The precise point positioning (PPP) is a promising technology for the real-time retrieval of atmospheric parameters with a single receiver in anywhere, all-weather and any time. The real-time atmospheric parameters can be applied to the time-critical meteorology, such as the severe weather nowcasting. The PPP is a satellite-based technology. Multi-constellation integration can enhance satellite geometry and increase measurement redundancy so that the solutions of atmospheric parameters are expected to be improved. Currently, the Global Navigation Satellite System (GNSS) family includes recovered GLONASS and modernized GPS as well as the emerging Galileo and BDS. A week of GNSS observations from 160 stations are processed to retrieve the tropospheric zenith total delay (ZTD) in real time. The four-constellation mixed real-time precise products including satellite orbit and clock corrections are adopted, and their quality is evaluated. The performance of ZTD estimates is assessed in terms of accuracy and convergence time by comparing with final tropospheric ZTD products provided by two analysis centers. The ZTDs retrieved from different constellation combinations (i.e., GPS/GLONASS/Galileo/BDS, GPS/GLONASS, and GPS-only), different processing models for ionospheric delays (i.e., ionospheric-free (IF) combined PPP, and uncombined (UC) PPP), and different modes (i.e., real-time mode, and post-processing mode) are compared.