The Gershgorin radii and centers ratio (GRCR) and the Gini index detector (GID) have been recently proposed as robust solutions with low computation complexity for centralized cooperative spectrum sensing. Subsequently, the sliding-window based versions of them, named SGRCR and SGID, have been devised for spectrum sensing in radar bands. While the SGID has superior performance in the specific scenario of dominant propagation path, i.e, high Rice factor K, the SGRCR exhibits relatively small performance variations with K, but is outperformed by the SGID when K is high. In this paper, motivated by the complementary behaviors of the GRCR and the GID, a hybrid sliding-window based GRCR-GID (HSGG) detection strategy is proposed. The new test statistic is formed by the weighted sum of the GRCR and GID test statistics for each sliding sensing window. Numerical results demonstrate that the hybrid detector combines the best attributes of the base detectors, achieving high performances under any Rice factor. Specifically, it performs a little worse than the SGRCR and much better than the SGID when K = 0, and as good as the SGID for mild-to-high values of K. Moreover, there are cases in which the HSGG can beat the SGRCR and the SGID.