Joint Estimation of Vertical Total Electron Content (VTEC) and Satellite Differential Code Biases (SDCBs) Using Low-cost Receivers

Transcription

1 Joint Etimation of Vetical Total Electon Content (VTEC) and Satellite Diffeential Code Biae (SDCB) Uing Low-cot Receive Baocheng Zhang 1*, Pete J.G. Teunien 2, 3*, Yunbin Yuan 1, Hongxing Zhang 1, Min Li 1 b.zhang@whigg.ac.cn p.teunien@cutin.edu.au Tel: Fax: State Key Laboatoy of Geodey and Eath Dynamic, Intitute of Geodey and Geophyic, Chinee Academy of Science, Wuhan, China 2. Global Navigation Satellite Sytem (GNSS) Reeach Cente, Cutin Univeity, Peth, Autalia 3. Geocience and Remote Sening, Delft Univeity of Technology, Delft, The Netheland Abtact Vetical Total Electon Content (VTEC) paamete etimated uing Global Navigation Satellite Sytem (GNSS) data ae of geat inteet fo ionophee ening. Satellite Diffeential Code Biae (SDCB) account fo one ouce of eo which, if left uncoected, can deteioate pefomance of poitioning, timing and othe application. The cutomay appoach to etimate VTEC along with SDCB fom dual-fequency GNSS data, heeinafte efeed to a DF appoach, conit of two equential tep. The fit tep eek to etieve ionopheic obevable though the Caie-to-Code Leveling (CCL) technique. Thi obevable, elated to the Slant Total Electon Content (STEC) along the atellite-eceive line-of-ight, i biaed alo by the SDCB and the Receive Diffeential Code Biae (RDCB). By mean of thin-laye ionopheic model, in the econd tep one i able to iolate the VTEC, the SDCB and the RDCB fom the ionopheic obevable. In thi wok, we peent a 1 / 30

2 ingle-fequency (SF) appoach, enabling the joint etimation of VTEC and SDCB uing low-cot eceive; thi appoach i alo baed on two tep and it diffe fom the DF appoach only in the fit tep, whee we tun to the Pecie Point Poitioning (PPP) technique to etieve fom the ingle-fequency GNSS data the ionopheic obevable, intepeted a the combination of the STEC, the SDCB and the biaed eceive clock at the pivot epoch. Ou numeical analye claify how SF appoach pefom when being applied to GPS L1 data collected by a ingle eceive unde both calm and ditubed ionopheic condition. The daily time eie of zenith VTEC etimate ha an accuacy anging fom a few tenth of a TEC unit (TECU) to appoximately 2 TECU. Fo 73 to 96 pecent of GPS atellite in view, the daily etimate of SDCB do not deviate, in abolute value, moe than 1 nanoecond fom thei gound-tuth value publihed by the Cente fo Obit Detemination in Euope (CODE). Keywod Global Navigation Satellite Sytem (GNSS); Vetical Total Electon Content (VTEC); Satellite Diffeential Code Biae (SDCB); Caie-to-Code Leveling (CCL); Pecie Point Poitioning (PPP); Thin-laye ionopheic model 1. Intoduction Global Navigation Satellite Sytem (GNSS) data ae a valuable ouce of infomation fo ening the Eath ionophee (Henández-Pajae et al. 1999; Komjathy et al. 2005; Li et al. 2015; Liu and Gao 2004; Mannucci et al. 1993). Although the ionopheic paamete that one can etimate fom GNSS data ae vaiou (Dyud et al. 2008; Lognonné et al. 2006; Yao et al. 2013), the Vetical Total Electon Content (VTEC) i geneally the mot widely ued (Bunini and Azpilicueta 2010; Bunini and Azpilicueta 2009); it empiical impotance lie in contibuting ueful undetanding to the phyic behind diffeent pace weathe phenomena (Gulyaeva et al. 2014; Komjathy et al. 2012), in poviding valuable inight into the poible caue of natual and man-made hazadou event (Atu et al. 2005; Dautemann et al. 2007; 2 / 30

3 Pak et al. 2011), and in deliveing coection to the ionopheic effect on ignal tanmitted by the othe pace geodetic technique than by the GNSS (Dettmeing et al. 2014; Sadon et al. 1994b). On the othe hand, the Satellite Diffeential Code Biae (SDCB), defined a the deviation of the atellite code intumental delay on one fequency fom thei countepat on anothe fequency (Sadon et al. 1994a), account fo one majo ouce of eo in Poitioning, Navigation and Timing (PNT) application that employ undiffeenced GNSS code and phae data (Montenbuck et al. 2014; Wang et al. 2016). Thi jutifie the need fo fit etimating the SDCB and then deliveing the etimate to inteeted PNT ue. Uually, the appoach fo jointly etimating the VTEC and the SDCB involve the ue of GNSS data on two fequencie, and thu equie the paticipation of one o moe geodetic-gade eceive. Heeinafte, we efe to thi appoach a dual-fequency (DF) appoach, which, in pinciple, i compied of two equential tep (Banville et al. 2014; Ciaolo et al. 2007; Stephen et al. 2011). In the fit tep, one align the pecie but ambiguou phae to the noiy but abolute code obevable on an ac-by-ac bai, theeby yielding the ionopheic obevable that ae a combination of the Slant Total Electon Content (STEC), the SDCB and the Receive Diffeential Code Biae (RDCB). Thi pocedue i temed a Caie-to-Code Leveling (CCL) technique (Bunini and Azpilicueta 2010; Bunini et al. 2008). The econd tep concen the application of thin-laye ionopheic model to thoe ionopheic obevable (Bunini et al. 2011), fom which the VTEC, the SDCB a well a the RDCB etimate aie. Although not eveyone agee that the DF appoach may be by fa the tate-of-the-at, it continue to eve the need of the ionopheic community. Hee we biefly eviit two typical ue of thi appoach. The fit ue i to poduce the naphot of the global VTEC in the fom of Global Ionophee Map (GIM) on a egula bai, a outine tak that the Intenational GNSS Sevice (IGS) geneally caie out (Felten 2003; Henández-Pajae et al. 2009; Mannucci et al. 1998). The econd ue, which we hall conide in ou analyi, i to geneate local VTEC uing GNSS data fom a ingle eceive. Thi ue i in paticula beneficial fo monitoing 3 / 30

