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Discrete Models for Scattering Populations

Published online by Cambridge University Press:  14 July 2016

Patrick Fayard*
Affiliation:
McMaster University
Timothy R. Field*
Affiliation:
McMaster University
*
Postal address: Department of Electrical and Computer Engineering, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada.
Postal address: Department of Electrical and Computer Engineering, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada.
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Abstract

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Jakeman's random walk model with step number fluctuations describes the coherent amplitude scattered from a rough medium in terms of the summation of individual scatterers' contributions. If the scattering population conforms to a birth-death immigration model, the resulting amplitude is K-distributed. In this context, we derive a class of diffusion processes as an extension of the ordinary birth-death immigration model. We show how this class encompasses four different cross-section models commonly studied in the literature. We conclude by discussing the advantages of this unified description.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2011 

References

[1] Balleri, A., Nehorai, A. and Wang, J. (2007). Maximum likelihood estimation for compound-Gaussian clutter with inverse gamma texture. IEEE Trans. Aerosp. Electron. Syst. 43, 775780.Google Scholar
[2] Bartlett, M. S. (1966). An Introduction to Stochastic Processes, with Special Reference to Methods and Applications. Cambridge University Press.Google Scholar
[3] Bewernick, R. L. et al. (2007). On the representation of birth-death processes with polynomial transition rates. J. Statist. Theory Pract. 1, 227231.Google Scholar
[4] Delignon, Y. and Pieczynski, W. (2002). Modelling non-Rayleigh speckle distribution in SAR images. IEEE Trans. Geosci. Remote Sensing 40, 14301435.Google Scholar
[5] Farina, A., Gini, F., Greco, M. and Verrazzani, L. (1997). High resolution sea clutter data: statistical analysis of recorded live data. IEE Proc. Radar Sonar Navig. 144, 121130.Google Scholar
[6] Fayard, P. and Field, T. R. (2008). Optimal inference of the scattering cross-section through the phase decoherence. Waves Random Complex Media 18, 571584.Google Scholar
[7] Field, T. R. (2005). Observability of the scattering cross-section through phase decoherence. J. Math. Phys. 46, 063305, 8 pp.Google Scholar
[8] Field, T. R. and Tough, R. J. A. (2003). Diffusion processes in electromagnetic scattering generating K-distributed noise. Proc. R. Soc. London A 459, 21692193.Google Scholar
[9] Field, T. R. and Tough, R. J. A. (2003). Stochastic dynamics of the scattering amplitude generating K-distributed noise. J. Math. Phys. 44, 52125223.Google Scholar
[10] Forman, J. L. and Sørensen, M. (2008). The Pearson diffusions: a class of statistically tractable diffusion processes. Scand. J. Statist. 35, 438465.Google Scholar
[11] Jakeman, E. (1980). On the statistics of K-distributed noise. J. Phys. A 13, 3148.Google Scholar
[12] Jakeman, E. and Tough, R. J. A. (1988). Non-Gaussian models for the statistics of scattered waves. Adv. Phys. 37, 471529.Google Scholar
[13] Ohira, T. (1997). Oscillatory correlation of delayed random walks. Phys. Rev. E 55, 12551258.Google Scholar
[14] Øksendal, B. (1988). Stochastic Differential Equations: An Introduction with Applications, 5th edn. Springer, Berlin.Google Scholar
[15] Risken, H. (1989). The Fokker–Planck Equation. Springer, Berlin.Google Scholar
[16] Ward, K. (1981). Compound representation of high resolution sea clutter. Electron. Lett. 17, 561563.Google Scholar
[17] Ward, K. D., Tough, R. J. A. and Watts, S. (2006). Sea clutter: Scattering, the K-distribution and Radar Performance. IET, London.Google Scholar
[18] Wong, E. (1964). The construction of a class of stationary Markov processes. In Proc. Symp. Appl. Math., Vol. 16, American Mathematical Society, Providence, RI, pp. 264276.Google Scholar