Bayesian State-Space Modelling of Spatio-Temporal Non-Gaussian Radar Returns

Radar backscatter from an ocean surface is commonly referred to as sea clutter. Any radar backscatter not due to the scattering from an ocean surface constitutes a potential target. This thesis is concerned with the study of target detection techniques in the presence of high resolution sea clutter. In this dissertation, the high resolution sea clutter is treated as a compound process, where a fast oscillating speckle component is modulated in power by a slowly varying modulating component. While the short term temporal correlations of the clutter are associated with the speckle, the spatial correlations are largely associated with the modulating component. Due to the disparate statistical and correlation properties of the two components, a piecemeal approach is adopted throughout this thesis, whereby the spatial and the temporal correlations of high resolution sea clutter are treated independently. As an extension of the previously reported work on target detection in coherent radar systems, a complex autoregressive process is proposed as the basis for characterisation of high resolution sea clutter spectra in incoherent radar systems. As no phase information is available in incoherent radar returns, the Gibbs sampler is used to facilitate sampling from the autoregressive process parameter posterior distribution, conditional on the observed amplitudes. To this end, the Hybrid Monte Carlo algorithm is employed to conditionally sample for the missing phases. Based on birth-death migration arguments for the evolution of a population of scattering centres on an ocean surface, a conditional heteroscedastic (i.e. non-constant prediction error variance) model is proposed for the modulating component of high resolution sea clutter in the logarithm domain. However, based on the results obtained for a large database of sea clutter range profiles, it is shown that there appears to be no strong evidence for heteroscedasticity. Instead, contrary to the widely held beliefs, rather than being Gamma distributed, it is demonstrated that the modulating component of sea clutter is better modelled as being log-Normal distributed, and hence Gaussian distributed in the logarithm domain. The findings presented in this dissertation are culminated in the context of Constant False Alarm Rate (CFAR) detection. In particular, a linearised state space model for the compound high resolution sea clutter in the logarithm domain is proposed. The state space model is used to obtain a Maximum A Posteriori (MAP) estimate of the underlying modulating component in the cell under test, based on which the CFAR detection threshold is set. The CFAR detection threshold is thus obtained as a simple weighted average of radar returns (in the logarithm domain) contained in the reference window. Finally, based on a large database of high resolution sea clutter range profiles, it is demonstrated that the proposed state space CFAR detector, in conjunction with pulse integration techniques, achieves a near ideal CFAR detection performance, particularly in spiky and spatially correlated clutter environment.