Impact of GLONASS pseudorange inter-channel biases on satellite clock corrections

Transcription

1 GPS Solut (2014) 18: DOI / y REVIEW ARTICLE Impact of GLONASS peudorange inter-channel biae on atellite clock correction Weiwei Song Wenting Yi Yidong Lou Chuang Shi Yibin Yao Yanyan Liu Yong Mao Yu Xiang Received: 27 November 2013 / Accepted: 22 February 2014 / Publihed online: 21 March 2014 Ó Springer-Verlag Berlin Heidelberg 2014 Abtract GLONASS carrier phae and peudorange obervation uffer from inter-channel biae (ICB) becaue of frequency diviion multiple acce (FDMA). Therefore, we analyze the effect of GLONASS peudorange inter-channel biae on the GLONASS clock correction. Different Analyi Center (AC) eliminate the impact of GLONASS peudorange ICB in different way. Thi lead to ignificant difference in the atellite and ACpecific offet in the GLONASS clock correction. Satellite and AC-pecific offet difference are trongly correlated with frequency. Furthermore, the GLONASS peudorange ICB alo lead to day-boundary jump in the GLONASS clock correction for the ame analyi center between adjacent day. Thi in turn will influence the accuracy of the combined GPS/GLONASS precie point poitioning (PPP) at the day-boundary. To olve thee problem, a GNSS clock correction combination method baed on the Kalman filter i propoed. During the combination, the AC-pecific offet and the atellite and ACpecific offet can be etimated. The tet reult how the feaibility and effectivene of the propoed clock W. Song W. Yi (&) Y. Lou (&) C. Shi Y. Liu Y. Xiang Reearch Center of GNSS, Wuhan Univerity, 129 Luoyu Road, Wuhan , China WtYi@whu.edu.cn Y. Lou ydlou@whu.edu.cn Y. Yao School of Geodey and Geomatic, Wuhan Univerity, Wuhan , China Y. Mao PetroChina Wet Eat Ga Pipeline Company, Shanghai, China combination method. The combined clock correction can effectively weaken the influence of clock day-boundary jump on combined GPS/GLONASS kinematic PPP. Furthermore, thee combined clock correction can improve the accuracy of the combined GPS/GLONASS tatic PPP ingle-day olution when compared to the accuracy of each analyi center alone. Keyword GLONASS Clock correction Dayboundary jump Inter-channel bia Clock combination Introduction The availability of precie atellite orbit and clock product ha enabled the development of precie point poitioning (PPP). Thi data proceing technique can achieve poitioning accuracy for tatic and mobile receiver at the millimeter to decimeter level and ha been widely applied in precie orbit determination, geodey, aerial photogrammetry, ea level meaurement, GPS meteorology and precie timing (Zumberge et al. 1997; Binath and Gao 2008; Kouba and Héroux 2001; Kouba 2003). Furthermore, with the revival of GLONASS and the increaing number of combined GPS/GLONASS receiver along with the availability of combined GPS/GLONASS orbit and atellite clock correction, PPP can now be extended to include GLONASS meaurement. The firt tet on combined GPS/GLONASS PPP were preented by Cai and Gao (2007). However, they could not make a ignificant improvement in PPP ince only two or three GLONASS atellite could be ued. Heelbarth and Wanninger (2008) teted GPS-only and combined GPS/GLONASS PPP uing kinematic obervation. Both tudie demontrated that adding GLONASS meaurement to GPS can ignificantly

2 324 GPS Solut (2014) 18: Table 1 Precie clock product for GPS/GLONASS PPP AC Interval Proce trategy for GLONASS peudorange inter-channel biae IAC 30 Etimated with clock etimation ESOC 5 min* Etimated with clock etimation GFZ 5 min** Etimated with clock etimation Available time Since Jan 2005 or earlier Since Oct 19, 2008 Since Apr 11, 2010 NRCan 30 Not etimated Since Jun 3, 2012 The ymbol * repreent the ESOC provided the precie clock correction in 30- interval ince January 24, 2010, while ** repreent the GFZ provided the precie clock correction in 30- interval ince June 2, 2013, but the lat epoch i till 23:55:00 reduce the time for PPP convergence. Píriz et al. (2009) ued 1-h tatic data from the International GNSS Service (IGS) to ae PPP. Thi reearch howed that GLON- ASS-only PPP olution in 1 h i not very reliable in ome cae, and a combined GPS/GLONASS PPP olution i more accurate and robut than the GPS-only olution. The IGS i the main ource of pot-miion precie atellite orbit and clock product. To provide more reliable and table clock correction olution, IGS combine clock correction from everal participating Analyi Center (AC) (Kouba 2003). It offer precie GPS atellite clock correction, but doe not