4 the patial and tempoal evolution of the ionophee ove a given location (Choi et al. 2012; Sezen et al. 2013). At the ame time, the attactivene of DF appoach lie alo in it ability to povide SDCB etimate a by-poduct. Note, inteetingly, that, thee i a vat body of liteatue on a ingle-fequency (SF) appoach, etimating VTEC fom the Code-Minu-Phae (CMP) obevable (Cohen et al. 1992; Schüle and Oladipo 2013; Schüle and Oladipo 2014; Xia 1992). One pominent advantage ove the DF appoach i that the SF appoach i moe cot-effective becaue it elie upon ma-maket (intead of geodetic-gade) eceive. Howeve, the inability of the SF appoach to etimate SDCB (along with VTEC) emain a bottleneck poblem. Thi come a no upie, ince CMP obevable do not encompa the SDCB. In thi wok, we popoe a novel SF appoach, enabling the joint etimation of VTEC and SDCB fom the oiginal GNSS code and phae obevable. Ou appoach conit alo of two tep and it diffe fom the DF appoach only in the fit tep, whee we coect the oiginal GNSS data with the pecie atellite obit and clock poduct deliveed by the IGS o a to contuct the obeved-minu-computed obevation, and then poce them into the ionopheic obevable though the Pecie Point Poitioning (PPP) technique (Zumbege et al. 1997). A we hall detail in the next ection, thee obevable contain the STEC, the SDCB and the biaed eceive clock at the fit (pivot) epoch, and one can thu etimate fom them the VTEC and the SDCB with the thin-laye ionopheic model. Thi i the main contibution of thi wok. The oganization of thi wok poceed a follow. Section 2 eview in bief the baic pinciple and technological apect of the CCL technique, and then decibe in detail how to deal with the ank deficiencie undelying the oiginal code and phae obevation equation, a key iue to be addeed fo the development of PPP technique. We cloe thi ection with an intoduction to the main fomulae of the thin-laye ionopheic model. Section 3 peent the expeimental eult fom applying ou SF and the DF appoache to GPS data collected by eceive of diffeent type and manufactue unde all poible ionopheic condition, in eeking to 4 / 30

5 claify the oveall pefomance of ou SF appoach in etimating the VTEC and the SDCB uing a ingle GPS eceive. We conclude in Section Methodology Thi ection tat with a eview of CCL technique, poceed to PPP technique, and end with a peentation of thin-laye ionopheic model. Caie-to-Code Leveling (CCL) Fo completene let u fit peent the CCL technique, which contitute the fit tep of the DF appoach. The point of depatue i the ytem of linea obevation equation, which ead (Leick et al. 2015), p i i i d d, j j, j, j i i i a, j j, j (1) with,, j and i the eceive, atellite, fequency and epoch indice, and whee p i and i, j denote, epectively, the code and the phae, j obevable. Hee we conide a meauement cenaio that one GNSS eceive tack dual-fequency code and phae data fom a total of m atellite ove t epoch, theeby implying 1, 1,, m, j 1,2 and i 1,, t. The paamete include, i i the combination of all fequency-independent effect, 2 2 the STEC expeienced on the fit fequency with coefficient j j 1 and j the wavelength,, j d the atellite code intumental delay and d, the j eceive countepat, a the eal-valued ambiguitie abobing the phae, j intumental delay. All paamete ae expeed in unit of ange, except which a unit conveion fom mete to Total Electon Content Unit (TECU) i applied afte the etimation poce. The enitivity of the ionopheic ange delay to STEC fo the GPS L1 ignal i mete pe TECU. The paamete aigned with epoch index i ae aumed time-vaying, wheea the emainde ae aumed time-contant. Thee ae thee inteelated tak that one need to undetake. The fit tak i to contuct geomety-fee code and phae obevation equation, i, to 5 / 30

6 taking the following fom, with,2,1 p i i d d,, i i a,, the opeato ceating a geomety-fee vaiable. Note that, (2) d d d and d, d,2 d,1 denote, epectively, the SDCB and the RDCB.,2,1 In the econd tak, we compute, on an ac-by-ac bai, an offet between p i and i,, which, denoted hee uing,, aveage of p i i,, the intepetation of a ead,, whee a i known a leveling bia., The thid tak applie, i, a, amount to the weighted ove t epoch ( i 1,, t ). Hence, it follow that a a d d (3),,, a to i,, o a to yield the ionopheic obevable 1 i i a,, 1 id d, (4) whee we ee that, thi ionopheic obevable i a linea combination of the oiginal STEC i, one SDCB d and one RDCB d,. Pecie Point Poitioning (PPP) We bae ou deivation on the ingle-fequency ( j 1) vaiant of Equation (1), which ead, p i i i d d,1,1,1 i i i a,1,1 (5) whee we conide the fact that 1 1. with We fit of all e-wite i in the fom, i g i i dt i dt i (6) g i the geometic ange, i the lant topopheic delay, dt i 6 / 30

