# A New GNSS Single-Epoch Ambiguity Resolution Method Based on Triple-Frequency Signals
## 1 Introduction  
Centimetre-level accuracy positioning can be achieved using the Global Navigation Satellite Systems (GNSS) carrier phase observation, which has been used in military and civilian fields [1; 2; 3]. To satisfy centimetre-level accuracy positioning requirements, the carrier Network Real-Time Kinematic (NRTK) positioning technology technique is commonly used. One key issue of the carrier phase-based real-time positioning technique is to fix the ambiguity On The Fly (OTF) [4]. Generally, the goal of OTF AR (ambiguity resolution) is to resolve ambiguities both correctly and as quickly as possible in terms of both the time span of observations and the computation time. OTF AR requires good station-satellite geometry and a low level of observation errors and biases. Moreover, it requires a fast and reliable algorithm. Over the past several decades, numerous AR algorithms have been developed. The most famous ones are the least-squares ambiguity search technique (LSAST) [5], the fast ARapproach (FARA) [6], the fast ambiguity search filter (FASF) [7] and the least-squares ambiguity decorrelation adjustment method (LAMBDA) [8; 9]. LAMBDA is currently a popular method both theoretically and practically among the ambiguity determination methods; it significantly reduces the computational complexity of the ambiguity search stage and has promoted the development of RTK in the 20 th century. Precise point positioning (PPP) [10] is another popular technique for precise positioning based on carrier phase observation. However, approximately 15 min is needed to achieve reliable integer ambiguity solutions. To take advantage of both PPP and NRTK, several methods have been developed to improve the performance of PPP services in specific areas by using regional reference networks [11; 12; 13]. To achieve instantaneous ambiguity resolution, a new strategy was proposed [14]. In the proposed method, precise zero-differenced atmospheric delays are derived from the PPP fixed solution of the reference stations, which are disseminated to and interpolated at user stations to correct for L1 or L2 phase observations or their combination. With the corrected observations, instantaneous ambiguity resolution can be achieved, thus achieving the position solutions equivalent to the network RTK. With the development of GPS, BDS, GLONASS and Galileo, GNSS is entering a new era. GNSS multiple-constellation and multiple-frequency signals will bring both opportunities and challenges to the fast AR. Most research [15; 16] has shown that the initialization and the centimetre-level position can be obtained in a very short time by using multiple-frequency observations. [PERSON] [17] clearly showed that the fusion of multiple GNSS significantly increases the number of observed satellites, optimizes the spatial observation geometry at a site, and improves the convergence, accuracy, continuity and reliability of positioning. In detail, the addition of the BDS, Galileo and GLONASS systems to the standard GPS-only processing reduces the convergence time by almost 70% and improves the positioning accuracy by approximately 25%. Research also shows that the GLONASS and BDS have the potential capability for real-time atmospheric parameter retrieval for time-critical meteorological applications as GPS does, and that the combination of multi-GNSS observations can improve the performance of a single-system solution in meteorological applications, with higher accuracy and robustness [18]. Three/Multiple-Carrier AR (TCAR/MCAR) [16] and Cascading Integer Resolution (CIR) [19] are the typical three/multiple-carrier AR methods. Both TCAR and CIR use the same geometry-free model to fix the ambiguities with a three- or four-step rounding procedure that is biased by the residual ionospheric delay. Following this study, a large amount of work has been carried out regarding triple-frequency AR using the TCAR/CIR or modified TCAR/CIR methods. [PERSON] and [PERSON] [20] used both a geometry-based and geometry-free TCAR model to process the ambiguity resolution.