provide GLONASS clock correction. Until now, GLONASS atellite clock correction were available only from the Information-Analytical Center (IAC), the European Space Operation Center (ESOC), the German Reearch Centre for Geocience (GFZ) and Natural Reource Canada (NRCan), the product information i lited in Table 1. At preent, GLONASS ue frequency diviion multiplexing (FDMA-frequency diviion multiple acce) to ditinguih ignal from individual atellite and only GLONASS FDMA ignal will be able to provide continuou dual-frequency coverage for the next decade. However, with the FDMA approach, GLONASS carrier phae and peudorange obervation uffer from inter-channel biae. The carrier phae inter-channel biae between receiver from different manufacturer can reach up to 5 cm for adjacent frequencie and thu up to 73 cm for the complete L1 or L2 frequency band (Wanninger 2012). Fortunately, carrier phae inter-channel biae eem table over time and can be modeled a linear frequency function. But peudorange inter-channel biae eem to be unique to individual receiver and antenna. Moreover, they cannot be modeled with a imple modeling function (Reuner and Wanninger 2011, Chuang et al. 2013). Neverthele, time reference ynchronization i typically achieved by uing etimated receiver and atellite clock correction derived from the peudorange obervation, given the exitence of ambiguitie in carrier phae obervation (Bock et al. 2009). GLONASS peudorange obervation are affected by inter-channel biae (ICB), o different peudorange ICB proceing trategie may lead the GLONASS clock reference to vary between different analyi center. We analyze the effect of GLONASS peudorange ICB on GLONASS clock reference and propoe a combined GNSS clock method counterpoiing the atellite and AC-pecific offet and day-boundary jump impact on GLONASS clock correction. Section 2 analyze the impact of GLONASS peudorange ICB on the clock reference of GLONASS; Sect. 3 dicue the difference in the atellite and ACpecific offet of the GLONASS clock between different analyi center and the relationhip of thee difference with frequency; Sect. 4 analyze day-boundary jump of GLONASS clock correction for each analyi center and their impact on the combined GPS/GLONASS PPP at the day-boundary; Sect. 5 preent ome preliminary tet reult and dicue the feaibility and effectivene of the propoed clock combination method. GLONASS peudorange ICB impact on clock reference Clock reference are determined by peudorange obervation, and highly precie carrier phae obervation determine only the accurate temporal change in clock correction (Ge et al. 2012). Therefore, a linearized obervation equation for the ionophere-free peudorange combination can be expreed a (omewhat implified and without an error term): P i c ¼ qi þ cdt r cdt i þ m i dt þ ICB i ð1þ where i i the atellite PRN, P c i the ionophere-free peudorange obervation, q i the range from atellite to receiver, c i the peed of light in vacuum, dt r and dt i are receiver and atellite clock biae, m i the tropopheric mapping function, dt i the zenith tropophere delay, ICB i the inter-channel peudorange bia. In clock etimation, the tation coordinate, atellite orbit and tropophere are aumed to be known. So: VPc i ¼ cdt r cdt i þ ICB i þ l i Pc ð2þ i where V Pc i and l Pc are the pot-fit and prefit reidual of the peudorange obervation. Since there are no peudorange ICB for GPS, Eq. (2) can be written a: VPc i ¼ cdt r cdt i þ l i Pc ð3þ Equation (3) how that the receiver and atellite clock biae are linear dependent and cannot be eparated

3 GPS Solut (2014) 18: from each other. However, there i no real clock reference. To obtain the atellite clock correction, one or ome tation equipped with atomic clock are elected a the reference tation and their receiver clock biae are fixed a the clock reference. Then the atellite clock biae are calculated, while the other receiver clock biae are related to the clock reference (Zhang et al. 2010). Unfortunately, the GLONASS peudorange obervation are affected by peudorange ICB and the effect are difficult to completely eliminate (Reuner and Wanninger 2011, Chuang et al. 2013, Kozlov et al. 2000). Auming that the uncalibrated ICB are dicb i, then (2) can be rewritten a: VPc i ¼ cdt r cdt i þ dicb i þ l i Pc ð4þ Not only are the atellite and receiver clock biae linear dependent a hown in (3), but alo dicb i ha a linear dependency with the atellite and receiver clock biae. Moreover, the peudorange ICB vary for different atellite. The hared portion of all atellite dicb i