1999.
208. A.G. Stove and D.L. Hurd, Performance evaluation for modern radars, Proceedings of the IEEE International Radar Conference, Adelaide, September 2003, pp. 547-553 (paper 44)
209. A. Wald, Sequential Analysis, Dover Books, 1973
210. W. Feller,’An introduction to probability theory and its applications’, Vols. I, II, John Wiley, New York, 1971.
211. A. Papoulis: ‘Probability, random variables and stochastic processes’, McGraw Hill, 1965.
212. M. Abramowitz and I.A. Stegun (Eds.), ‘A handbook of mathematical functions’, Dover, New York, 1972.
213. I.N. Sneddon, ‘The use of integral transforms’, section 4.4, Tata-McGraw Hill, New Delhi, 1974.
214. P.M. Morse and H. Feshbach, ‘Methods of theoretical physics’ Vol. I, p. 781, McGraw Hill, New York, 1953.
215. G.H. Golub and C.F. Van Loan, ‘Matrix computations’, Johns Hopkins University Press, 1989.
216. H. Jeffreys and B.S. Jeffreys, ‘Mathematical physics’, chapter 4, University Press, Cambridge, 1966.
217. D. Middleton, ‘An introduction to statistical communication theory’, McGraw Hill, New York, 1960.
218. S.O. Rice, ‘Mathematical analysis of random noise’, Bell Syst. Tech. J., 23, 282, 1944;
219. S.O. Rice, ‘Mathematical analysis of random noise’, Bell Syst. Tech. J., 25, 46, 1945.
220. M.G. Kendall, ‘The advanced theory of statistics’, Vol. 1, Griffin, London, 1943.
221. E. Renshaw, ‘Modelling biological populations in space and time’, University Press, Cambridge, 1991.
222. N.T.J. Bailey,’The elements of stochastic processes’, section 8.7, John Wiley & Sons, New York, 1964.
223. J. Lighthill, ‘Waves in fluids’, Chapter 3, University Press, Cambridge, 1978.
224. N. Wax (Ed.), ‘Selected papers on noise and stochastic processes, Dover, New York, 1954. This valuable collection of reprints contains refs 9 and 16.
225. B. Oksendal, ‘Stochastic differential equations, Springer Universitext, Berlin, 2000.
226. J.L. Doob, ‘The Brownian movement and stochastic equations’, Ann. Math., 43, 351, 1942.
227. R.J.A. Tough, ‘A Fokker Planck description of K distributed noise’, J. Phys. A, 20, 551, 1987.
228. T.R. Field and R.J.A. Tough, ‘Diffusion processes in electromagnetic scattering generating K distributed noise’, Proc. Roy. Soc. A459, 2169, 2003.
229. T.R. Field and R.J.A. Tough, ‘Stochastic dynamics of the scattering amplitude generating K distributed noise’, J. Math. Phys., 44, 5212, 2003.
230. N.G. van Kampen, ‘Stochastic processes in physics and chemistry’, North Holland, Amsterdam, 1984.
231. T.J. Bailey, ‘Stochastic birth, death and migration processes for spatially distributed populations’, Biometrica, 55, 237-257, 1968.
232. E. Renshaw, ‘Stepping stone models for population growth’, J. Appl. Probability, 11, 16-31, 1974.
233. E. Jakeman, ‘Photon correlation and light beating spectroscopy.’, H.Z. Cummins and E.R. Pike, Eds., Plenum Press, London, 1974.
234. R.J.A. Tough, ‘Theestimatorsofnormalisedmomentsofthegammadistribution’, J. Phys. A 27, 7883 (1994).
235. A. Wald, ‘Sequential analysis’, John Wiley, New York, 1962.
236. K.A. Stroud and D.J. Booth, ‘Advanced engineering mathematics’, Palgrave McMillan, Basingstoke, 2003.
237. S. Wolfram, ' The Mathematica book’, University Press, Cambridge, 1996.
238. G.A. Gibson, ‘Advanced calculus’, Macmillan, London, 1944.
239. M. Abramowitz and I.A. Stegun, ‘Handbook of mathematical functions’, Dover, New York, 1965.
240. I.S. Gradshteyn and I.M Ryzhik, ‘Table of integrals, series and products’, Academic Press, New York, 1965.
241. I.S. Gradshteyn and I.M Ryzhik, ‘Table of integrals, series and products’, http://functions.wolfram.com/1
242. D. Middleton, ‘Introduction to statistical communication theory’, Appendix 1, McGraw Hill, New York, 1960.
243. G.N. Watson, ‘A treatise on the theory of Bessel functions’, University Press, Cambridge, 1966.
244. L.D. Landau and E.M. Lifshitz, ‘Quantum mechanics - non-relativistic theory’, Pergamon Press, Oxford, 1958.
245. N.N. Lebedev, ‘Specialfunctions and their applications’, Dover, New York, 1972.
246. W.C. Meecham, ‘On the use of the Kirchhoff approximation for the solution of reflection problems’, J. Rational Mech. Anal., 5, 332-334, 1956.
