## 1. Introduction

[2] Total Electron Content (TEC) is a key parameter in the investigation of spatial and temporal structure and variability of the ionosphere. TEC is defined as the line integral of electron density along a ray path or as a measure of the total number of electrons along a path of the radio wave. In recent years, Global Positioning System (GPS) dual frequency signals have been widely used to estimate both regional and global TEC values. TEC can be derived from the delay of the traveling time of the transmitted dual-frequency GPS signals, recorded at the earth-based receivers. Yet, variation of the ionospheric refractive index with frequency is a major source of error in computation of group delay and phase advance of GPS observables. Absolute TEC can be measured from the differential delay of the GPS code on the two GPS frequencies. For both GPS precise positioning applications and for accurate TEC estimation the effect of interfrequency satellite and receiver differential delay biases should be removed from GPS measurements [*Coco et al.*, 1991; *Warnant*, 1997; *Otsuka et al.*, 2002; *Chen et al.*, 2004; *Brunini et al.*, 2005]. The receiver biases are also referred to as receiver instrumental bias, receiver differential bias, receiver offset, differential code bias (DCB) and interfrequency bias (IFB).

[3] Historically, the interfrequency biases are considered to be instrumental and they are thought to be due to the delays caused by the analog hardware of satellite and receiver [*Lanyi and Roth*, 1988; *Warnant*, 1997; *Goodwin and Breed*, 2001]. With the assumption that the calibration differences are due to instrumentation, the interfrequency biases are modeled to be temperature- and hardware-dependent [*Bishop et al.*, 1996; *Warnant*, 1997]. The differential code biases are investigated by various researchers. Some methods are developed to obtain TEC and differential biases by considering more than one station in their computation and model TEC on the double differences of GPS recordings [*Hernandez-Pajares et al.*, 2004; *Makela et al.*, 2001; *Warnant*, 1997; *Sardon et al.*, 1994]. For single-station TEC and differential receiver bias estimates, there are two basic approaches that can be found in the literature. First group of studies models TEC by a polynomial of coordinates in Earth-Sun reference system. Both satellite and receiver biases are also included in the model. The polynomial coefficients and biases being the unknowns, the observations form a linear system of equations that is solved by least squares method [*Lanyi and Roth*, 1988; *Coco et al.*, 1991; *Jakowski et al.*, 1996; *Warnant*, 1997; *Lin*, 2001; *Kee and Yun*, 2002; *Otsuka et al.*, 2002; *Chen et al.*, 2004]. In the second group of studies, for a selected measurement time, TEC is computed from different satellites over a certain angle of elevation, and the computed TEC values are considered be close to each other. This proximity is found by calculating standard deviation of TEC obtained from all satellites. To obtain the optimum receiver bias value, trial receiver biases are used in TEC computation and the receiver bias that minimizes the standard deviation is chosen as the receiver bias value for that GPS station [*Ma and Maruyama*, 2003; *Zhang et al.*, 2003]. Both of the above methods can be applied to estimate differential receiver biases for a single station, yet they have to be used off-line.

[4] Differential satellite and receiver biases can also be obtained from internet for a few number of GPS stations from International GPS Service (IGS) analysis centers, namely, the Center for Orbit Determination in Europe (CODE) University of Berne, Switzerland; Jet Propulsion Laboratory (JPL) Pasadena, CA, USA; European Space Operations Center (ESOC) of European Space Agency (ESA), Darmstadt, Germany; and gAGE/UPC of Polytechnical University of Catalonia, Barcelona, Spain. Global Ionospheric TEC maps (GIM) and interfrequency bias solutions of these analysis centers and are available at the web sites ftp://igs.ensg.ign.fr/pub/igs/iono or ftp://cddis.gsfc.nasa.gov/gps/products/ionex/ in the form of IONosphere Map EXchange Format (IONEX) files. Most of the IGS receiver differential biases provided in the IONEX files are monthly averages of daily values and do not represent the daily variations. The algorithms to compute the receiver bias values are not clearly explained in the literature, and thus the results can not be duplicated by other users. Also, the values provided for DCBs in IONEX files from various centers are not always in accordance with each other [*Brunini et al.*, 2005].

[5] In the work of *Grejner-Brzezinska et al.* [2004], the receiver DCBs are computed using BERNESE software. Although a value is obtained for receiver DCB using the BERNESE software, the computation method is not disclosed to the users in the manual. The temporal and spatial variability of TEC biases are investigated in detail by *Brunini et al.* [2005]. It is concluded that bias estimates suffer from the same shortcomings of GPS-TEC assumptions and equatorial regions need more attention in modeling and computation of TEC. From the above discussion and from *Kee and Yun* [2002], it can be summarized that receiver differential biases have to be included in the TEC computation model for calibration purposes and there is a certain need to develop an online bias estimator that can be applied to any single station for any ionospheric state and compute TEC along with DCBs.

[6] In this study, a new algorithm for the computation of single station receiver differential bias is introduced. The new algorithm uses the model of slant TEC (STEC) computed from difference in GPS observables. The vertical TEC (VTEC) is obtained from IGS-IONEX files and the conversion from VTEC to STEC is done by the mapping function explained in section 2. The receiver bias is extracted from the equation for de-noised difference of pseudorange and VTEC. The algorithm is originally developed by *Nayir* [2007b] and presented by *Nayir* [2007a]. The DCB bias estimates obtained from this method will be called as IONOLAB-BIAS and they are currently used in IONOLAB-TEC available at http://www.ionolab.org online. The IONOLAB-BIAS estimates are compared with the polynomial VTEC model, the minimization of standard deviation of VTEC method, and the receiver DCB estimates from the IGS centers, both for quiet and disturbed days of the ionosphere and for stations from all ionospheric regions. It is observed that IONOLAB-BIAS provides a strong alternative to online single station DCB estimation and it is very robust for various ionospheric states and regions.

[7] In section 2, the model for the GPS observables and the computation of TEC is provided. The IONOLAB-BIAS is described in section 3. The polynomial model of *VTEC* and minimization of standard deviation of *VTEC* methods are reviewed briefly in section 4. The comparison of these three methods and also the comparison with IGS DCB estimates are provided in section 5.