will be aborbed into the receiver clock biae, while the remaining portion of all atellite dicb i will be aborbed into the atellite clock biae and affect the clock reference. Equation (4) can be rewritten a: VPc i ¼ cd ~t r cd~t i þ l i Pc ð5þ where d~t r and d~t i are receiver and atellite clock biae which contain the effect of the peudorange ICB reidual. The GLONASS clock reference contain the reidual peudorange ICB that cannot be eliminated, o the clock correction for each analyi center can be expreed a follow rc a;b ¼rc þro a;b þro a;b ð7þ where r repreent the ingle difference operator between analyi center a and b. Aume that rc = 0, ince ro a,b i common to all atellite, then: ro a;b ¼ 1 n ro a;b ¼rc a;b 1 n X n rc a;b i¼1 X n rc a;b i¼1 ð8þ where n i the number of atellite. Figure 1 how a time erie of GPS and GLONASS ro a,b between the NRCan, ESOC and GFZ analyi center and the IAC analyi center on day of year (DOY) 153 in In thi figure, the GPS ro a,b are all cloe to zero, but the GLONASS ro a,b can reach everal nanoecond and vary for different atellite, which indicate the atellite and AC-pecific offet of GPS clock correction are almot the ame for all analyi center while that of GLONASS vary for each analyi center. Thi i becaue different analyi center poibly elect different reference tation. However, ince GPS i not affected by peudorange ICB, only different reference tation lead the ACpecific offet to vary. But for GLONASS, the peudorange ICB can reach everal meter which differ with reference tation (Reuner and Wanninger 2011; Chuang c a ¼ c þ o a þ o a ð6þ where c a i clock correction for atellite, c i the clock correction for atellite etimated by carrier phae obervation, o a i the AC-pecific clock offet (common for all atellite), o a i the atellite and AC-pecific clock offet (Mervart and Weber 2011). Satellite and AC-pecific offet analyi The effect of peudorange ICB on the GLONASS clock reference may be different for different analyi center ince they elect different reference tation a well a different peudorange ICB proceing trategie. The difference in (6) between the analyi center how that: Fig. 1 Time erie of ro a,b between NRCan, ESOC and GFZ analyi center and IAC analyi center on day of year (DOY) 153 in The left panel how the time erie for GPS atellite G01, G02 and G03, and the right panel diplay the time erie for GLONASS atellite R01, R02 and R03

4 326 GPS Solut (2014) 18: Fig. 2 GLONASS ro a,b over three conecutive day for GPS week 1,722 and 1,743 for different analyi center. In order to how the relationhip between ro a,b and frequency more clearly, the fitted line and the correlation coefficient are alo hown in thi figure et al. 2013). Meanwhile, different analyi center proce the peudorange ICB in different way, o the impact of the reidual peudorange ICB on clock correction reference vary, ubequently the atellite and AC-pecific offet vary for each analyi center. Aume that o a i contant within a 24-h period. Therefore, the average ro a,b for each atellite can be computed. Figure 2 how the relationhip of GLONASS ro a,b for different analyi center and frequencie over three conecutive day for GPS week 1,722 and 1,743. In Fig. 2, the GLONASSro a,b for the two atellite haring the ame frequency are quite cloe. Furthermore, ro a,b ha a ignificant linear correlation with frequency, the average correlation coefficient between ro a,b and the fitting traight line for NRCan, ESOC and GFZ analyi center reach 0.790, and 0.864, repectively. The frequencydependent error in peudorange obervation tem from ionopheric delay and ICB. Since clock etimation uually ue ionophere-free combination obervation to eliminate the ionopheric delay effect (Ge et al. 2012; Bock et al. 2009; Kouba 2003), o ro a,b i trongly correlated with frequency, confirming that the atellite and AC-pecific offet i affected by peudorange ICB. However, the degree of correlation between ro a,b and the frequency differ for different analyi center. Thi i poibly due to the different peudorange ICB proceing trategie. The Fig. 3 Time erie for clock difference between adjacent epoch of GLONASS R01, R02 and R03 for each analyi center on DOY 154 and 155 in The clock correction for the GFZ analyi center were extrapolated to 23:59:30 ince the lat epoch of clock correction for the GFZ analyi center i 23:55:00 ESOC, GFZ and IAC analyi center add the additional peudobia parameter during clock etimation but NRCan analyi center doe not (ftp://igw.unavco.org/pub/center/ analyi/gfz.acn, ea.acn, emr.acn, iac.acn).