7 the atellite clock and dt i the eceive clock. Next we take advantage of pecie atellite obit and clock poduct extenally povided, fom which a-pioi known atellite poition dt i aie. Note, impotantly, that, dt x i and atellite clock i ae biaed and ead (Kouba and Héoux 2001), dt i dt i d if (7) 1 the ionophee-fee atellite code intumental delay. with dif 2 d,1 d,2 Futhemoe, let u aume that the eceive poition x i ae a-pioi known; thi i a enible aumption, ince one incline to deploy GNSS eceive at known location in the aea of inteet when ening the ionophee. Additionally, we make ue of an empiical model to compute appoximate value fo,0 i. i, denoted uing Incopoating thee conideation into Equation (5) one obtain whee p,1 p i c i i d dt i i d d,1 if,1,1 i c i i d dt i i a,1 if,1 i denote the coected code obevable, eulting fom applying the a-pioi known geometic ange and the appoximate lant topopheic delay obevable,1 g i, the a-pioi known atellite clock dt i p i ; likewie, i Notably, hee we decompoe,1 zenith topopheic delay (ZTD),0 i to the oiginal code denote the coected phae obevable. i into thee type of paamete, including the i with mapping function given a c i, the (8) ionophee-fee atellite code intumental delay dt i. d and the eceive clock if Equation (8) epeent a ank-deficient ytem, with which one cannot etimate the paamete uniquely. We tend to eliminate the ank deficiency in thi equation, of ize 2m 1, by mean of e-paameteization. We focu fit on the code obevation equation. The idea i to lump the i, 7 / 30

8 the d and the if,1 d, theeby foming the biaed STEC i, 1 i i d (9) 1 whee ue ha been made of dif d,1 d ; thi equality account fo the emegence of SDCB Next we lump d, which now ente the STEC i. dt i and d,1 into jut a ingle paamete, which ead, with dt i the biaed eceive clock.,1 dt i dt i d (10) When it come to the phae obevation equation, we have the following equality, d dt i i a dt i i a (11) if,1,1 1 the biaed ambiguitie. with a,1 a,1 d,1 d dif Conideing Equation (9), (10) and (11), we can e-wite Equation (8) a whee the dt i, the i p i c i i dt i i,1 i c i i dt i i a,1,1 and the,1 a ae till not individually etimable, (12) becaue thee i a ank deficiency occuing among them, which i of ize one. To olve thi we opt fo not etimating the biaed eceive clock at the fit epoch dt 1 whee with, theeby eulting in the full-ank vaiant of Equation (12), which ead, p i c i i dt i i,1 i c i i dt i i a,1,1 1 1 dt i dt i dt dt i dt i i dt 1 i d dt 1,1,1 a a 2dt 1 1 dt i the etimable eceive clock, i the etimable STEC, and,1 a the (13) (14) etimable ambiguitie. 8 / 30

9 Regading Equation (14), thee emak ae in ode. Fit, the dt i begin to be peent at the econd epoch and beyond, ince they epeent the dift of the oiginal eceive clock epoch. dt i with epect to the fit Second, the i, the ionopheic obevable that the PPP technique can etimate fom the ingle-fequency GNSS data, ae found to be a linea function of the STEC i, the SDCB d and the biaed eceive clock at the fit epoch dt 1. Recall the i given in Equation (4), which ae the ionopheic obevable one can etimate fom the dual-fequency GNSS data uing the CCL technique. We ague that the i ae lagely imila to the i in tem of intepetation; they both can be ued a input to the thin-laye ionophee model (which we hall decibe late) fo jointly etimating the VTEC paamete and the SDCB. A cloe compaion between the 1 dt can be teated a if they wee the d, i with the i how that, the, ince they ae two nuiance paamete of the ame numbe and natue (eceive-dependent, time-contant). An exception to thi aie, howeve, when a imultaneou lo of lock on all atellite occu. Stating at the epoch the eceive lock onto a ufficient numbe of atellite again, the biaed eceive clock at thi epoch, intead of i i dt 1, begin enteing the. Thi mean, in thi cae, that the numbe of nuiance paamete in the become geate than the numbe of d,. and Thid, the a abob a et of inetimable paamete including,1 d,1, d, d if dt 1 ; thi i a diect conequence to ank deficiency elimination. Fotunately, the time contancy of the a emain unaffected in thi poce, theeby enuing,1 the full exploitation of the phae data. In ummay, Equation (13) account fo the functional model of ou PPP technique. Fo completene ake, we point out that we bae the tochatic modeling of the GNSS obevable on the elevation-dependent weighting tategy. Moeove, in addition to pecie atellite obit and clock poduct, we alo conide applying a 9 / 30

