Sea Clutter: Scattering, the K Distribution and Radar Performance
2: Thales UK, UK
This book examines the statistics of radar scattering from the sea surface in terms of their relevance to radar operating in a maritime environment; including remote sensing , surveillance and targeting appliances. A lot of the work in the book iss based on the compound Kdistribution model for the amplitude statistics of sea clutter. In addition, the book addresses the specification of performance required by customers and the measurement of performance of systems supplied to customers.
Inspec keywords: electromagnetic wave scattering; statistical distributions; radar detection; radar clutter
Other keywords: radar sea clutter; statistical modelling; oceanographic modelling; K distribution model; detection systems; grazing angle; electromagnetic scattering; radar performance
Subjects: Radar equipment, systems and applications; Electromagnetic wave propagation; Radar theory; Signal detection
 Book DOI: 10.1049/PBRA020E
 Chapter DOI: 10.1049/PBRA020E
 ISBN: 9780863415036
 eISBN: 9780863419935
 Page count: 472
 Format: PDF

Front Matter
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1 Introduction
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This book attempts to bring together those aspects of maritime radar relating to scattering from the sea surface, and their exploitation in radar systems. The presentation aims to emphasise the unity and simplicity of the underlying principles and so should facilitate their application in these changing circumstances.
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2 The characteristics of radar sea clutter
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In this chapter, sea clutter is described in terms of its observed characteristics. These observations will provide the foundations upon which the themes of subsequent chapters are developed.
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3 Modelling radar scattering by the ocean surface
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This chapter discusses radar scattering and sea clutter.
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4 Statistical models of sea clutter
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In this chapter the authors develop the models of sea clutter that will provide a basis for our subsequent discussion and calculation of radar performance. As the authors saw in the previous chapter, a direct approach to the modelling of sea clutter provides many useful insights. Nonetheless the interactions between the ocean, atmosphere and microwave radiation are far too complicated to be described usefully in strictly deterministic terms. Consequently the models we develop in this chapter are unashamedly statistical in character. The development of these statistical models is driven by the observations of real sea clutter described in Chapter 2, where it was noted that lowresolution, spatially uniform, clutter has Gaussian amplitude statistics. By introducing a simple random walk model for the clutter process we can construct this familiar Gaussian (Rayleigh) model for lowresolution sea clutter from first principles and characterise its interaction with target returns. This analysis, in turn, can be modified to take account of the effects of increased radar resolution; in this way we are led to the K distribution and related models. An advantage of this approach is that it demonstrates clearly how performance analysis germane to low resolution Rayleigh clutter can be extended quite straightforwardly to the Kdistributed case. These few simple principles under pin much of the radar performance analysis presented in the rest of this book.
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5 The simulation of clutter and other random processes
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In this chapter we consider simulation techniques that enable us to study various aspects of radar performance, in circumstances where an analytic attack may not be possible, or particularly informative. To complement the analytic clutter modelling discussed in Chapter 4, we will develop methods for the numerical simulation of unwanted radar returns. The clutter models in Chapter 4 are exclusively statistical; this prejudice is still evident in our choice of simulation methods. In essence, we address the problem of generating correlated random numbers with prescribed one and two point statistics (i.e. pdf and correlation function) that incorporate the physical insights developed in Chapters 24.
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6 Detection of small targets in sea clutter
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One of the main applications of maritime radar is to the detection of small targets, partially obscured by the unavoidable clutter returns from their environment. In this chapter we attempt to identify procedures that allow this detection to be carried out effectively and consider to what extent we can quantify their performance. The statistical models of clutter and target returns developed in earlier chapters provide us with a framework within which we can address these issues in a reasonably systematic fashion and so define and identify optimal detection procedures.
