We address the covariance matrix estimation problem for radar adaptive detection in a non-Gaussian clutter environment. We first propose an estimation method based on α log-determinant divergence, which estimates the true covariance accurately by solving the geometric mean of the sample covariance matrix (SCM). Since the estimation performance would be seriously degraded when the number of secondary data is insufficient, a knowledge-aided method is then proposed. Under the similarity constraint between the a priori covariance and the true one, a closed form expression is derived by minimizing the α log-determinant divergence between the real covariance and the SCM. Simulation results verify the accuracy of the proposed algorithms in covariance estimation and superiority in target adaptive detection.