Diseño de detectores robustos en aplicaciones radar

Abstract

The automatic radar detection problem can be formulated as a binary hypothesis test, where the system must decide in favour of hypothesis H1 (target present) or H0 (target absent). The Neyman-Pearson (NP) criterion is the most extended for this task. This type of detector maximizes the probability of detection (PD), while maintaining the probability of false alarm (PF A) lower than or equal to a given value. When the likelihood functions are known, a decision rule based on comparing the Likelihood Ratio with a detection threshold fixed attending to PF A requirements (LRT), is an implementation of the NP detector. Due to its parametric nature, if the interference and/or target statistical features assumed in the design differ from real ones, the detection losses can be very important. In practical situations, the interference parameters can be estimated and tracked from the operating environment in some degree, but target ones are really difficult to estimate. Because of that, different target models are assumed, considering that parameters such as the one-lag correlation coefficient or the Doppler shift are random variables with known probability density functions (PDFs). In these cases, the detection problem must be formulated as a composite hypothesis test, for which the decision rule based on the Average Likelihood Ratio (ALR) is an implementation of the NP detector. This approach usually leads to intractable integrals without a closed-form solution, and sub-optimum solutions based on numerical approximations of the ALR, or the Generalized Likelihood Ratio (GLR), can be proposed. This PhD. Thesis tackles the study of the suitability of Artificial Intelligence (AI) based radar detectors as alternative solutions for the problem of detecting targets with unknown parameters in different radar clutter environments. Learning machines trained in a supervised manner using a suitable error function, have been previously proved to be able to approximate the optimum NP detector in simple hypothesis tests [Jarabo2009]. The calculus of the function approximated by the learning machine after training is a key element for the analysis of the suitability of an error function for training a learning machine to approximate the NP detector. In [Jarabo2005a, Jarabo2009] the function approximated by a learning system such us a MultiLayer Perceptron (MLP), a Radial Basis Function Neural Network (RBFNN) or a Second Order Neural Network (SONN) when trained using the mean-squared error and the cross-entropy, was calculated. In this PhD Thesis, the theoretical study presented in [Jarabo2009] has been extended to composite hypothesis tests, confirming that the proposed sufficient condition can be applied for testing if an error function is suitable for training learning machines in a supervised manner, for approximating the ALR based detector for any pair of likelihood functions. Another important contribution of this PhD. Thesis, is the theoretical study of the function approximated by a Super Vector Machine (SVM), when the error used for training is the classification error proposed by [Shawe2004]. This is an important contribution in the field, because provides important keys to justify, from theoretical foundations, the observed performances and limitations of C-SVMs and 2C-SVMs in different detection applications presented in the literature. This PhD. Thesis has been carried out in the scope of research projects such as the Spanish Ministry, the Comunidad de Madrid, the University of Alcalá, and the company AMPER SISTEMAS, S.A., which focused on marine radar applications, radar sea clutter models have been studied and used for generating synthetic data sets for training, validating and testing the proposed AI solutions, and for simulating a radar scenario. Three cases of study have been considered taking into account different clutter models and target unknown parameters: detection of Gaussian fluctuating targets with unknown correlation coefficient or unknown Doppler shift, in presence of Additive White Gaussian Noise (AWGN); detection of Gaussian fluctuating targets with unknown correlation coefficient or unknown Doppler shift, in presence of correlated Gaussian clutter and AWGN; and detection of non fluctuating targets with unknown Doppler shift, in presence of spiky K-distributed clutter. For all these cases, an analysis of the sensitivity of the LRT detectors for targets of known parameters has been carried out in a first step, in order to study the detection loss associated to a mismatch between the assumed design target parameters and the actual ones. Constrained approximations of the GLR test have been designed, to be used as references for the design and performance analysis of the AI proposed solutions, in terms of detection capabilities and computational complexity. For each case of study, detectors based on MLPs, RBFNNs, SONNs and SVMs have been designed and tested. The proposal of SONN based solutions is another important contribution of the PhD Thesis. SONNs with only one quadratic neural unit present a high robustness against target correlation coefficient and Doppler shift, in Gaussian interference. Mixture of experts are also designed for improving the detection capabilities and/or reducing the computational cost. Different combination techniques have been considered. Some of them, as far as the author knows, are novel contributions. A final AI solution has been proposed as a compromise between detection performance and computational cost for each case of study. These detectors have been finally evaluated in a simulated radar scenario, comparing their performances with those provided with CA-CFARs.