BIOGRAPHY INTRODUCTION

Transcription

1 Zero-baeline Analyi of PS/BeiDou/alileo Between-Reeiver Differential Code Biae (BR- DCB): Time-wie Retrieval and Preliminary Charaterization B. Zhang, P.J.. Teunien, NSS Reearh Centre, Curtin Univerity, Autralia eoiene and Remote Sening, delft Univerity of Tehnology, The Netherland BIORAPHY Baoheng Zhang i a reearh fellow in the NSS Reearh Centre at Curtin Univerity. Hi reearh i foued on multi-nss integer ambiguity reolution enabled Preie Point Poitioning (PPP-RTK), with an emphai on ode and arrier-phae bia etimation and haraterization, ionopheri delay retrieval and prototype PPP-RTK network oftware development. Peter J.. Teunien i Siene Diretor of the CRC-SI, Profeor of eodey and Navigation and Head of Curtin NSS Reearh Centre. Hi urrent reearh fou i on modeling next-generation NSS for improved parameter etimation and validation. ABSTRACT When ening the Earth ionophere uing multiple lobal Navigation Satellite Sytem (NSS) peial are need to be taken of the reeiver Differential Code Bia (DCB) ontribution to the error budget. For thi reaon timely and aurate retrieval of multi-nss reeiver DCB with the goal of gaining inight into their harateriti would be of relevane. In thi ontribution we propoe a method able to time-wiely retrieve the Between-Reeiver DCB (BR-DCB) from ode meaurement olleted by a zero-baeline etup, thereby eliminating mot ommon error oure. We bae our invetigation on dual-frequeny PS (L+L), BeiDou (B+B) and alileo (E+E5a) meaurement olleted in 3 with a 3 eond ampling rate by four geodeti grade reeiver (two Trimble NETR9, one Septentrio POLARX4 and one Javad TRE-3TH) onneted to one ommon antenna. For eah reeiver-pair, we proe the PS/EO/ISO/MEO/alileo meaurement eparately and then obtain the time-wie etimate of five group of BR-DCB. With the ue of tatitial hypothei teting heme, we onfirm that: (). the time-wie etimate of BR-DCB for all teted reeiver-pair exhibit good intraday tability; and (). the daily weighted average (DWA) etimate of EO/ISO/MEO BR-DCB are inonitent for reeiver-pair of mixed type, due to the preene of BeiDou ode Inter-Satellite-Type-Biae (ISTB). We alo identify likely fator aounting for the variability in the DWA etimate of BR-DCB over a -year interval a: (). reeiver firmware upgrade; and (). daily maximum temperature variation at reeiver ite. INTRODUCTION The pae-borne and ground-baed lobal Navigation Satellite Sytem (NSS) meaurement with extenive patial overage and high temporal reolution are partiularly ideal data oure for tudying the ionophere []. Over the pat few deade, the ionopheri information retrieved from the PS meaurement broadat at two frequenie ha enabled u to undertand the intrini mehanim of the pae weather effet [, 3], to explore the potential aue of the eimi hazard [4, 5], and to improve the empirial preiion of pae geodeti appliation [6]. In addition to the PS that i undergoing uninterrupted modernization, the Chinee BeiDou and the European alileo are urrently under development for global operation a well [7]. So far, the BeiDou ontellation oniting of 4 atellite in orbit (five EO + five ISO + four MEO) ha beome operational in the Aian-Paifi region [8]. The alileo i till in the deployment phae and urrently ha four In- Orbit-Validation (IOV) atellite operating. The remaining alileo atellite will oon be launhed, in order to omplete the ontellation for the Full Operational Capability (FOC) phae [9]. With thee general fat in mind, one would expet that the available multi-nss data et would allow u to aquire muh deeper inight into the atual tate of the ionophere than before [, ]. Preie etimation of vertial Total Eletron Content (vtec) parameter from dual- or multi-frequeny NSS meaurement i a ruial prerequiite for NSS-baed ionophere tudie []. For thi purpoe one ha to takle the atellite and reeiver Differential Code Bia (DCB) ontribution to the error budget [3]. The near ontant pae environment onboard the NSS ontellation give rie to fairly promiing long-term tability of the atellite DCB [4, 5]. A a onequene, we would be able to determine the atellite DCB with relatively high auray (a good a. n) and thu get rid of their impat on the etimated vtec eaily [6, 7]. In ontrat,

