# Improving GNSS PPP Convergence: The Case of Atmospheric-Constrained, Multi-GNSS PPP-AR
## 1 Introduction  
Traditionally, the effects of ionosphere and troposphere refraction are mitigated in the Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) measurement processing technique using dual- or triple-frequency linear combinations and systematic modelling, respectively [1; 2; 3; 4; 5]. The purpose of such mitigation hinges on improving PPP convergence and initialization which has been a challenging but promising area of GNSS research. Recent developments and contributions highlight the changing definition of conventional PPP from the use of dual- to triple-frequency measurements. Additional frequencies coupled with expanding satellite constellations have improved reliability and integrity of multi-GNSS PPP solutions [6; 7; 8; 9]. Thus, the progression towards the improvement of multi-GNSS PPP solution quality and initial convergence is only natural given that measurement strength and satellite geometry are continually being enhanced. It is well known that by accessing the slant ionospheric information, PPP convergence and initialization can be significantly improved [10; 11; 12; 13]. The usage of raw observations in an uncombined PPP processing is gradually becoming the standard approach as an alternative to ionosphere-free PPP solutions. One key advantage involves the flexibility in processing the observations from all existing GNSS constellations while avoiding noise amplification due to linear combinations [14; 15; 16]. The consequential benefit is the ability to extract the slant ionospheric delays which can be used to quickly re-initialize the solution. In the context of this paper, the raw observations from available GNSSs were processed without employing linear combinations to eliminate the first order ionospheric delay, but rather estimate it. Having access to the slant ionospheric terms enable various analyses tobe made in comparison to the a priori ionospheric delays obtained through atmospheric products. For more and detailed information on how to decompose the linear ionospheric combination to its uncombined format in order to estimate the slant ionospheric term, the reader is referred to these research contributions that discusses it at length: [17; 18; 19; 20]. Using a priori estimates from atmospheric products, either from regional or global networks of stations, it has been shown that it is possible to obtain cm-level accuracy within a few minutes, rather than the typical 20 to 30 min of PPP convergence time [17; 21; 22; 23; 24; 25]. Single-frequency ambiguity resolution (AR) has been a prominent topic demanding innovative solutions due to its relatively long convergence time period [14; 26; 27; 28]. Isolating and resolving ambiguities to integers can be hastened by using a priori atmospheric constraints, which consequentially leads to improved accuracy and stability in the position estimates [17; 18; 22]. The purpose of this study is to demonstrate how close multi-GNSS PPP performance is to RTK-like performance by focusing on the increasing improvements seen in the reduction of convergence time. As it is well-known, typical RTK performance is correlated and limited to baselines of less than approximately 20 km. Longer baseline lengths prevent measurement errors from being effectively accounted for. By mathematically differencing GNSS measurements from multiple receivers, the key objective of relative positioning is to reduce or eliminate error sources. One key benefit of PPP is that it removes the need for a local GNSS network and allows for centimetre- to millimetre-level positioning accuracy with a single GNSS receiver. The disadvantage of conventional PPP is the limitation of needing tens of minutes to obtain centimetre-level positioning, as defined in terms of convergence period. Similarly, when considering typical RTK positioning performance, the potential delocalization of the ionosphere and troposphere introduces systematic errors that prevent baselines from being extended beyond 20 km if reliable user solutions are to be obtained [29].