In order to eliminate the subjectivity of expert experience, get rid of the dependence on trajectory characteristics and reduce the burden of experimental parameter tuning, a Parameter Independent Clustering BAsed on SIlhoutte Coefficient (PICBASIC) algorithm was proposed. Firstly, existing Euclidean distance based track pairing methods were compared, and a trajectory similarity calculation model based on Dynamic Time Warping (DWT) distance and Gaussian kernel function was established. Secondly, the air traffic trajectories were partitioned and clustered by spectral clustering. Finally, a cluster number optimization method based on silhouette coefficient was proposed, and it had the function of quantitative evaluation of clustering results. Experiments were carried out by using real arrival trajectories to verify the validity of the proposed algorithm. PICBASIC judged that the clustering quality would be respectively optimum if the 365 trajectories of runway 28L were clustered into 5 clusters and the 530 trajectories of runway 28R were clustered into 6 clusters. The average silhouette coefficients in the two situations were respectively 0.8099 and 0.8056. Under the same experimental conditions, the difference rates of average silhouette coefficient between PICBASIC and MeanShift clustering were respectively -1.23% and 0.19%. The experimental results demonstrate that PICBASIC can tolerate the speed and length differences of trajectories, dispense with manual guidance or experimental parameter tuning and filter out the adverse impact of abnormal trajectories on the clustering quality.