This paper deals with unsupervised radar clutter clustering to characterize pathological clutter based on their Doppler fluctuations. Operationally, being able to recognize pathological clutter environments may help to tune radar parameters to regulate the false alarm rate. This request will be more important for new generation radars that will be more mobile and should process data on the move. We first introduce the radar data structure and explain how it can be coded by Toeplitz covariance matrices. We then introduce the manifold of Toeplitz co-variance matrices and the associated metric coming from information geometry. We have adapted the classical k-means algorithm to the Riemaniann manifold of Toeplitz covariance matrices in [1], [2]; the mean-shift algorithm is presented in [3], [4]. We present here a new clustering algorithm based on the p-mean definition in a Riemannian manifold and the mean-shift algorithm.