10 numbe of coection, including the olid Eath tide, the phae wind-up effect, and the atellite and eceive phae cente offet and vaiation, to the code and phae data. Thin-laye ionophee model A we mentioned ealie, one need to efe to the thin-laye ionophee model to etimate the VTEC, along with the SDCB, fom the ionopheic obevable whoe invee covaiance matix i ued a weight matix. Roughly peaking, thi model take advantage of two fact. Fit, the STEC can vay, and thi vaiability i diven by a vaiety of facto of which geomagnetic latitude, local time and elevation angle ae mot pominent. Second, the SDCB and othe nuiance paamete, uch a the RDCB, likely emain contant ove time unde nomal envionmental condition. The thin-laye model exploit the fit fact by appoximating the whole ionophee with a pheical hell located at a pe-pecified height, ay, 450 kilomete, above the Eath uface. At the point whee atellite-to-eceive ay path piece the hell, called the Ionopheic Penetation Point (IPP), we elate the STEC VTEC 2009), i uing a mapping function M i and the i which ead (Bunini and Azpilicueta 1 R 2 1 co e i M i R (15) with i M i i and i. e and whee R i the mean Eath adiu in kilomete, i i the elevation angle of atellite a een fom eceive at epoch Next, thi model mathematically chaacteize the tempoal and patial vaiability of the i a, fo intance, the um of a polynomial function and a finite Fouie eie (Li et al. 2015), a b co in ab IPP REC IPP k IPP k IPP a0 b0 k1 (16) v i E C k S k whee and IPP denote, epectively, the geomagnetic latitude of the IPP REC 10 / 30

11 and of the eceive. with 2 ti 14 IPP denote the ola longitude of the IPP, 24 t the local time to which the epoch i coepond. i coefficient that ae unknown. E, ab C and k S ae k We conclude thi ection with Figue 1, which depict the chematic diagam of DF appoach, and that of ou SF appoach. By the ue of thi figue we eview the pimay featue of each appoach a follow. The DF appoach adopt GNSS data at two ditinct fequencie, and it conit of two equential tep. In the fit tep, we contuct the geomety-fee code and phae obevable, to which, we apply the CCL technique in ode to obtain the ionopheic obevable, intepeted a a linea combination of the STEC, the SDCB and the RDCB. The thin-laye ionophee model fulfill the ole of iolating the inteeted paamete (the VTEC and the SDCB), along with the nuiance one (the RDCB), fom the ionopheic obevable. Ou SF appoach i faily imila in implementation to the DF appoach, but it bae joint etimation of the VTEC paamete and the SDCB meely on ingle-fequency GNSS code and phae data coected by the pecie atellite obit and clock poduct extenally povided by, fo intance, the IGS. The tak of etieving the ionopheic obevable, containing the STEC, the SDCB and the biaed eceive clock at the fit epoch, i now accomplihed by the PPP technique. Afte thi, we again tun to the thin-laye ionophee model. 3. Reult We begin thi ection by decibing the expeimental etup, followed by illutating numeical eult, fom which the majo finding we identify ae alo detailed. Expeimental Setup We applied the DF a well a ou SF appoache to two et of GPS data, collected by eceive of diffeent type (ma-maket, geodetic-gade) unde diffeent ionopheic condition (ola activity, geomagnetic latitude). Thi i helpful fo u to gain a thoough undetanding of the oveall pefomance of each appoach. 11 / 30

12 The fit et of GPS data wa ampled evey 30 econd by fou co-located eceive duing Apil 19 (DOY 110) to May 25 (DOY 146), Thee eceive, deignated epectively a CUAU, SPU3, CUT2 and SPA8, ae deployed at the main campu of Cutin Univeity (Peth, Autalia), and the ditance between any two of them doe not exceed 400 mete. We point out futhe that, CUAU and SPU3 ae two low-cot UBLOX EVK-M8T eceive, connected to geodetic-gade antenna and offeing GPS L1 data. Would one ue patch antenna, the data o collected can be pone to evee multipath effect. One olution to thi iue i to ue the modified ideeal filteing (Choi et al. 2004), but we leave thi outide the cope of ou cuent analyi. The CUT2 and SPA8 ae, epectively, a TRIMBLE NETR9 eceive and a SEPTENTRIO POLARXS eceive; they upply GPS L1+L2 data fo ou ue. In addition, becaue of the co-location, the effect due to the ionophee on GPS data ought to be ame fo each eceive. We hall daw on thi fact in the following analyi. The econd et of GPS L1+L2 data wa collected by a few hunded of globally ditibuted eceive (ee Figue 2 fo thei location) at a 30-econd ampling ate, duing a ola maximum month Mach 2014 and a ola minimum month Mach 2015, namely, two epaate month one yea apat. On a eceive-by-eceive and day-by-day bai, we geneated one o two daily time eie of the VTEC fo the IPP at the zenith of each GPS eceive, called zenith VTEC; each time eie epeent eult obtained fom a paticula appoach. Note that thi poce alo poduced the daily etimate of the SDCB fo GPS atellite in view of each eceive. In ou data poceing, we ued a cut-off elevation angle of 30 degee o a to dicad paticulaly noiy GPS data. We empiically et the zenith-efeenced tandad deviation to 30 cm fo the code and to 0.3 cm fo the phae. When implementing the PPP, a leat-quae batch adjutment i ued to poce the GPS L1 data, coected by IGS Final obit and clock poduct, into ionopheic obevable along with thei covaiance matix. We etimated the ZTD a piece-wie contant with an update ate of two hou. In addition, we aligned the C1, if any, to the P1 uing the monthly value of P1-C1 SDCB publihed by the Cente fo Obit Detemination in Euope (CODE). Thi implie that, the type of the SDCB that two 12 / 30

