Radar Target Detection with Kernel-Based Generalized Likelihood Ratio Test

This article deals with target detection in a monostatic radar in the presence of Gaussian disturbance with the unknown covariance matrix. This problem has been formulated as a composite hypothesis-testing problem and solved by resorting to the two-step generalized likelihood ratio (GLR) test principle, the so-called sample covariance matrix-based GLR detector (SCM-GLR). Here, this problem is handled with the use of the kernel theory to improve its detection performance in terms of signal-to-noise ratio (SNR) gain. To do so, firstly, we reformulate the test statistic of the SCM-GLR detector as a function of Euclidean inner product. Then, we kernelize the conventional SCM-GLR using the so-called kernel trick, such that the inner product of the conventional SCM-GLR is replaced with proper polynomial kernel functions allowing for richer feature space to be deployed in the detection. Finally, the detection performance of the proposed kernelized detector is compared with its counterpart to show its SNR gain of about 1.5dB.