5 GPS Solut (2014) 18: Day-boundary jump analyi Figure 3 how the time erie of clock correction difference between adjacent epoch of GLONASS R01, R02 and R03 for each analyi center on DOY 154, 155 in The clock correction difference in the ame day were le than 0.3 n; thu, the clock correction are relatively continuou during the ame day. However, the clock correction difference jump obviouly at the day-boundary for NRCan, ESOC and GFZ analyi center, and the jump of the ESOC analyi center reach 12 n. The clock drift of GLONASS R01, R02 and R03 i in only everal picoecond per econd (Hauchild et al. 2013); thu, the changing of the clock correction cannot reach up to 12 n in a 30- time pan. The hown day-boundary jump are caued by the changing of the clock reference. Since the analyi center elect different reference tation on different day, GLONASS clock reference vary; thu, day-boundary jump occur in the GLONASS clock correction. In order to compute day-boundary jump for each atellite, the clock correction were extrapolated to the firt epoch of the next day. Firt, the fitted clock drift were calculated uing the clock correction of the lat 10 min in the clock olution file. Then, the fitted clock correction can be computed uing fitted clock drift and the lat epoch clock correction in the clock olution file, ~c a ðt 2Þ¼c a ðt 1Þþv c Dt ð9þ where ~c a ðt 2Þ i the fitted clock correction of the firt epoch of the next day, c a (t 1 ) i the clock correction of the lat epoch provided by clock file, v c i the fitted clock drift and Dt i the time interval. Since the fitted clock correction are known, day-boundary jump were obtained a: DBJ a ¼ c a ðt 2Þ ~c a ðt 2Þ ð10þ where DBJ a repreent the clock day-boundary jump and c a (t 2 ) repreent the real firt epoch clock correction provided by the clock olution file. Figure 4 how the day-boundary jump for all the GPS and GLONASS atellite between DOY 154 and 155 in 2013 for each analyi center, the mean value and tandard deviation (STD). The maximum and minimum for each analyi center were computed and lited in Table 2. Thu, the GPS and GLONASS clock correction exhibit both day-boundary jump, but the day-boundary jump in GPS are almot the ame for each atellite. Furthermore, the GPS STD of all the analyi center are le than 0.3 n. The difference between the maximum and the minimum value are all le than 1.3 n. Unfortunately, the day-boundary jump in GLONASS vary greatly. The GLONASS STD of NRCan, ESOC, GFZ and IAC are ignificantly larger than that of GPS, reaching 0.619, 0.702, and n, repectively. The difference between Fig. 4 The clock day-boundary jump for all the GPS and GLON- ASS atellite for each analyi center between DOY 154 and 155 in 2013 the maximum and minimum value are alo lager than that of GPS, reaching 2.9, 2.9, 2.1 and 1.6 n, repectively. A the lat epoch of clock correction for ESOC, NRCan and IAC wa 23:59:30 but that for GFZ wa 23:55:00, when calculating the clock day-boundary jump, GFZ needed 5 min extrapolation, while the other three analyi center only needed 30- extrapolation. However, the longer extrapolation time decreae day-boundary jump calculation accuracy. Figure 5 how the day-boundary jump STD of GPS and GLONASS for each analyi center from DOY 155 in 2012 to DOY 181 in Since a few of the GLONASS STD are much larger than other, the Y-axi labeling of the middle panel i o large a to obcure the ditribution of the GLONASS STD. Therefore, the detail are drawn in the bottom panel. Except for ome individual STD, the GPS STD are le than 0.4 n. The average STD of NRCan, ESOC and IAC analyi center are 0.21, 0.23 and 0.22 n, repectively. Since the extrapolation time i relatively longer for GFZ analyi center when calculating the day-boundary jump, the average STD i lightly larger than that of the other three analyi center, reaching 0.31 n. For GLONASS, the day-boundary jump STD for each analyi center are much larger a compared to that of GPS becaue of the impact of peudorange ICB on the clock reference. Some STD can even reach up to dozen of nanoecond. The average STD for the NRCan, GFZ and IAC analyi center reached 0.70, 0.49 and 0.31 n, repectively, while the average STD of the ESOC

