# 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  
Processing carrier phase observations in baseline mode or as a single station in precise point positioning (PPP) mode requires the estimation of carrier phase ambiguities. The ambiguities of the original signals, L1 and L2, or of linear combinations of these signals, are either treated as real numbers (float solution) or fixed to their true integer values (fixed solution) [7]. In the context of the L2 quarter cycle problem, we are interested in real number L2 ambiguity estimates, and especially in fractional biases between ambiguity estimates. On L2, a GPS L2 quarter cycle bias equals 6 cm in distance. When forming the widelane linear combination WL [widelane cycles] of dual-frequency phase measurements [cycles] at frequencies 1 and 2 by:  
\[WL_{12}=\varphi_{1}-\varphi_{2}, \tag{1}\]  
we obtain a signal with a much larger wavelength (86.2 cm) that is also affected by L2 quarter cycle biases. An L2 quarter cycle bias causes a WL bias of \(-0.25\) cy, which corresponds to \(-22\) cm in distance and, thus, is much easier to identify. Furthermore, because of smaller residual errors from ionospheric refraction and orbits, detection of quarter cycle biases is simpler in short baselines as compared to long baselines. Figure 1: Development of the global positioning system (GPS) space segment with respect to L2C capable satellites (data source: IGS file of antenna corrections IGS14_2000.ATX). Widelane ambiguities can also be estimated using the Melbourne-Wubbena linear combination (MW). Using code measurements C [m] and carrier phase measurements [cycles] at frequencies 1 and 2, the linear combination MW [widelane cycles] is formed by:  
\[MW_{12}=\frac{l_{12}}{\lambda_{1}}C_{1}+\frac{l_{12}}{\lambda_{2}}C_{2}-\ \varphi_{1}+\varphi_{2} \tag{2}\]  
with  
\[l_{12}=\frac{\lambda_{2}-\lambda_{1}}{\lambda_{1}+\lambda_{2}} \tag{3}\]  
and \(\lambda_{1},\lambda_{2}\)[m] being the carrier wavelengths. This linear combination has properties of being ionosphere-free and geometry-free and, thus, it is independent of baseline length. On the other hand, it is affected by code multipath, noise, and code delays. For more information on widelane signals, see reference [8]. In case of undifferenced observations (PPP mode), satellite induced code and phase delays have to be corrected to enable ambiguity fixing. This is done by applying fractional cycle bias (FCB) corrections for all satellites. They can be estimated from the observation data of global networks of reference stations. As they are found to be fairly stable for the MW linear combination, a daily update seems to be sufficient to account for their temporal variations. CNES-CLS (Centre National d'Etudes Spatiales--Colcete Localisation Satellites, France) determines and publishes FCB\({}_{MW}\) values under the name of widelane satellite biases (WSB) on its file transfer protocol (FTP) server [9]. FCB\({}_{MW}\) values provided by CNES-CLS refer to code observations on P(Y)1 and P(Y)2. Thus, we call them _FCB\({}_{MW,PIP2}\)_ [WL cy]. Since not all receivers observe P(Y)1, but they all observe the C/A code C1 on the first frequency, C1 and P(Y)2 are used to form MW. Thus, we have to apply P(Y)1-C1 differential code biases _DCB\({}_{PIC1}\)_ [ns] to obtain _FCB\({}_{MW,CIP2}\)_ [WL cy]:  
\[ \begin{array}{ll}FCB_{MW,CIP2}&=FCB_{MW,PIP2}-\frac{f_{1}^{2}-f_{1}f_{2}}{f_ {1}+f_{2}}\cdot DCB_{PIC1}\\ &\approx FCB_{MW,PIP2}-0.196\cdot DCB_{PIC1}\end{array} , \tag{4}\]  
with \(f_{1}f_{2}\) [Hz] being the carrier frequencies. Monthly _DCB\({}_{PIC1}\)_ values are determined and published by CODE (Center for Orbit Determination in Europe, Bern, Switzerland) [10]. Making use of these monthly values, we calculated _FCB\({}_{MW,CIP2}\)_ and corrected the MW widelane ambiguity estimates.