Correlation filtering based tracking model has received lots of attention and achieved great success in real-time tracking, however, the lost function in current correlation filtering paradigm could not reliably response to the appearance changes caused by occlusion and illumination variations. This study intends to promote the robustness of the correlation filter learning. By exploiting the anisotropy of the filter response, three sparsity related loss functions are proposed to alleviate the overfitting issue of previous methods and improve the overall tracking performance. As a result, three real-time trackers are implemented. Extensive experiments in various challenging situations demonstrate that the robustness of the learned correlation filter has been greatly improved via the designed loss functions. In addition, the study reveals, from an experimental perspective, how different loss functions essentially influence the tracking performance. An important conclusion is that the sensitivity of the peak values of the filter in successive frames is consistent with the tracking performance. This is a useful reference criterion in designing a robust correlation filter for visual tracking.