In this chapter, we have established a well-defined framework, provided by the likelihood ratio concept and the statistical models developed in Chapters 3 and 6, within which useful detection schemes can be developed in a systematic way. The closely related problem of parameter estimation is also considered: maximum likelihood techniques derived from Bayes' theorem prove to be quite tractable for simple Gaussian clutter models, and can be incorporated into generalised likelihood ratio-based detection methods. Some relatively simple examples of the application of these principles have been discussed in detail, to the point where contact is made with the small target detection strategies discussed in Chapters 12 and 13. The principles demonstrated here can then be applied to other detection scenarios. The estimation of parameters characterising non-Gaussian clutter is more problematic: the maximum likelihood derived equations are now much less easy to solve. Nonetheless, useful estimation methods have been derived that can be applied to gamma, Weibull and K-distributed data. The compound representation of clutter developed in Chapters 3 and 6 plays a central, but rather subtle, role in this work. Small target detection procedures are applied to localised samples of data, to which the relatively simple and tractable Gaussian derived methods can be applied. Consequently, we should expect the methods described in Section 10.7 to be relatively effective even in spiky, non-Gaussian clutter; their performance can then be improved incrementally and relatively straightforwardly, when prior knowledge of the gamma distribution of local power can then be brought to bear, as is described in Section 10.10.

Chapter Contents:

• 10.1 Introduction
• 10.2 Statistical models for probabilities of detection and false alarm
• 10.3 Likelihood ratios and optimal detection
• 10.4 Some simple performance calculations
• 10.5 The generalised likelihood ratio method
• 10.6 A simple Gaussian example
• 10.6.1 A simple likelihood ratio-based approach
• 10.6.2 Generalised likelihood ratio-based approach
• 10.7 The detection of a steady signal in Rayleigh clutter
• 10.7.1 Generalised likelihood ratio-based approach
• 10.7.2 Peak within interval detection
• 10.8 Applications to coherent detection
• 10.9 The estimation of clutter parameters
• 10.9.1 Maximum likelihood estimators for gamma and Weibull parameters
• 10.9.2 Tractable, but sub-optimal, estimators for K and Weibull parameters
• 10.10 Implications of the compound form of non-Gaussian clutter
• 10.10.1 Modified generalised likelihood ratio-based detection
• 10.10.2 Modified peak within interval detection
• 10.11 Concluding remarks
• References

Inspec keywords: object detection; clutter; maximum likelihood estimation; Bayes methods; gamma distribution

Other keywords: K distributed data; maximum likelihood technique; Weibull; sea clutter; parameter estimation; gamma distribution; Bayes theorem; tractable Gaussian derived method; nonGaussian clutter; generalised likelihood ratio based detection method; Gaussian clutter models; statistical model; target detection

Subjects: Signal processing and detection; Other topics in statistics; Electromagnetic compatibility and interference; Radar theory