For cm-level kinematic GPS positioning, it is common practice to use both the carrier phase and code observations for the existing kinematic positioning. Nevertheless, the code observations are generally highly sensitive to environmental multipath. The multipath effects on code observations can reach several meters, and hence have been one of the main error sources affecting the reliability of the required phase ambiguity resolution process and positioning accuracy. With the foreseeable three-frequency modernized GPS constellation, its refined signals, useful linear combinations of triple-frequency phase observations and highly-robust triple-frequency ambiguity resolution can be achieved. Therefore, it is of interest to study the feasibility of kinematic positioning that only uses triple-frequency phase observations for modernized GPS. In this study, we introduce a new algorithm with various phase linear combinations and focused on examining the availability and performances of ambiguity resolution of the algorithm with simulated triple-frequency GPS data. The experimental results show that (1) both algorithms use phase observations, and therefore are equally sensitive to phase multipath; (2) compared with the existing algorithm, the ambiguity resolution of the algorithm are more robust than that of the existing algorithm, especially under severe code multipath scenarios.