This study considered zenith total delay (ZTD) estimation from precise point positioning (PPP) based on GPS only (PPP GPS), GLONASS only (PPP GLO), and GPS+GLONASS (PPP GPS+GLO) using both a conventional strategy when applying a model for the hydrostatic component with an estimation of the wet component and an alternative strategy. The proposed alternative strategy is to estimate both the hydrostatic and the wet components of the tropospheric delay using different process noises with different mapping functions for both components in an extended Kalman filter (EKF). It was found that the receiver clock offsets and the estimated ambiguities would absorb some errors in the ZTD when using the conventional strategy. The RMS values of the differences between the double differenced (DD) GPS ZTD and the PPP ZTD, using the alternative strategy, were 6.5, 7.3, and 6.7 mm for PPP GPS, PPP GLO, and PPP GPS+GLO, respectively. The results were validated over one continuous week and then over one year. Validation was also performed through comparison with the IGS ZTD values, for 12 weeks, with an overall RMS of 5.9 mm and against IGS real-time products with an overall RMS of 8.1 mm. Furthermore, the alternative strategy also provided significant improvements in the 5 cm convergence time in the vertical coordinate component of the float ambiguity solutions to be on average, 51, 36 and 27 minutes for PPP GPS, PPP GLO and PPP GPS+GLO solutions respectively.