6 328 GPS Solut (2014) 18: Table 2 Mean value, tandard deviation, maximum and minimum value for dayboundary jump for each analyi center AC NRCan (n) ESOC (n) GFZ (n) IAC (n) GPS GLONASS GPS GLONASS GPS GLONASS GPS GLONASS Average STD Maximum Minimum Fig. 5 Day-boundary jump STD of GPS and GLONASS for each analyi center from DOY 155 in 2012 to DOY 181 in The top panel how the day-boundary jump STD of GPS for each analyi center, while the middle and the bottom panel how the STD of GLONASS. The bottom panel i the partially enlarged detail of the GLONASS STD ince the Y-axi labeling of the middle panel i too large to how ditribution of the GLONASS STD clearly Analyi Center reached up to 4.87 n. The day-boundary jump of the ESOC analyi center have ignificantly improved ince MJD (18 Dec, 2012), the average STD wa reduced from 8.28 to 1.40 n. Currently, each analyi center only provide GPS/ GLONASS clock correction with a 30- interval (Table 1), but kinematic PPP application require atellite clock correction at a ampling rate equal to the obervation rate, uch a 1 HZ. The clock correction between the interval mut be obtained by interpolation uing the clock correction before and after the obervation epoch time (Heelbarth and Wanninger 2008). But day-boundary jump will lead to interpolation error at the dayboundary. Moreover, only the hared portion of the interpolation error for all atellite can be aborbed by receiver clock bia, while the remaining portion of the error will affect PPP accuracy. Figure 6 how the 3D deviation time erie of GPS-only and combined GPS/ Fig. 6 3D deviation time erie of GPS-only and combined GPS/ GLONASS dynamic PPP olution compared to the IGS weekly olution at tation ZIM2, at GPS time from 20:00:00 to 23:59:59 on DOY 154 in In order to how the variation more clearly, only the time erie for the lat 10 min i hown GLONASS dynamic PPP olution compared to the IGS weekly olution at tation ZIM2, at GPS time from 20:00:00 to 23:59:59 on DOY 154 in The data ample wa 1 Hz and the weight ratio of GLONASS and GPS obervation in the leat-quare adjutment wa et to 1:2. The accuracie of the combined GPS/GLONASS PPP were uperior to that of GPS-only PPP a illutrated in Fig. 6. For the NRCan analyi center, there were about 10 cm ytematic error after PPP convergence, while the ytematic error in the combined GPS/GLONASS PPP were ignificantly reduced. But the accuracie of the combined GPS/GLONASS PPP decreaed ignificantly from the econd of day (SOD) 86,370, while thi phenomenon did not appear in the GPS-only PPP. Thi i becaue the difference in the GPS day-boundary jump for each atellite were mall. A a conequence, mot of the interpolation error in atellite clock correction were aborbed into the receiver clock bia and have little effect on PPP. But for GLONASS, the day-boundary jump vary hapely for each atellite o that the interpolation error cannot be aborbed by the receiver clock bia and will

7 GPS Solut (2014) 18: affect the combined GPS/GLONASS PPP at the dayboundary. Since the lat epoch of GFZ clock correction wa 23:55:00 (SOD ), the time interval of clock interpolation wa too long, and therefore, the clock interpolation accuracy reduced, o the combined GPS/ GLONASS PPP accuracy began to decline from SOD The GPS-only PPP accuracy wa alo reduced. Furthermore, a can be een in Table 2, the dayboundary jump STD for ESOC clock correction wa maximal and had the greatet impact on the PPP accuracy. The day-boundary jump STD for the IAC clock correction wa minimal and had the minimal impact on the PPP accuracy, indicating that the impact magnitude of dayboundary jump on combined GPS/GLONASS PPP i related to the day-boundary jump STD. GNSS clock olution combination The combined GPS/GLONASS PPP can improve the accuracy, reliability and the acceleration of PPP convergence (Cai and Gao 2007, Heelbarth and Wanninger 2008). However, the GLONASS clock day-boundary jump differ greatly between atellite for each analyi center, affecting the accuracy of the combined GPS/ GLONASS PPP at the day-boundary. Currently, the IGS only provide GPS preciion clock olution but no GLONASS precie