# Detection of RINEX-2 Files With Mixed GPS L2P(Y)/L2C Carrier Phase Observations
## 2 L2 Quarter-Cycle Bias and its Effect on Ambiguity Estimation
After fixing and removing the widelane ambiguity, the ionosphere-free linear combination (IF) of the dual-frequency GPS carrier phase observations is obtained by:  
\[IF_{12}=\left(77\cdot\varphi_{1}-60\cdot\varphi_{2}\right)\ /\ 17 \tag{5}\]  
and has a wavelength of 10.7 cm [11; 12]. Here, an L2 quarter cycle bias produces a bias of:  
\[\delta_{IF}=\left(-60\cdot 0.25\ cy\right)\ /\ 17=-0.88\ cy \tag{6}\]  
which is mainly absorbed by an ambiguity shift of one full cycle. What remains is a residual error of:  
\[\delta_{IF}^{\prime}=1.00\ cy-0.88\ cy=0.12\ cy\approx\ 1.3\ cm. \tag{7}\]  
Thus, the effect of an L2 quarter cycle bias on IF is much smaller than the effects on L2 or on the WL. This conclusion is true for both the ambiguity fixing (biases in units of cycles) and the coordinate solutions (biases in metric units). In conclusion, IF is not well suited for the detection of L2 quarter cycle biases, nor will coordinate solutions based on IF encounter large and thus easily detectable coordinate errors. A following example will illustrate the effects of quarter cycle biases on estimated ambiguities. RINEX-2 observation files of the Spanish station BCNL were identified to contain mixed L2P(Y)and L2C carrier phase measurements without alignment. L2 and WL ambiguities were estimated in baselines to stations without an L2 quarter cycle problem; a baseline of 55 km to station BELL (Figures 2 and 3, panels a1, b1), and a long baseline of 566 km to station AJAC (Figures 2 and 3, panels a2, b2). Data processing was performed with the baseline processing engine Wa2 and used precise International GNSS Service (IGS) orbits and IGS global ionosphere maps [13]. Furthermore, PPP solutions of station BCNL were computed using software WaPPP to estimate MW widelane ambiguities (Figures 2 and 3, panel b3). The IGS antenna phase center corrections were applied for satellite and receiver antennas. The elevation mask angle was set to 10 deg. Figure 2 shows the distribution of fractional ambiguities of unaligned L2P(Y)/L2C carrier phase observations at BCNL. The same observation dataset was re-used for Figure 3, but L2C carrier phase observations were shifted by 0.25 cycles to align all L2 phase observations. The L2 quarter cycle problem at BCNL can be identified by comparing the distributions of fractional ambiguities of two groups of satellites--12 satellites with L2P(Y) observations and 18 satellites with L2C (Figures 2 and 3, upper and lower sub-panels). With L2 quarter cycles biases being present (Figure 2), the distribution peaks show a separation of approximately a quarter cycle. With observations being aligned (Figure 3), the distribution peaks are aligned as well. In shorter baselines with less residual ionospheric delays, L2 quarter cycle biases can be detected much better than in longer baselines. In addition, the WL shows the bias much clearer than L2. MW widelane ambiguity distribution is especially suited for quarter cycle bias detection because it is ionosphere-free and has an important additional advantage--the data processing requires only measurements of the one station to be examined. Figure 2: Distribution of fractional ambiguities of unaligned L2P(Y)/L2C carrier phase observations: **(a1)** L2, short baseline, **(a2)** L2, long baseline, **(b1)** WL, short baseline, **(b2)** WL, long baseline, **(b3)** Melbourne-Wübbena linear combination, PPP; each panel consists of 2 sub-panels: upper sub-panels refer to L2C, lower sub-panels refer to L2P(Y); the bin width is 0.05 cycles.