The general objective of this study is to analyze the performance of Precise Point Positioning (PPP) convergence and initialization while stochastically constraining the atmosphere. One specific objective of this study is to review the performance of dual- and triple-frequency PPP solutions using uncombined measurements. The research question to be answered is whether there is any significant benefit in constraining the atmosphere, specifically the ionospheric parameter, in dual- and triple-frequency PPP processing? For thorough performance analysis in the uncombined PPP case, data from 70 globally distributed multi-GNSS stations were processed for the month of February, 2016. The uncombined triple-frequency PPP results with GIM ionospheric constraints showed reduced convergence time compared to unconstrained solutions. At the 68th percentile, a 60% and 78% reduction in convergence was observed for dual- and triple-frequency PPP with ionospheric constraints, respectively. However, more than 50% improvement was observed for constrained triple-frequency uncombined GNSS PPP solution convergence and initialization in the first 5 minutes as compared to dual-frequency PPP solutions. It was concluded that by applying atmospheric constraints in an uncombined multi-GNSS approach, significant improvements were observed for both dual- and triple-frequency PPP implementations.