2 however, one may experiene ignifiant ingle-reeiver (abolute) or/and between-reeiver (relative) DCB variation during a time period of one day or even a few hour, poibly aued by the hanging temperature ondition at the reeiver antenna, along the able, or in the internal reeiver hardware [8, 9]. Suh temporal variability of reeiver DCB, if not irumvented properly, will partially aount for both the levelling error underlying the line-of-ight ionopheri obervable [], a well a the vtec modelling error [-3]. With the ultimate goal of improving the reliability of vtec etimation, o far a variety of approahe have been propoed to determine the harateriti (typially the tability) of the reeiver DCB retrieved either from the vtec etimation proe a a by-produt [4, 5], or from differening the ionopheri obervable determined for two o-loated reeiver [, 6]. However, for the following two reaon thee approahe may till be inadequate. Firt, when uing uh method the retrieved reeiver DCB may till be affeted by un-modelled biae. Seond, the o-obtained time erie of reeiver DCB are uually of low time reolution (a few hour to one day) and may thu fail to identify any poible reeiver DCB variation over horter time interval (e.g. le than hour). In thi ontribution, we firt develop an approah for retrieving Between-Reeiver DCB (BR-DCB) baed on a zero-baeline et up. Without relying on the vtec etimation proe or the formation of ionopheri obervable, our approah i able to ahieve time-wie BR-DCB retrieval by employing only a ingle epoh of between-reeiver, between-frequeny double-differened (DD) NSS ode meaurement. Owing to the fat that for zero-baeline mot ommon error oure are atually anelled out in our DD ode meaurement [7], the reidual error oure affeting our BR-DCB retrieval an thereby be minimized. With the ue of dual-frequeny PS/BeiDou/alileo meaurement olleted in 3 with a ampling rate of 3 eond by four multi-nss reeiver onneted to one ommon antenna, we then invetigate: (). the intra-day tability in the time-wie etimate of BR-DCB; (). the oniteny between the daily weighted average (DWA) etimate of EO/ISO/MEO BR-DCB for a ommon reeiver-pair; (3). the fator aounting for the variability in the DWA etimate of BR-DCB. METHOD DESCRIPTION In thi etion, we outline the proedure of our time-wie BR-DCB retrieval approah. Next to that, we briefly illutrate two tatitial hypothei teting heme that are adopted to validate the intra-day tability in time-wie etimate of BR-DCB and the oniteny between DWA etimate of EO/ISO/MEO BR-DCB. Time-wie BR-DCB retrieval Let u aume that, at ertain epoh i, two reeiver forming a zero-baeline are able to imultaneouly trak everal NSS atellite at two frequenie. With repet to one atellite, it between-reeiver ingle-differened (SD) ode obervation equation take the form, E p i = dt i + b i () { j ( )} () j () where E{} denote the expetation operator, j =,, denote the frequeny index, p ( i ) denote the dualfrequeny SD ode meaurement for atellite that belong to NSS ontellation tranmitting ode diviion multiple ae (CDMA) ignal. Unknown parameter are: dt ( i ) the SD reeiver lok, bj ( i ) the frequeny-dependent SD reeiver ode biae. The ytem of obervation equation repreented by () i not olvable, ine all the unknown parameter are not individually etimable. For thi reaon we further differene the SD ode obervation equation between two frequenie and eventually get, E p i = b i () { ()} (),,, where p ( i) p ( i) p ( i) meaurement and b ( i) b ( i) b ( i) j = i the DD ode = i the BR-DCB parameter of our interet., The formal preiion of p () i an be given a, { () i } D p, σ = in{ θ () i }, where D{ } i the diperion operator, (3), σ denote the zenith-referened undifferened ode tandard deviation,, θ ( i) denote the elevation angle of atellite at epoh i. At every epoh, after etting up the funtional (tohati) model imilar to () ((3)) for all the atellite belonging to one ommon ontellation, we an readily retrieve the BR-DCB, along with their formal preiion, uing the leat-quare etimator. The epoh-wie leatquare olution i therefore a weighted average over all atellite, in whih the reiproal value of (3) i ued a weighting. We remark that, when applying the BR-DCB retrieval approah deribed above to BeiDou ontellation, one hould be aware of the poible preene of the ode Inter-Satellite-Type-Biae (ISTB) for reeiver-pair of mixed type [8]. Aording to [9], the exitene of ode ISTB ould not be learly explained by reeiver deign parameter. One poible aue might be a bia indued by the multipath for the EO atellite whih i ontant and reeiver dependent. By definition, the BeiDou ode ISTB aoiated with gm two atellite type, denoted a Bj () i, an be interpreted a gm g m B i = b i b i (4) j ( ) j ( ) j ( ) g m where b ( i ) ( ( ) j b i ) denote the SD reeiver ode j biae involved in the SD ode obervation equation formulated for atellite type g ( m ).

