Currently, there are four dominant GNSS systems, i.e., GPS (G), Galileo (E), GLONASS (R), and BDS-3 (C), capable of providing multi-frequency positioning services worldwide. To fully take advantage of the multi-system multi-frequency signals on precise point positioning (PPP) for global clients, we resolved the triple-frequency PPP ambiguity resolution (PPP-AR) for the first time with the integration of GPS, Galileo, GLONASS, and BDS-3 triple-frequency observations. Especially, some new signals, e.g., GLONASS code-division multiple-access (CDMA) L3 and BDS-3 B2a observations, are integrated carefully into our proposed GERC triple-frequency PPP-AR model. Besides, to overcome the problem of GLONASS inter-frequency biases (IFBs) from the frequency-division multiple-access (FDMA) strategy, the uncalibrated phase delay (UPD) determination method based on the homogeneous receivers is presented. Then we comprehensively addressed the processing of multi-system inter-frequency clock biases (IFCBs) determination and calibration in the context of GERC triple-frequency PPP-AR. Datasets from twenty tracking stations of the regional EUREF Permanent Network (EPN) equipped with identical JAVAD receivers are utilized to validate our developed GERC multi-frequency UPD determination and PPP-AR. The quality of UPD estimates in terms of the residual distribution was studied first. Generally, the higher the accuracy of the UPD corrections, the smaller the residuals achieved. Results demonstrate that almost 100% of extra-wide lane (EWL) ambiguity residuals of each GNSS constellation were within 0.15 cycles. Moreover, the percentages of wide lane (WL) and narrow lane (NL) ambiguity residuals smaller than 0.25 cycles were also larger than 95%. Therefore, based on the precise UPD products, high-accuracy PPP-AR can be performed. Our results show that integrating the additional third frequency and multi-GNSS does contribute to improving the PPP-AR performance. The best convergence performance of about 0.71 min was achieved by the GERC triple-frequency PPP-AR, which is much shorter than that of G (7.32 min), GR (4.95 min), GC (3.10) and GE (1.39 min). Compared with the GERC dual-frequency PPP-AR (1.82 min), the triple-frequency solution also realized an improvement of about 61%. This result is encouraging because it demonstrates that the positioning errors of multi-GNSS PPP-AR can be rapidly converged within 1 min. We further investigated the PPP-AR performance with different session lengths of several solutions. When the session length reaches 10 min, the GERC triple-frequency PPP-AR solution realizes positioning errors of [0.28 0.36 0.98] cm, while that of GPS-only is [1.34, 0.73, 2.26] cm in the east, north and up directions.