The demand for high-precision real-time positioning is critical for applications such as autonomous vehicles, urban planning, and location-based services. Real-time kinematic (RTK) can provide centimeter-level positioning services and is widely used. However, the traditional intra-system double-difference model in RTK requires sacrificing one reference satellite per constellation, leading to insufficient satellite pairs for ambiguity resolution in challenging environments. To address this issue, we propose a single-difference triple-carrier ambiguity resolution (TCAR) algorithm. This algorithm estimates relative measurement biases in advance, and these biases require re-estimation whenever the receiver is replaced or restarted. These estimated biases are then used to correct real-time GNSS measurements, enabling instantaneous single-difference TCAR. Random sampling consensus (RANSAC) is employed to detect and exclude satellites with incorrectly fixed ambiguities before positioning. To validate the effectiveness of the proposed algorithm, both static and vehicular experiments were conducted in challenging urban environments. In the static experiment, the results demonstrate that the positional availability of the proposed algorithm (92.1%) is significantly higher than that of the two comparative algorithms, which achieved 68.3% and 54.5%, respectively. The positioning accuracies of the three algorithms are comparable, with 3D Root Mean Square Errors (RMSEs) of 5.03 cm, 4.41 cm, and 5.43 cm. In the vehicular experiment, the proposed algorithm achieved nearly 100% positional availability in typical urban areas, with an RMSE of 5.28 cm, outperforming the two comparative algorithms, with availabilities of 94.7% and 78.2%, and 3D RMSEs of 6.33 cm and 3.64 cm. These results highlight the ability of the proposed algorithm to provide continuous, reliable and precise real-time positioning in challenging urban environments.