The insufficient number of available samples can cause inaccurate estimation of the clutter covariance matrix (CCM) in space-time adaptive processing (STAP), resulting in degraded clutter suppression performance. To tackle this problem, a CCM estimation approach based on knowledge aided and geometric methods is proposed in this paper. A combination of environmental as well as structural (Persymmetric or Symmetric structure) knowledge information is utilized to model the covariance matrix of each sample as a knowledge-aided Hermitian positive definite (KAHPD) covariance matrix. The estimation problem is introduced into the Riemannian manifold composed of the KA-HPD covariance matrices, and the geometric method is used for nonlinear processing. Based on the Kullback-Leibler (KL) divergence and the KL mean, the final estimated CCM is designed as a weighted combination of each KA-HPD covariance matrix. Experiment results show that the two designed structural covariance matrix estimators possess superior clutter suppression performance.