13 appoache delive i alway P1-P2. Reult of the fit data et We focu fit on Figue 3, depicting the ionopheic obevable detemined fo two eceive SPU3 and SPA8 fom thei GPS L1 (uing the PPP) o L1+L2 (uing the CCL) data collected on May 5, 2016 (which i an abitay choice). We plit thi figue into thee panel fo cleae peentation, with each panel howing the eult fo a diffeent eceive o data ouce. Moeove, in each panel the eult fo diffeent GPS atellite ae coloed diffeently. Taken togethe, we make thee emak hee. Fit, we ee that in thi cae the ionopheic obevable can take negative value fo ome atellite, fo intance PRN 23, a maked with an aow. Thi i, howeve, not unexpected, given thei intepetation (ee Equation 4 and 14). Second, conideing, again, the ionopheic obevable obtained fo GPS atellite 23 in Figue 3a-3c, they follow an ode of inceaing moothne, theeby indicating that thei quality i mainly diven by the code data. Thid, a hould be the cae, we can eadily ecognize that the oveall patten in the ionopheic obevable i moe o le identical fom panel to panel, with highe patio-tempoal vaiability and lage magnitude at daytime than at night, eflecting the typical ignatue of the ionophee. Now tun to Figue 4, whee each panel how five time eie of zenith VTEC etimate with a time eolution of five minute fo a pai of mixed eceive (one low-cot UBLOX eceive and one geodetic-gade eceive), and fo one andomly elected day. Oveall, it follow that in each panel the thee time eie, hown with olid line and efeed to the left y axi, agee well with one anothe; in accodance with ou expectation, each time eie exhibit a ponounced diunal vaiation, with maxima and minima nea local noon and midnight, epectively. To futhe quantify thi ageement, we calculated the mean bia and the tandad deviation (STD) fo two SF time eie (olid ed and geen line) by uing the coeponding DF time eie (olid blue line) a a efeence, and peent the eult in Table 1. Note futhe that in each panel the dahed ed and geen line with ateik (efeed to the ight y axi) how, epectively, the two SF time eie that each ha been diffeenced with epect to the DF time eie. The main concluion to be dawn fom Figue 4, in conjunction with Table 1, i taightfowad. The application of ou 13 / 30

14 SF appoach to GPS L1 data povided by a geodetic-gade eceive (SPA8 o CUT2) and by a low-cot eceive (SPU3 o CUAU) hall delive VTEC etimate of vitually the ame quality, a evidenced by the fact that thee etimate have appoximately the ame mean biae and STD value (ee Table 1). Thi appea to be quite favoable, ince it jutifie the ubequent analyi of ou SF appoach uing a global netwok of geodetic-gade eceive (intead of low-cot one, which ae not available), fom which futhe finding we hall daw can till be conideed epeentative. It i notewothy that, along with the zenith VTEC etimate dicued above, we obtained alo daily etimate of SDCB, whoe offet with epect to the coeponding monthly poduct deliveed by the CODE, expeed in abolute value (and thu called abolute offet heeafte), ae hown in Figue 5, following the ame aangement a Figue 4. Let u efe to the pecentage of atellite with abolute offet le than 1 nanoecond a a pefomance meaue. Then it follow that, uch a pecentage fo the DF appoach eide between 78% (Figue 5f) and 97% (Figue 5c), geneally lowe than that fo ou SF appoach, amounting to 100% fo ed ba and vaying fom 90% (Figue 5d) to 100% (Figue 5a and 5f) fo geen ba. Thi implie that DF appoach can pefom woe than ou SF appoach, a fa a the ingle-eceive baed SDCB etimation i concened. We umie thi may be attibuted to two eaon. Fit, wheea the CCL aume the geometic effect on GPS data to be completely unknown, the PPP exploit a-pioi knowledge about the geometic effect by taking advantage of pecie atellite obit and clock poduct extenally povided a coection. Second, moe impotantly, the DF appoach i uceptible to the ytematic eo induced by time-vaying RDCB (Ciaolo et al. 2007). Roughly peaking, one aumption, tacitly made by the DF appoach, that RDCB emain contant ove time, i in vey many cae definitely contadictoy to the expeimental fact. Fotunately, thi i not the cae with ou SF appoach, ince the ionopheic obevable fom which it etimate the SDCB ae RDCB-fee. Reult of the econd data et The expeimental eult o fa epoted ae not altogethe adequate, ince they wee obtained unde limited ionopheic condition (37 conecutive day, fou 14 / 30

15 eceive at a middle-latitude ite), and thu lead to finding which, though uggetive, ae by no mean concluive. Fo thi eaon, we futhe poceed the econd et of GPS data, in ode to acetain how well ou SF appoach wok unde divee ionopheic condition. Conideing the fact that we have got a lage et of eult, we do not attempt to cove all of them; athe, without lo of geneality and fo the ake of claity, we hall only peent the eult fo 12 eceive whoe geogaphic location ae highlighted in Figue 2 with black ta. Let u focu fit on Figue 6, coniting of ix panel, with each howing two time eie of zenith VTEC etimate detemined uing, epectively, L1+L2 and L1 data fom a common eceive with a time eolution of five minute. Each time eie cove a peiod of 24 hou fom 12:00 am to 12:00 am (UTC) next day, o moe peciely, one full day in Mach 2014, a ola maximum month. It i woth mentioning that, ix eceive involved hee ae diviible into thee pai, with each pai being located in in high-, middle- and low-latitude egion, epectively. See the leftmot fou column of Table 2 (top block) fo moe detail. Uing the DF time eie (blue line) a a efeence, we calculated, on a panel-by-panel bai, two quality meaue including the mean bia and the STD, fo the SF time eie (ed line), and peent the eult in the lat column of Table 2 (top block). Two finding emege hee. Fit, ou SF appoach i capable to delive zenith VTEC etimate that ae cloe to unbiaed, a evidenced by the fact that, the mean biae computed ae mall in magnitude and can be conideed inignificant fom a pactical viewpoint. Second, the quality of SF time eie deceae a the level of the ionopheic activity inceae. Notably, the high STD value (between 1.60 and 1.75 TECU) occu at two low-latitude ite, IQQE and ADIS, which ae nea the geomagnetic equato and mot likely ubject to ditubed ionopheic activity. A compaed to thi wot-cae cenaio, we ee educed STD value fo the emaining fou ite by a facto of moe than two owing to elatively calm ionopheic activity. Figue 7 i analogou to Figue 6, except that it involve diffeent eceive and diffeent day in Mach 2015, a ola minimum month. Likewie, Table 2 (bottom block) ummaize the eceive chaacteitic and the tatitic of the SF time eie. The peent eult not only confim the two finding above, but alo eveal that the SF time eie obtained fo a middle-latitude ite DUND at day 60 of 2015 exhibit 15 / 30