247. E.T. Copson, ‘An introduction to the theory offunctions of a complex variable’, Chaps. 5 and 6, Clarendon Press, Oxford, 1970.
248. D. Holliday, ‘Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory’, IEEE Trans. Antennas Propagat., AP-35, 120-122, 1987.
249. J.A. Stratton, ‘Electromagnetic theory’, Section 8.14, McGraw Hill, New York, 1945.
250. J.T. Johnson, ‘A numerical study of low grazing angle backscatter from ocean like impedance surfaces with the canonical grid method’, IEEE Trans. Antennas Propagat., 46, 114-120, 1998.
251. T.B.A. Senior and J.L. Volakis, ‘Approximate boundary conditions in electromagnetics’, IEE Electromagnetic Waves Series 41, IEE Press, Stevenage, UK, 1995.
252. W.T. Shaw and A.J. Dougan, ‘Curvature corrected impedance boundary conditions in an arbitrary basis’, IEEE Trans. Antennas Propagat., 53, 1699-1705, 2005.
253. H.D. Ngo and C.L. Rino, ‘Application of beam simulation to scattering at low grazing angles: methodology and verification’, Radio Sci., 29, 1365-1379, 1994.
254. D.H. Berman and J.S. Perkins, ‘The Kirchhoff approximation and first-order perturbation theory for rough surface scattering’, J. Acoust. Soc. Am., 78, 1045, 1985.
255. W.T. Shaw and A.J. Dougan, ‘Half-space Green’s function and applications to scattering of electromagnetic waves from ocean like surfaces’, Waves Random Media, 5, 341-359, 1995.
256. W.T. Shaw and A.J. Dougan, ‘Green’s function refinement as an approach to radar back-scatter: general theory and applications to LGA scattering’, IEEE Trans. Antenna andPropagat., 46, 57, 1998.
257. D.E. Kerr, ‘Propagation of short radio waves’, McGraw-Hill, New York, 1951.
258. H. Levine and J.S. Schwinger, ‘On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen’, Commun. PureAppl. Math., 3, 355-391, 1950.
259. D. Lovelock and H. Rund, ‘Tensors, differentialforms and variationalprinciples’, John Wiley and Sons, New York, 1975.
260. W.H. Peake, ‘Theory of radar return from terrain’, 1959 IRE Convention Record, Vol. 7, pp. 27-41.
261. H. Jeffreys and B.S. Jeffreys, ‘Mathematical physics’, Section 9.08, University Press, Cambridge, 1966.
262. R.F. Harrington, ‘Field computation by moments methods’, Macmillan, New York, 1968.
263. E.F. Knot, J.F. Shaeffer and M.T. Tuley, ‘Radar cross section’, Artech House, Boston, 1993.
264. C.L. Rino and H.D. Ngo, ‘Application of beam simulation to scattering at low grazing angles: oceanic surfaces’, Radio Sci., 29, 1381-1391, 1994.
265. R. Petit (ed.), ‘Electromagnetic theory of gratings’, Springer, Berlin, 1980.
266. E.T. Goodwin et al., ‘Modern computing methods.’, Notes on Applied Science, No. 16, Chap. 4, HMSO, 1961.
267. A. Messiah, ‘Quantum mechanics’, Vol. 2, Section 16.16, North Holland, Amsterdam, 1961.
268. W.H Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, ‘Numerical recipes in FORTRAN; The art of scientific computing.’, 2nd. edn., University Press, Cambridge, 1992.
269. D. Holliday, L.L. DeRaad, Jr. and G.J. St.-Cyr, ‘Forward-backward: a new method for computing low grazing angle scattering’, IEEE Trans. Antennas Propagat., 44, 722-729, 1996.
270. M. Spivack, ‘A numerical approach to rough surface scattering by the parabolic wave equation method’, J. Acoust. Soc. Am., 87, 1999, 1990.
271. D. Holliday, L.L. DeRaad, Jr. and G.J. St.-Cyr, ‘Forward-backward method for scattering from imperfect conductors’, IEEE Trans. Antennas Propagat., 46, 101-107, 1998.
272. D. Holliday, L.L. DeRaad, Jr. and G.J. St.-Cyr, ‘Wedge scattering by the method of iteration’, IEEE Trans. Geosci. Remote Sens., 33, 449-456, 1995.
273. D. Holliday, L.L. DeRaad, Jr. and G.J. St.-Cyr, ‘Volterra approximation for low grazing angle shadowing on smooth ocean-like surfaces, IEEE Trans. Antennas Propagat., 43, 1199-1206, 1995.