Interactive comment on “ Estimating Satellite and Receiver Differential Code Bias Using Relative GPS Network

In the article the authors suggested a technique for “Estimating Satellite and Receiver Differential Code Bias”. While the problem of DCB estimation is important enough it is difficult to find what new was done in the article. The authors used well-known approach based on spherical harmonics (SH), which was suggested by S. Schaer et al. (1998). Similar approach based on SH was used for M_DCB: MATLAB code by Jin et al. (2012). Recently a lot of article have been published containing new results on DCB and DCB estimation, for example applying convolution algorithm (Q. Li et al., 2018 ), applying SH along with trigonometric series (Z. Li et al., 2015), applying spherical cap harmonic for regional modeling (Liu et al., 2010), using combination of Minimum scalloping/Least squares/ Zero TEC method (Rideout & Coster, 2006), as well as indicating problems and solution for Compass/Beidou DCB (Z. Li et al.,


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TEC is an important parameter in the study of ionospheric dynamics, structures, and variabilities. The ionosphere is a dispersive 26 medium for space geodetic techniques operating in the microwave band (Böhm, and Schuh, 2013) that allows calculation of 27 TEC using GPS dual-frequency radio transmissions. The global availability of GPS has made it a valuable tool for sensing the 28 Earth' the regional and global ionosphere estimation or the use of a reference instrument or model. Estimating DCBs for receivers and satellites from GPS observations depending 36 on two approaches, the relative and absolute methods. The relative method utilizes a GPS network, while the absolute method 37 determines DCBs from a single station (Sedeek et al., 2017). In the current study, we applied relative method to calculate 38 DCBs of satellites and GPS receivers. 39 There has also been growing interest in measuring the accuracy of these methods, and how different factors, e.g. ionospheric 40 activity, plays a role in these methods ( combination of pseudo-range observables (P-code). Weighted Least Square was used to consider variation of satellites 52 elevation angle. The code was evaluated and compared with other researchers' codes in section "Results and analysis". In the 53 "Conclusion" section we summarize the overall paper results. 54

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For a GPS satellite, the pseudorange and carrier phase observations between a receiver and a satellite can be expressed as ( Here, we consider a measurement scenario that one GPS receiver tracks dual frequency code and phase data from a total of m 77 satellites over t epochs, thereby implying r = 1, s = 1, ….. m, j = 1, 2 and i = 1, ….., t. 78 Firstly, the code read the Rinex files and extract the pseudo range and carrier phase observations which are the range distances 79 between the receivers and satellites measured using L1and L2 frequencies. The "geometry-free" linear combination of GPS 80 observations is used to derive the observable. The geometric range, clock-offsets and tropospheric delay are frequency 81 independent and can be eliminated using this combination. The "geometry-free" linear combinations for pseudo range and 82 carrier phase observations are given as (Al-Fanek 2013): 83 Φ4= ,1 ( )-,2 ( )= ,2, -,1, + 1 1 − 2 2 + Φ + Φ + 12 (4) 85 is the combination of multipath and measurement noise on ,1 ( ) and ,2 ( ) (m), and 86 12 = √( 1 ) 2 + ( 2 ) 2 is the combination of multipath and measurement noise on ,1 ( ) and ,2 ( ) (m). 87 To reduce the multipath and noise level in the pseudo range observables, the carrier phase measurements are used to compute 88 a more precise relative smoothed range. Although the carrier-phase observables are more precise than the code derived, they 89 are ambiguous due to the presence of integer phase ambiguities in the carrier phase measurements. To take advantage of the 90 low-noise carrier phase derived and unambiguous nature of the pseudo range, both measurements are combined to collect the 91 best of both observations. 92 Smoothed P4,sm observations can be expressed as follows (Jin et al. 2012): 93 where t stands for the epoch number, is the weight factor related with epoch t, and 95 4, when t is equal to 1, which means the first epoch of one observation arc, P4,sm is equal to P4. 97 98