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7 Imaging ocean surface features
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In the previous chapter we considered how we might best detect small, localised targets in a background of sea clutter. The identification of the likelihood ratio as an optimum discriminant, and of its more practically useful approximations, pro vided us with a unifying framework for this discussion. However, small target returns are not the only features of interest in maritime radar imagery. Largescale correlated structures arising from surface currents, ship wakes, the presence of sur factants and other sources can frequently be discerned and are a valuable source of information in many circumstances. In this chapter we will discuss how such ocean surface features might best be enhanced and detected. Once again the like lihood ratio concept is a very useful guiding principle, which leads us to methods that enable us to both enhance these features and exploit our prior knowledge of their structure to detect them more effectively. So, paradoxically, a discussion of the processing of images that are frequently interpreted and assessed in qualitative terms, will involve us in a fair amount of detailed formal analysis. Much of this will be based on the multivariate Gaussian distribution.
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8 Radar detection performance calculations
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An important application of the understanding of sea clutter developed in Chapters 24 is the prediction of radar detection performance. While many of the phenomena associated with sea clutter are not understood in detail in physical terms, empirically derived statistical models do provide us with the means with which we might calculate detection performance and show how observed clutter characteristics can affect radar performance. This modelling of detection performance is the subject of the current chapter. Here we address the 'endtoend' problem, which takes as its input radar system parameters and yields estimates of detection probability, but postpone the discussion of the maintenance of a constant false alarm rate (CFAR), and the associated losses, until the next chapter. The confirmation that real radar systems do in fact perform in a manner consistent with these calculations is presented in Chapter 10; thus this and the following two chapters now justify, in a practical context, much of the analysis presented in the rest of the book.
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9 CFAR detection
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A radar is often required to detect targets against a changing background of clutter and thermal noise, the clutter reflectivity and statistics varying with range and look direc tion, dependent on the chosen radar parameters, operating height and the prevailing weather conditions. For a scanning radar over the sea, this change is continuous and usually unpredictable.
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10 The specification and measurement of radar performance
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One of the ultimate aims of modelling sea clutter is to inform the development of improved radar systems that meet the operational needs of their users. However, the translation from a user's requirements to the entry into service of an equipment that meets these needs in an acceptable way is a very complex process. From the viewpoint of a radar designer, an important part of the process is the methodology for specifying and measuring radar detection performance. This methodology is the subject of this chapter, with emphasis being placed on the issues relating to maritime radars and the detection of targets in sea clutter.
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Appendix 1: Elements of probability theory
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In this appendix we give an informal review of probability theory and other matters relevant to the modelling of clutter and its impact on radar systems. Our selection of topics is rather eclectic and our treatment pragmatic; the principal aim is to remove those obstacles to the evaluation of radar performance presented by any unfamiliarity with the concepts and practice involved in calculating probabilities.
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Appendix 2: Some useful special functions
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This is a short review of some special functions that are useful in the study of clutter and its impact on radar performance.
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Appendix 3: Scattering from a corrugated surface
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In this appendix the authors have set up the integral equation formulation o fthe scalar scattering problem. Complete solutions, such as those describing the reflection and transmission of radiation by a planar interface, can be extracted from this only in the most idealised of circumstances. Nonetheless, the integral equation formulation provides us with a framework within which many aspects of scattering by a rough surface can be developed systematically. Approximate descriptions of scattering by a perfectly conducting surface can be derived, both through iterative solution of the integral equation (physical optics and small height perturbation theory) and progressive refinement of the Green's function (half space and Lorentz reciprocity based calculations). The latter Lorentz reciprocity based approach also allows us to derive the small height perturbation theory result for an imperfectly conducting rough surface with relatively little trouble; this in turn can be modified to take account of the large scale swell structure of the sea surface through its incorporation into the composite model. Methods for the numerical solution of the scattering integral equations have been developed. Sufficient detail has been given for explicit expressions to be identified and coded up for both perfectly and imperfectly conducting surfaces. The modelling of low grazing angle scattering invariably encounters difficulties that arise from the finite size of scattering surface that can be accommodated within the computer; these has been ameliorated by introducing semiinfinite adjunct planes. A different and improved method for the calculation of the terms in the integral equations that arise from these planes has been described, which also allows us to treat the imperfectly conducting surface through the use of the impedance boundary condition that was derived.
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Back Matter
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