3 gm Further differening Bj () i at two frequenie will yield the following identity gm gm g g m m B () i B () i = b () i b () i b () i b () i (5) g g m m where b () i b () i and b () i b () i are in fat the BeiDou BR-DCB retrieved by DD ode meaurement belonging to atellite type g and m, repetively. From (5) it follow that, would dual-frequeny BeiDou ode ISTB be preent and different, one ha to retrieve atellite type dependent BeiDou BR-DCB. Finally, it i worth mentioning that our time-wie BR-DCB retrieval approah i unlikely to benefit from further involvement of the arrier-phae meaurement. Uually, thi fat hold true in the ae where the realvalued ambiguity parameter are etimated (ambiguityfloat enario). Moreover, even if the (between-reeiver, between-atellite) DD ambiguity parameter have been uefully reolved into integer (ambiguity-fixed enario), the ontribution of inorporating arrier-phae meaurement to the BR-DCB retrieval i till virtually negligible [3]. In parallel, in order to aertain the poible dependeny of BeiDou BR-DCB upon the atellite type, we ontrut the following tet tatiti T whih read g m where b ( b T = b b g m g + σ m b b σ g g b ( i) b ( i) ( m ( ) m b ( ) i b i (9) ) denote the DWA etimate of, f. equation 5), while it formal preiion i given a σ g ( σ m ). T b b ha a tandard normal ditribution. One would deide for a g m ignifiant differene between b and b if T > N α ( ) hold for a given ignifiane level α..5, EXPERIMENTAL ANALYSIS Data preparation and proeing Statitial hypothei teting With a total of t time-wie etimate of BR-DCB over one day available, the DWA etimate of them, denoted a b, an be alulated a follow b b () i σ () i b = = σ () i t i= t i where b () i i weighted aording to it formal preiion b () i σ. In addition, with the ue of the error propagation law, we an alo obtain the formal preiion of b whih i denoted a σ and read b σ = (7) b t σ () i i= b It i remarked that omputation of b () i and σ b a given above will form the bai for our illutration of two tatitial hypothei teting heme in the following. Tet tatiti T ued to diagnoe the intra-day tability of b () i an be ontruted a T t i= b ( b () i b ) σ () i b (6) = (8) where T i Chi-quare ditributed with t degree of freedom, auming that b () i i normally ditributed. The ritial value of T an be written a χα ( t, ) in whih the level of ignifiane i et to α. One would onlude that b () i doe not exhibit any ignifiant T < t, our. hange over time if ( ) χ α Fig. Curtin NSS geodeti grade antenna (CUT) and four multi-nss reeiver of three type (given in braket) ued in thi tudy. Top antenna etup with SCIS radome. Bottom reeiver antenna onnetivity The experimental data et are meaured by four multi- NSS reeiver from the PS (L+L), the BeiDou (B+B) and the alileo (E+E5a) ontellation in 3 with a ampling rate of 3 eond and a ut-off elevation angle of 5 degree. A hown in Fig., all the reeiver are plaed at the main ampu of Curtin Univerity in Bentley (Perth) and ommonly onneted to a Trimble TRM 598. geodeti grade antenna with SCIS radome. Table preent an overview of the bai harateriti of the four reeiver, while Table ummarize the ignal of the dual-frequeny, multi- NSS ode meaurement ued.

