## 1 Introduction
GLONASS also broadcasts on multiple frequencies, though the signal structure is different from other constellations: the constellation uses a frequency division multiple access (FDMA) technique, leading to each satellite broadcasting on a separate frequency. The constellation is being modernized, with new satellites being launched that broadcast on three code division multiple access (CDMA) frequencies: a similar technique as other GNSS constellations. All of these new GNSS signals and constellations were shown to have direct positive impacts on PPP performance [15; 16; 17; 18]. Given all the frequencies being broadcast by an ever-growing number of satellites, it is necessary to move away from a combined view of measurement processing into an uncombined method to simplify the models and limit the number of possible combinations. Combined here refers to forming a linear combination of measurements, while uncombined refers to processing the raw measurements without combining the measurements. An uncombined variation of the DCM was introduced in [19], for which a triple-frequency model was derived. The model's performance was assessed using the Galileo constellation and the benefits of adding a third frequency to AR processing were established. In this manuscript, the triple-frequency DCM model is extended to other constellations, leading to a four-GNSS PPP solution for which ambiguities are resolved on GPS, Galileo and BeiDou. Ambiguity resolution is not attempted on GLONASS, as it is challenging due to the FDMA signal structure. On top of including all major constellations, the results presented within this manuscript make use of all available frequencies, up to a maximum of three frequencies. Indeed, while many satellites broadcast on three frequencies, many still only broadcast on two, such as GPS-II satellites for instance. Excluding such satellites in a triple-frequency solution would lead to a degradation of the performance compared to that of a dual-frequency solution in which those satellites are included. This manuscript processes both dual-frequency and triple-frequency satellites simultaneously, and fixes their ambiguities as well. Doing so requires careful handling of the PPP states, as well as the reference satellite choice. The focus from this work is to expand the uncombined triple-frequency DCM into an all-constellation model, as well as to allow simultaneous processing of dual- and triple-frequency measurements from all four GNSS constellations. The proposed algorithm is tested on a network of IGS stations for which hourly datasets were processed over a week. A comparison of performance between a solution with only dual-frequency satellites, only triple-frequency satellites, and a mix of dual- and triple-frequency satellites (referred to as mixed dual-/triple-frequency in the rest of the manuscript) is introduced first. The comparison is followed by an analysis of the mixed dual-/triple-frequency results through a convergence time and accuracy analysis, as well as a typical performance of a sample dataset. Finally, the algorithm is tested on kinematic automotive data that show the possibility of instantaneous centimetre-level positioning with a moving receiver. The manuscript ends with conclusions and future work proposal.