This paper considers the problem of approximating a kernel matrix in an autoregressive Gaussian process regression (AR-GP) in the presence of measurement noises or natural errors for modeling complex motions of pedestrians in a crowded environment. While a number of methods have been proposed to robustly predict future motions of humans, it still remains as a difficult problem in the presence of measurement noises. This paper addresses this issue by proposing a structured low-rank matrix approximation method using nuclear-norm regularized l₁-norm minimization in AR-GP for robust motion prediction of dynamic obstacles. The proposed method approximates a kernel matrix by finding an orthogonal basis using low-rank symmetric positive semi-definite matrix approximation assuming that a kernel matrix can be well represented by a small number of dominating basis vectors. The proposed method is suitable for predicting the motion of a pedestrian, such that it can be used for safe autonomous robot navigation in a crowded environment. The proposed method is applied to well-known regression and motion prediction problems to demonstrate its robustness and excellent performance compared to existing approaches.