16 the lowet mean bia (-0.07 TECU) and alo the mallet STD (0.38 TECU), thu coeponding to a bet-cae cenaio. We attibute thi upeio pefomance to the fact that the thin-laye ionophee model i highly likely to wok well unde calm ionopheic condition. Finally, we diect ou attention to the daily etimate of SDCB, which we obtain togethe with the daily time eie of zenith VTEC etimate hown in Figue 6 and 7. Fo conciene, we hall etict ouelve to the eult (given in Figue 8 a abolute offet) fo ix (intead of 12) eceive and fo ix (intead of nine) day. Conide, again, the pecentage of atellite with abolute offet le than 1 nanoecond a a pefomance meaue. We ee, fo ou SF appoach, that, thi pecentage i a high a 96% (Figue 8d-8f) at the ola minimum month (Mach 2015), iepective of the location of the eceive; thi value dop and can vay fom 73% (Figue 8c) to 85% (Figue 8a) at the ola maximum month (Mach 2014). Unde thee cenaio, both DF and ou SF appoache pefom cloe to each othe. Howeve, an obviou exception occu fo a low-latitude ite (ADIS) and fo a day in Mach 2014 (DOY 60), whee the pecentage expeienced by DF appoach i 36%. 4. Concluion The cutomay dual-fequency (DF) appoach fo joint etimation of Vetical Total Electon Content (VTEC) and Satellite Diffeential Code Biae (SDCB) equie GNSS code and phae data on two fequencie, and can be chaacteized by two equential tep: etieving ionopheic obevable and applying to them a thin-laye ionopheic model. In thi wok, we have developed a ingle-fequency (SF) appoach, which etain exactly the ame applicability a the DF appoach, but, in addition to thi, ha the maked advantage of being wokable with low-cot ma-maket GNSS eceive, poviding code and phae data on only one fequency. Both DF and ou SF appoache follow the ame two-tep poce; the main diffeence lie in that, they employ, epectively, the Caie-to-Code Leveling (CCL) and the Pecie Point Poitioning (PPP) to implement the fit tep. We aeed the pefomance of ou SF appoach on two et of GPS eal data. The fit data et, coveing a time peiod of 37 conecutive day, wa collected by 16 / 30

17 two ma-maket and two geodetic-gade eceive that wee deployed cloe to each othe at a middle-latitude ite. The econd data et came fom a global netwok of appoximately 200 geodetic-gade eceive fo the ola minimum month Mach 2014 and the ola maximum month Mach On a eceive-by-eceive, day-by-day bai, ue ha been made of DF and/o ou SF appoache to etimate daily time eie of zenith VTEC with a time eolution of five minute, along with daily etimate of SDCB fo GPS atellite in view of each eceive. Empiical analyi of the eult o obtained waant two concluion. Fit, both appoache ae capable of deliveing zenith VTEC etimate that ae eaonably conitent. Fo a common eceive (o multiple co-located eceive), the oveall conitency between two daily time eie deived, epectively, by DF and ou SF appoache, in tem of STD, i found to be at the level of a few tenth of a TECU to oughly 2 TECU. Second, ou SF appoach appea pomiing a a mean to calibate SDCB unde vaying ionopheic condition; it can povide daily etimate of SDCB with abolute offet le than 1 nanoecond fo 73 to 96 pecent of GPS atellite in view, conideing a a efeence the monthly poduct publihed by the CODE. When it come to the DF appoach, thi pecentage tay moe o le the ame in mot cae, but may dop haply to le than 40% duing extemely ditubed ionopheic condition. Acknowledgement Thi wok wa patially funded by the National key Reeach Pogam of China Collaboative Peciion Poitioning Poject (No. 2016YFB ) and the National Natual Science Foundation of China (No , ). The fit autho i uppoted by the CAS Pionee Hunded Talent Pogam. All thi uppot i gatefully acknowledged. Refeence Atu J, Ducic V, Kanamoi H, Lognonné P, Muakami M (2005) Ionopheic detection of gavity wave induced by tunami. Geophyical Jounal Intenational 160: / 30