clock olution, o it i neceary to provide the combined GPS/GLONASS preciion clock olution. The GLONASS orbit combination can ue the ame method a that of GPS and the orbit accuracie of NRCan, ESOC, GFZ and IAC are cloe to each other, up to centimeter ( A a conequence, orbit combination i not dicued here. Before combining clock correction, the clock reference for each atellite mut be eliminated (Kouba and Springer 2001). Since the AC-pecific offet and the atellite and AC-pecific offet of the GLONASS clock correction both differ harply between analyi center, they are etimated during clock combination. From (6), it can be obtained: c i;y ¼ c y þ o i;y þ o i;y ð11þ where y repreent the GPS or GLONASS ytem, c i,y repreent the clock correction of analyi center i, o i,y and o i,y repreent the AC-pecific offet and atellite and AC-pecific offet of analyi center i and c y repreent the combined clock correction. When etimating the parameter, c y i conidered a a random walk proce, o i,y i white noie and o i,y i a contant within 24 h. Equation (11) how that c y, o i,y and o i,y are linear dependent, o the o i,y for each analyi center and c y were contrained a: Fig. 7 RMS of the combination reidual for each atellite on DOY 154 in 2013 X m ¼1 X m ¼1 o i;y ¼ 0 c y ¼ 0 ð12þ where m repreent the number of atellite GPS or GLONASS ytem. In order to improve the accuracy of the combined clock correction at the initialization time, an invere filter wa ued. Figure 7 how the RMS of the combination reidual for each atellite on DOY 154 in The clock correction of each analyi center are conidered to be equal weight during the clock combination. All the RMS of the combination reidual in Fig. 7 are le than 0.15 n, while mot of them are le than 0.05 n. So the clock combination algorithm preented here i feaible. However, the RMS of GPS combination reidual for IAC in thi figure are ignificantly larger than that of other analyi center, indicating that the IAC GPS clock correction accuracy i the leat atifactory among the analyi center on DOY 154 in Figure 8 diplay the daily etimation of GLONASS atellite and AC-pecific offet for each analyi center on DOY in To illutrate the tability of thee etimation in different day, the STD of the etimation were computed and hown in Fig. 9. A thee figure reveal, the GLONASS atellite and AC-pecific offet of each analyi center are relatively table. The average STD of GFZ and IAC are only 0.15 n. The GPS atellite and AC-pecific offet of each analyi center are maller than that of GLONASS, motly le than 0.1 n. Therefore, the etimation are not preented here.

8 330 GPS Solut (2014) 18: Fig. 10 Time erie of the reproceed olution with the data in Fig. 6 Fig. 8 Satellite and AC-pecific offet valuation of each analyi center on DOY in 2013 Fig. 9 STD of the atellite and AC-pecific offet valuation in different day of each analyi center and the average STD are hown on the upper right corner A the combined clock correction obtained by (11) and (12) lack clock reference, they mut be provided. The GLONASS atellite and AC-pecific offet of GFZ and IAC are the mot tabile between day. But the IAC GPS clock correction accuracy i the leat atifactory among the analyi center, o the GFZ clock reference were elected a the combination clock reference. To further reduce the impact of the day-boundary jump, the weighted average of the atellite and AC-pecific offet over the adjacent two day wa ued a the atellite and AC-pecific offet for the econd day. In order to tet whether the combination clock correction can weaken the effect of the day-boundary jump on the combined GPS/GLONASS PPP, the data in Fig. 6 were reproceed uing the combination clock correction. Figure 10 preent the reproceed time erie olution; the combined GPS/GLONASS PPP accuracy did not become ignificantly wore at the day-boundary when uing the combination clock correction. Thi indicate that the impact of day-boundary jump can be ignificantly weakened. The RMS of N, E, and U component reach 1.7, 1.8 and 3.5 cm, repectively, uing the combination clock correction. Figure 11 how the RMS tatitic of the combined GPS/GLONASS tatic PPP ingle-day olution uing different