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To determine the receiver DCB, there are two different methods. The first one is to calibrate the receiver device and obtain the 100 DCB directly. This method calculates the DCB of the receiver device ignoring that from the antenna cabling used during 101 observation (Hansen, 2002 Where: 124 β is the geocentric latitude of IPPs (Ionosphere Peirce Point), 125 s is the solar fixed longitude of IPPs, 126 N is the degree of the spherical function, 127 M is the order of spherical harmonic function; fourth order is used. 128 Pmn is regularization Legendre series and 129 Amn and Bmn are the estimated spherical harmonics coefficients. 130 By substituting eq (8), eq (10) and eq (11) into eq (9) we get: 131 Only one GPS station has more than 20,000 observations per a day. When applying equation (12)

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The first evaluation made by this paper is the evaluation of weight function. MSDCBE used a weight function depending on 178 the satellite elevation angle as mentioned before. Table 1 shows the differences and RMS between satellites and receivers 179 estimated from 1 to 31 January 2010 using multiple GPS stations of both MSDCBE (weighted) and M_DCB (unweighted). 180 all satellites DCBs differences are less than 0.128 except G1 whose RMS = 0.250. The maximum difference of MSDCBE 184 estimated receivers DCBs is 0.150 ns of receiver GOPE and the minimum is 0.045 ns of receiver SOFI (Figure 3). The 185 maximum RMS of MSDCBE estimated receivers DCBs is 0.125. On the other side, M_DCB results show that Receiver DCB 186 biases are slightly larger than those for satellites, but most of them are less than 0.4 ns except G1 whose DCB bias reaches 187 0.746 ns. The RMS of all differences is lower than 0.3 ns (Jin et al. 2012). Figure 4 shows the mean differences between 188 receiver DCB values estimated by MSDCBE and those released by CODE, IGS, and JPL combined from 1-31 Jan 2010. The 189 figure shows that the results of MSDCBE are mostly close to those of CODE than IGS and JPL. By comparing the figure 4  190 with the corresponding chart published by Jin et al. (2012), it is clearly appeared that all differences between MSDCBE 191 receivers' DCBs results and between CODE, IGS and JPL are less than those from M_DCB except station GOPE almost equal. ONSA, PTBB, SOFI and WTZA. Figure 5 shows these results which demonstrate that using nine receivers gives more accurate 204 DCBs. Also, the satellites DCBs differences (figure 6) almost improved but not like receivers DCBs, because satellites DCBs 205 are small values compared with those of receivers. 206 (1-5) Jan 2010 212

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In this section the performance of multi station network against single station DCB estimation will be evaluated.   The current study proposes a new MATLAB code called MSDCBE able to calculate DCBs of GPS satellites and receivers. 230 This code was compared with two other codes and evaluated using IAAC data and from all the above, we can conclude that: 231 1. The estimated DCBs results affected by using weight function according to satellite elevation angle observations. In 232 addition, results show a good agreement with IGS, CODE and JPL results than using multi station estimation DCB 233 without weight function. 234 2. When using multi station DCB estimation, number of input stations influences in DCB results. However, it is 235 recommended to enlarge the size of used network, but it needs high computer requirements and much more analysis 236 time (only one station have more than 20,000 observation per a day). 237 3. The most effective factor in DCBs estimation is using multi station network instead of single station that appeared 238 from results which improved from 1.1866 ns and 0.7982 ns maximum DCB mean differences for M_DCB and 239 ZDDCBE single station analysis to 0.1477 ns for MSDCBE. So, using multi station network DCB estimation-if 240 available-is strongly recommended. 241  G1  G2  G3  G4  G5  G6  G7  G8  G9  G10  G11  G12  G13  G14  G15  G16  G17  G18  G19  G20  G21  G22  G23  G24  G25  G26  G27  G28  G29  G30  G31 G32 Differences