# Detection of RINEX-2 Files With Mixed GPS L2P(Y)/L2C Carrier Phase Observations
## 5 Coordinate Errors Due to Quarter Cycle L2 Biases  
If carrier phase ambiguities are estimated as real values and not fixed to integer values (float solution), the quarter cycle L2 bias does not cause any effects to coordinate solutions since it is completely absorbed by the real value ambiguities. However, after fixing ambiguities to integer values, the biases cause coordinate errors. The size of the coordinate errors depends on a large number of factors, among which are the ratio of non-L2C and L2C GPS satellites, the completeness of ambiguity fixing, the geometry of satellite-receiver constellation, the elevation mask angle, the observation weighting, the length of static observation session, and the kind of coordinate solution. Experiences with our own software modules, Wa2 and WaPPP, show that on short baselines, the L2 quarter cycle problem leads to an incomplete fixing of ambiguities. On long baselines or with PPP, however, the algorithms accept larger residual ionospheric effects or larger biases in general, which enables complete ambiguity fixing. In order to be able to estimate the size of the coordinate errors, at least for certain positioning modes, zero-baseline tests were performed. Two observation datasets were selected which form a zero-baseline:  
1. an original observation data set or a simulated data set, and
2. a duplicate of data set (1) with quarter cycle L2 biases introduced/removed for all L2C carrier phase observations, while L2P(Y) carrier phase observations remained unchanged. Since the quarter cycle biases are the only difference between the two data sets, only they affect the differential coordinate solution. All other error sources, such as the effects caused by the ionosphere, troposphere, orbit errors, multipath, etc., cancel out in the baseline processing since they are completely identical in corresponding data sets 1 and 2. We altered the global navigation satellite system (GNSS) baseline processor Wa2 in such a way that the fixing algorithms intended for long baselines (WL, IF) could also be used for these zero-baselines. A complete ambiguity fixing could always be achieved. The coordinate solution after ambiguity fixing can be computed in several different ways. All results shown in this section are based on the IF linear combination of carrier phase observations and the estimation of tropospheric zenith delays being enabled. This setting simulates long baselines or PPP solutions with all ambiguities being fixed. According to Equation (7), when using the IF linear combination, the largest portion of an L2 quarter cycle bias is absorbed by an incorrect fixing of the ambiguity by 1 cycle. What remains is a phase bias in the order of just 1 cm. A first example shows the geographical distribution of coordinate errors for long-term (24 h) static observations (Figure 6). It is mainly based on simulated data, computed for DoY 150, 2018 with an elevation mask of 5 degrees. The simulation was performed for 16,380 stations in a regular grid with \(2^{\circ}\times 2^{\circ}\) spacing. In order to confirm the results, seven real stations were selected from the data set of the last section, and a similar zero-baseline computation was performed with their RINEX-2 observation data. The coordinate errors reach up to 1.3 mm, 2.1 mm, and 12.6 mm in the north, east, and height components, respectively. There is a distinct geographical distribution with areas of larger coordinate errors and others with small ones (Figure 6). The results based on simulated observations match very well with those of the real datasets. Any differences are due to missing observations in the real datasets above the 5 deg elevation mask angle. Observation errors are not able to affect the solutions since they cancel out by forming zero-baselines. One of the real data sets belongs to station BIK0 (Bishkek, Kyrgyzstan). Here, daily coordinate errors are smaller than 1 mm in all three coordinate components. We picked this one to show the epoch-wise variations of coordinate errors (Figure 7).