This paper proposes a real-time nonlinear filtering approach for the SLAM problem, termed as compressed Unscented Kalman filter (CUKF). A partial sampling strategy was recently proposed to make the computational complexity of the UKF quadratic with the state-vector dimension. However, the quadratic complexity remains intractable for the large-scale SLAM. To address this problem, we firstly prove the equivalence of the partial and full sampling strategies for the decoupled nonlinear system. Then a compressed form is presented by reformulating the cross-correlation items. Finally, experimental results based on simulated and practical datasets validate the effectiveness of the proposed approach.