clock correction of 120 IGS tation on DOY 154 in The bet reult are from the GFZ, with a RMS of 0.4, 0.6 and 1.3 cm in the Eat, North and Up component, repectively. The IAC reult are the leat atifactory, with the RMS for Eat, North and Up component at 1.5, 1.0 and 2.0 cm, repectively. Thi i becaue the IAC GPS clock correction accuracy i the leat atifactory among the analyi center. Fortunately, the accuracy i further improved after clock combination, with RMS in the Eat, North and Up component at 0.3, 0.6 and 1.3 cm, correpondingly. A compared to IAC, the accuracy of the combined GPS/GLONASS PPP uing combined clock correction i improved by 80, 40 and 35 % in the Eat, North and Up component, in that order. Concluion We analyzed the effect of GLONASS peudorange interchannel biae on the GLONASS clock correction reference. There were three ignificant finding. Firt, different analyi center eliminate the impact of GLONASS peudorange ICB in different way which lead to ignificant difference in atellite and AC-pecific offet for GLONASS clock correction. Second, the atellite and AC-pecific offet difference are trongly correlated with frequency number. Third, the GLONASS peudorange ICB alo lead to day-boundary jump in GLONASS

9 GPS Solut (2014) 18: Fig. 11 RMS tatitic for the combined GPS/GLONASS tatic PPP ingle-day olution of 120 IGS tation on DOY 154 in The panel from the top to the bottom repreent the clock correction reult of NRCan, ESOC, GFZ, IAC and combined clock reult, repectively. The weight ratio of GLONASS and GPS obervation in the leat-quare adjutment i et a 1:2, and the real coordinate were provided by the IGS weekly olution clock correction for the ame analyi center between adjacent day. Thi in turn will influence the accuracy of the combined GPS/GLONASS PPP at the day-boundary. Given thee three factor, it i recommended that analyi center ue the ame preproceing trategy for GLON- ASS peudorange ICB and provide thee correction to uer. Additionally, we propoe a GNSS clock correction combination method and give ome preliminary tet reult. Thee reult how that combined clock correction can effectively weaken the influence of clock day-boundary jump on the combined GPS/GLONASS dynamic PPP. Furthermore, the combined clock correction can improve the accuracy of the combined GPS/GLONASS tatic PPP ingle-day olution a compared to accuracy of each analyi center alone. Thi illutrate the feaibility and effectivene of the propoed clock combination method. However, there are till ome improvement to be made in the clock combination method. Firt, the propoed combination clock reference imply elect the clock reference of GFZ and hould be unified to the IGS time cale. Second, the impact of the GLONASS peudorange ICB on the clock reference mut be eliminated. Third, we did not detect the clock correction outlier and thoe mut be detected. Fourth, we aumed equal weight for each analyi center, but it i preferable to et the weight ratio according the clock correction accuracy for each analyi center. Acknowledgment We thank Simon Banville, at NRCan, and Maorong Ge, at GFZ, for their valuable uggetion on thi tudy. The IGS i acknowledged for providing high-quality combined GPS/ GLONASS precie orbit and clock correction a well a tracking data. Thi tudy wa upported by the National Natural Science Fund (Grant No ), the National High Technology Reearch and Development Program of China (863 Program) (Grant No. 2012AA12A202) and alo by China Potdoctoral Science Foundation (Grant No. 2012M511671). Reference Binath S, Gao Y (2008) Current tate of precie point poitioning and future propect and limitation. In: Sideri MG (ed) Oberving our changing Earth. Springer, New York, pp Bock H, Dach R, Jäggi A, Beutler G (2009) High-rate GPS clock correction from CODE: upport of 1 Hz application. J Geodey 83: Cai C, Gao Y (2007) Performance analyi of precie point poitioning baed on combined GPS and GLONASS. In: Proceeding of ION GNSS-2007, Intitution of Navigation, Fort Worth, Texa, September, pp

