This article is concerned with the real-time localization problem for the dynamic multi-agent systems with measurement and communication noises under directed graphs. The barycentric coordinates are introduced to describe the relative position between agents. A novel robust distributed localization estimation algorithm based on iterative learning is proposed. The relative-distance unbiased estimator constructed from the historical iterative information is used to suppress the measurement noise. The designed stochastic approximation method with two iterative-varying gains is used to inhibit the communication noise. Under the zero-mean and independent distributed conditions on the measurement and communication noises, the asymptotic convergence of the proposed methods is derived. The numerical simulation and the QBot-2e robot experiment are conducted to test and verify the effectiveness and the practicability of the proposed methods.