18 Banville S, Collin P, Zhang W, Langley RB (2014) Global and egional ionopheic coection fo fate PPP convegence. Navigation 61: Bunini C, Azpilicueta F (2010) GPS lant total electon content accuacy uing the ingle laye model unde diffeent geomagnetic egion and ionopheic condition. J Geodey 84: Bunini C, Azpilicueta FJ (2009) Accuacy aement of the GPS-baed lant total electon content. J Geodey 83: Bunini C, Camilion E, Azpilicueta F (2011) Simulation tudy of the influence of the ionopheic laye height in the thin laye ionopheic model. J Geodey 85:637 Bunini C, Meza A, Gende M, Azpilicueta F (2008) South Ameican egional ionopheic map computed by GESA: A pilot evice in the famewok of SIRGAS. Advance in Space Reeach 42: Choi K, Bilich A, Laon KM, Axelad P (2004) Modified ideeal filteing: implication fo high-ate GPS poitioning. Geophyical eeach lette, 2004, 31(22). Choi KH, Lee JY, Kim HS, Kim J, Lee HK (2012) Simultaneou etimation of ionopheic delay and eceive diffeential code bia by a ingle GPS tation. Meauement Science and Technology 23: Ciaolo L, Azpilicueta F, Bunini C, Meza A, Radicella S (2007) Calibation eo on expeimental lant total electon content (TEC) detemined with GPS. J Geodey 81: Cohen CE, Penm B, Pakinon BW Etimation of abolute ionopheic delay excluively though ingle-fequency GPS meauement. In: Poceeding of the 5th Intenational Technical Meeting of the Satellite Diviion of The Intitute of Navigation (ION GPS 1992), pp Dautemann T, Calai E, Haae J, Gaion J (2007) Invetigation of ionopheic electon content vaiation befoe eathquake in outhen Califonia, Jounal of Geophyical Reeach: Solid Eath 112 Dettmeing D, Limbege M, Schmidt M (2014) Uing DORIS meauement fo modeling the vetical total electon content of the Eath ionophee. J Geodey 88: Dyud L, Jovancevic A, Bown A, Wilon D, Ganguly S (2008) Ionopheic meauement with GPS: Receive technique and method. Radio Science 43 Felten J (2003) The intenational GPS evice (IGS) ionophee woking goup. Advance in Space Reeach 31: Gulyaeva TL, Aikan F, Henandez Pajae M, Veelovky I (2014) Noth outh component of the annual aymmety in the ionophee. Radio Science 49: Henández-Pajae M, Juan J, Sanz J (1999) New appoache in global ionopheic detemination uing gound GPS data. Jounal of Atmopheic and Sola-Teetial Phyic 61: Henández-Pajae M, Juan JM, Sanz J, Ou R, Gacia-Rigo A, Felten J, Komjathy A, Schae SC, Kankowki A (2009) The IGS VTEC map: a eliable ouce of ionopheic infomation ince J Geodey 83: / 30

19 Komjathy A et al. (2012) Detecting ionopheic TEC petubation caued by natual hazad uing a global netwok of GPS eceive: The Tohoku cae tudy. Eath, planet and pace 64: Komjathy A, Spak L, Wilon BD, Mannucci AJ (2005) Automated daily poceing of moe than 1000 gound baed GPS eceive fo tudying intene ionopheic tom. Radio Science 40 Kouba J, Héoux P (2001) Pecie point poitioning uing IGS obit and clock poduct. GPS olution 5:12-28 Leick A, Rapopot L, Tatanikov D (2015) GPS atellite uveying. John Wiley & Son, Li Z, Yuan Y, Wang N, Henandez-Pajae M, Huo X (2015) SHPTS: towad a new method fo geneating pecie global ionopheic TEC map baed on pheical hamonic and genealized tigonometic eie function. J Geodey 89: Liu Z, Gao Y (2004) Ionopheic TEC pediction ove a local aea GPS efeence netwok. GPS Solution 8:23-29 Lognonné P et al. (2006) Gound-baed GPS imaging of ionopheic pot-eimic ignal. Planetay and Space Science 54: Mannucci A, Wilon B, Yuan D, Ho C, Lindqwite U, Runge T (1998) A global mapping technique fo GPS-deived ionopheic total electon content meauement. Radio cience 33: Mannucci AJ, Wilon BD, Edwad CD (1993) A new method fo monitoing the Eath' ionopheic total electon content uing the GPS global netwok. In: Poceeding of ION GPS-93, the 6th intenational technical meeting of the atellite diviion of The Intitute of Navigation, Salt Lake City, UT, Septembe 1993, pp Montenbuck O, Hauchild A, Steigenbege P (2014) Diffeential Code Bia Etimation uing Multi GNSS Obevation and Global Ionophee Map. Navigation 61: Pak J, von Fee RR, Gejne Bzezinka DA, Moton Y, Gaya Pique LR (2011) Ionopheic detection of the 25 May 2009 Noth Koean undegound nuclea tet. Geophy Re Lett 38 Sadon E, Riu A, Zaaoa N (1994a) Etimation of the tanmitte and eceive diffeential biae and the ionopheic total electon content fom Global Poitioning Sytem obevation. Radio Science 29: Sadon E, Riu A, Zaaoa N (1994b) Ionopheic calibation of ingle fequency VLBI and GPS obevation uing dual GPS data. J Geodey 68: Schüle T, Oladipo OA (2013) Single-fequency GNSS etieval of vetical total electon content (VTEC) with GPS L1 and Galileo E5 meauement. Jounal of Space Weathe and Space Climate 3:A11 Schüle T, Oladipo OA (2014) Single-fequency ingle-ite VTEC etieval uing the NeQuick2 ay tace fo obliquity facto detemination. GPS olution 18: Sezen U, Aikan F, Aikan O, Ugulu O, Sadeghimoad A (2013) Online, automatic, nea eal time etimation of GPS TEC: IONOLAB TEC. Space Weathe 19 / 30