10 332 GPS Solut (2014) 18: Chuang S, Wenting Y, Weiwei S, Yidong L, Yibin Y, Rui Z (2013) GLONASS peudorange inter-channel biae and their effect on combined GPS/GLONASS precie point poitioning. GPS Solution, GPS Solution 17(4): Ge M, Chen J, Douša J, Gendt G, Wickert J (2012) A computationally efficient approach for etimating high-rate atellite clock correction in realtime. GPS Solution 16(1):9 17 Hauchild A, Montenbruck O, Steigenberger P (2013) Short-term analyi of GNSS clock. GPS Solution 17(3): Heelbarth A, Wanninger L (2008) Short-term tability of GNSS atellite clock and it effect on precie point poitioning. In: Proceeding of ION GNSS-2008, Intitution of Navigation, San Diego, California, September, pp Kouba J (2003) A guide to uing International GPS Service (IGS) product. IGS report, International GPS Service Kouba J, Héroux P (2001) Precie point poitioning uing IGS orbit and clock product. GPS Solut 5(2):12 28 Kouba J, Springer T (2001) New IGS tation and atellite clock combination. GPS Solut 4(4):31 36 Kozlov D, Tkachenko M, Tochilin A (2000) Statitical characterization of hardware biae in GPS? GLONASS receiver. In: Proceeding of ION GPS-2000, U.S. Intitution of Navigation, Salt Lake City, Utah, September, pp Mervart L, Weber G (2011) Real-time combination of GNSS orbit and clock correction tream uing a Kalman filter approach. In: Proceeding of ION GNSS-2011, Intitution of Navigation, Portland OR, September, pp Píriz R, Calle D, Mozo A, Navarro P, Rodríguez D, Tobía G (2009). Orbit and clock for GLONASS precie-point-poitioning. In: Proceeding of ION GNSS-2009, Intitution of Navigation, Savannah, Georgia, September, pp Reuner N, Wanninger L (2011) GLONASS inter-frequency biae and their effect on RTK and PPP carrier-phae ambiguity reolution. In: Proceeding of ION GNSS-2011, Intitution of Navigation, Portland OR, September, pp Wanninger L (2012) Carrier phae inter-frequency biae of GLON- ASS receiver. J Geodey 86(2): Zhang X, Li X, Guo F, Li P, Wang L (2010) Server-baed real-time precie point poitioning and it application. Chin J Geophy Chin Edit 53(6): Zumberge JF, Heflin MB, Jefferon DC, Watkin MM, Webb FH (1997) Precie point poitioning for the efficient and robut analyi of GPS data from large network. J Geophy Re 102(B3): Wenting Yi i currently a PhD tudent at the Wuhan Univerity. He ha obtained hi Bachelor degree from Wuhan Univerity, P.R.C., in Hi current reearch focue mainly involve GNSS precie poitioning technology. Yidong Lou i currently an Aociate Profeor at GNSS Reearch Center, Wuhan Univerity. He obtained hi PhD in Geodey and Surveying Engineering from the Wuhan Univerity in Hi current reearch interet i in the realtime precie GNSS Orbit determination and real-time GNSS precie point poitioning. He i one of the member who have developed the PANDA oftware which ha been widely ued in china. Chuang Shi i the head for GNSS Reearch Center of Wuhan Univerity. He graduated from Wuhan Univerity and obtained hi PhD degree in Hi reearch interet include network adjutment, precie orbit determination of GNSS atellite and LEO and real-time precie point poitioning (PPP). Weiwei Song i currently a pot-doctorate fellow at the Wuhan Univerity. He ha obtained hi PhD degree from Wuhan Univerity, P.R.C., in Hi current reearch mainly focue on real-time GNSS precie poitioning technology. Yibin Yao i currently a profeor at the Wuhan Univerity. He obtained hi B.Sc., Mater and Ph.D. degree with ditinction in Geodey and Surveying Engineering at the School of Geodey and Geomatic in Wuhan Univerity in 1997, 2000 and Hi main reearch interet include GPS/ MET and high-preciion GPS data proceing.

11 GPS Solut (2014) 18: Yanyan Liu i currently a PhD tudent at the Wuhan Univerity. He ha obtained hi Bachelor degree from Wuhan Univerity, P.R.C., in Hi current reearch focue mainly involve GNSS precie poitioning technology. Yu Xiang i currently working at Wuhan Univerity. He ha erved a a enior oftware engineer for 6 year in Geomatic Information Center of Hubei Province. Hi reearch focue mainly on the practical application of GNSS and GIS. Yong Mao i a manager in PetroChina Wet Eat Ga Pipeline Company. He ha obtained hi Bachelor degree from Southwet Jiaotong Univerity, P.R.C., in Hi current reearch focue mainly involve the practical application of GNSS.