Non-stationary glint noise is often observed in a radar tracking system. The distribution of glint noise is non-Gaussian and heavy-tailed. Conventional recursive identification algorithms use the stochastic approximation (SA) method. However, the SA method converges slowly and is invalid for non-stationary noise. This paper proposes an adaptive algorithm, which uses the stochastic gradient descent (SGD) method, to overcome these problems. The SGD method retains the simple structure of the SA method and is suitable for real-world implementation. Convergence behavior of the SGD method is analyzed and closed-form expressions for sufficient step size bounds are derived. Since noise data are usually not available in practice, we then propose a noise extraction scheme. Combining the SGD method, we can perform on-line adaptive noise identification directly from radar measurements. Simulation results show that the performance of the SGD method is comparable to that of the maximum-likelihood (ML) method. Also, the noise extraction scheme is effective that the identification results from the radar measurements are close to those from pure glint noise data.