20 11: Stephen P, Komjathy A, Wilon B, Mannucci A (2011) New leveling and bia etimation algoithm fo poceing COSMIC/FORMOSAT 3 data fo lant total electon content meauement. Radio Science 46 Wang N, Yuan Y, Li Z, Montenbuck O, Tan B (2016) Detemination of diffeential code biae with multi-gnss obevation. J Geodey 90: Xia R Detemination of abolute ionopheic eo uing a ingle fequency GPS eceive. In: Poceeding of the 5th Intenational Technical Meeting of the Satellite Diviion of The Intitute of Navigation (ION GPS 1992), pp Yao Y, Chen P, Zhang S, Chen J (2013) A new ionopheic tomogaphy model combining pixel-baed and function-baed model. Advance in Space Reeach 52: Zumbege J, Heflin M, Jeffeon D, Watkin M, Webb FH (1997) Pecie point poitioning fo the efficient and obut analyi of GPS data fom lage netwok. Jounal of Geophyical Reeach: Solid Eath 102: / 30

21 Table 1. Deciptive tatitic fo two daily time eie of zenith VTEC etimate deived uing GPS L1 data (dahed ed and geen line with ateik in Figue 4): mean bia tandad deviation (STD), in TECU. DOY SF & SPA8 SF & SPU3 SF & CUT2 SF &CUAU n/a n/a n/a n/a n/a n/a 111 n/a n/a n/a n/a n/a n/a / 30

22 Table 2. The main chaacteitic of 12 eceive involved in Figue 6 and 7, a well a the mean bia and the tandad deviation (STD) (both expeed in in TECU) of the SF time eie (ed line), computed uing the coeponding DF time eie (blue line) a a efeence. Station DOY Receive type Longitude-latitude Mean bia STD BAKE 73 TPS NET-G3A 96.0 W, 64.3 N NRC1 61 JAVAD 75.6 W, 45.5 N TRE_G3TH DELTA ADIS 60 JPS LEGACY 38.8 E, 9.0 N OHI3 88 LEICA GR W, 63.3 S SUTV 60 JPS EGGDT 20.8 E, 32.4 S IQQE 79 TRIMBLE NETR W, 20.3 S SVTL 74 JAVAD 29.8 E, 60.5 N TRE_G3TH DELTA LAMA 80 LEICA GRX1200+GNSS 20.7 E, 53.8 N DAKR 71 TPS NET-G3A 17.4 W, 14.7 N MAW1 78 LEICA GRX1200GGPRO 62.9 E, 67.6 S DUND 80 TRIMBLE NETR E, 45.9 S ULDI 79 TRIMBLE NETRS 31.4 E, 28.3 S / 30

23 Figue 1. Schematic diagam of the cutomay DF appoach (in black), and that of ou SF appoach (in ed); the middle pat hown in blue i common to both appoache. 23 / 30

24 Figue 2. Geogaphic location of a few hunded of eceive (olid ed dot) that povide the econd et of GPS data analyzed in thi wok. The blue line mak the geomagnetic equato. The black ta highlight 12 eceive, deployed in the high-, middle- and low-latitude egion. 24 / 30

25 Figue 3. Ionopheic obevable (in TECU) extacted fom GPS L1 o L1+L2 data fo eceive SPU3 and SPA8 on May 5 (DOY 126), 2016, and hown a a function of Local Time (UTC+8). Diffeent colo coepond to diffeent atellite. In each panel, the aow point to the eult fo GPS atellite / 30

26 Figue 4. Time eie of zenith VTEC etimate with a 5-min time eolution fo a ingle expeimental day that i andomly elected. We aange a total of ix panel in two ow, with each ow epeenting the eult fo one pai of mixed eceive (one ma-maket and one geodetic-gade). Each panel contain five line. The olid blue and ed line (efeed to the left y axi) epeent two daily time eie obtained uing, epectively, L1+L2 and L1 GPS data fom a geodetic-gade eceive (SPA8 o CUT2); the geen line (efeed to the left y axi) epeent the time eie obtained uing L1 data fom a low-cot eceive (SPU3 o CUAU). The dahed ed and geen line with ateik (efeed to the ight y axi) how, epectively, the two SF time eie (olid ed and geen line) that each ha been diffeenced with epect to the coeponding DF time eie (olid blue line). 26 / 30

27 Figue 5. Abolute offet between the daily etimate of SDCB, obtained along with daily time eie of zenith VTEC etimate depicted in Figue 4, and the coeponding monthly poduct publihed by the Cente fo Obit Detemination in Euope (CODE). The aangement of thi figue i the ame a that of Figue 4. In all panel, the eult fo each GPS atellite ae hown by tacking the thee ba on top of each othe. 27 / 30

28 Figue 6. Two daily time eie of zenith VTEC etimate with a 5-min time eolution, etimated, epectively, fom GPS L1+L2 data (in blue) and fom GPS L1 data (in ed) collected by a common eceive on a day in Mach Six panel, aanged in thee column, how the eult fo thee pai of eceive, which, fom left to ight, ae located in high-, middle- and low-latitude egion. 28 / 30

29 Figue 7. Panel (a)-(f) ae analogou to thoe in Figue 6, except that they how eult fo anothe ix eceive pead thoughout the globe and fo a few day in Mach / 30

30 Figue 8. Panel (a)-(f): daily etimate of SDCB, obtained along with daily time eie of zenith VTEC etimate depicted in Figue 6a, 6b, 6c, 7d, 7e and 7f. In each panel, the eult ae given a abolute offet in nanoecond elative to the coeponding monthly poduct publihed by the Cente fo Obit Detemination in Euope (CODE). 30 / 30