4 Table Four experimental multi-nss reeiver harateriti Reeiver name Reeiver type Antenna type Remark CUT Trimble TRM598. firmware verion (pivot) NETR9 SCIS wa upgraded from 4.7 to 4.8 at day 75, 3 CUT Septentrio CUT CUT3 POLARX4 Trimble NETR9 Javad TRE- 3TH the ame firmware verion upgrade proe a CUT removed during day 4-46 and day 54-6, 3 We define three independent reeiver-pair, all referring to the CUT a pivot reeiver. For eah of them we time-wiely retrieve five group of BR-DCB uing the PS/EO/ISO/MEO/alileo ode meaurement, repetively. We emphaize here again that, to invetigate the poible dependeny of BeiDou BR-DCB upon the atellite type, the ode meaurement from BeiDou EO/ISO/MEO atellite are proeed eparately, a if they were from three different ontellation. Table Overview of dual-frequeny, multi-nss ode meaurement ued in thi tudy Syt. Band Frequeny Component (MHz) PS L C L 7.6 W BeiDou B I B 7.4 I alileo E X: CUT, CUT3 C: CUT, CUT E5a X: CUT, CUT3 Q: CUT, CUT For the zenith-referened undifferened ode tandard deviation we ue the value of 3 m, whih i a reaonable approximation to the empirial value etimated uing multi-nss data from the ame reeiver [3, 3]. We derive the atellite poition that are bai input to elevation angle omputation from the broadat ephemeride. We remark that, reeiving broadat ephemeride from BeiDou (alileo) ontellation by at leat one of our experimental reeiver beome poible only after day 49 (7) of 3. When we ompute the ritial value for tet tatiti T ( T ), the level of ignifiane α ( α ) i hoen equal to 5%. We hall for the ake of brevity retrit our preentation to a eleted et of repreentative BR-DCB reult. All onluion drawn about the harateriti of the preented BR-DCB hold true for the ret of our BR- DCB reult a well. Analyi of intra-day tability in time-wie etimate of BR-DCB We firt tet the time-wie etimate of CUT-CUT (Trimble-Septentrio) alileo BR-DCB and depit a erie of omputed tet tatiti T (blue irle) along with their ritial value χα ( t, ) (red dot) in Fig.. A few gap preent in the time erie of T ( χα ( t, ) ) orrepond to the time period without navigation ephemeride (e.g. day -7) or lak of viible IOV atellite above ut-off elevation angle. Due to the fat that we aign a fixed value (5%) to the level of ignifiane χ t, are α, the value omputed for α ( ) thereby olely driven by the degree of freedom ( t ) and may vary dramatially from day to day. For thoe day (e.g ) when only one IOV atellite i intermittently viible the value taken by χα ( t, ) an drop down to 5 or even maller. Quite learly, it follow here that T < χ α ( t, ) alway hold true for all the teting day and thu an be taken a indiation of intra-day tability in the time-wie etimate of BR-DCB onidered here. Tet tatiti Intra day tability teting of CUT CUT alileo BR DCB T χ (t,) α Day of Year Fig. Tet tatiti T (blue irle) ued to diagnoe the intra-day tability in the time-wie etimate of CUT- χ t, CUT alileo BR-DCB. Critial value ( ) (red dot) omputed uing level of ignifiane α = 5%, together with the degree of freedom ( t ) Similarly, Figure 3 preent the tatitial hypothei teting reult for diagnoing the intra-day tability in the time-wie etimate of CUT-CUT (Trimble-Trimble) PS BR-DCB. Contrary to Fig. in whih the χα ( t, ) varie remarkably, it follow here that the χ t, tay almot ontant over the entire value of α ( ) one year period, mainly due to the nearly invariant ( t ) ranging from 85 to 879. Again, we ee from Fig. 3 that, the omputed value of T (<5) are alway α 5 Critial value

5 ignifiantly maller than that of ( t, ) χ (>3). Thi onfirm that the time-wie etimate of BR-DCB teted here are uffiiently table over every ingle day of 3. Tet tatiti α Intra day tability teting of CUT CUT PS BR DCB T χ (t,) α Day of Year Fig. 3 Tet tatiti T (blue irle) ued to diagnoe the intra-day tability in the time-wie etimate of CUT- χ t, (red CUT PS BR-DCB. Critial value ( ) dot) omputed uing level of ignifiane α = 5%, together with the degree of freedom ( t ) We remark that our tet tatiti only have a hiquare ditribution if the BR-DCB etimator are normally ditributed. We verify thi by diplaying firt of all the alileo BR-DCB etimate retrieved at day a a hitogram in Fig. 4 (ubplot a), whih ha 354 ample and 4 bin of width.5 n. Alo, we depit therein the empirial probability denity funtion (PDF) of N (.6,.57) a a red urve, whih orrepond to the empirial mean (.6 n) and the empirial tandard deviation (.57 n) of thoe ample. enerally, we an reognize from ubplot (a) that the hitogram fit reaonably well with the empirial normal PDF, thereby implying the BR-DCB etimate retrieved at thi day indeed obey a normal ditribution. However, we have to point out that, the hitogram eem to be lightly aymmetri a thee etimate are heterogeneou in their formal preiion. Furthermore, we ue the Quantile- Quantile (QQ) plot (ubplot b) a another tool to graphially demontrate the loe-to-normality of ample depited in ubplot (a). In uh a QQ plot, the ordered ample are plotted againt the quantile of the empirial normal ditribution N (.6,.57). Similar to what we have learnt from ubplot (a), the linearity of the blue roe hown in ubplot (b) alo ugget that the ample are loe-to-normally ditributed. Additionally, we addre in Fig. 5 the hitogram of time-wie etimate of PS BR-DCB retrieved at day 7 (ubplot a) a well a the orreponding QQ plot (ubplot b). Conidering firt the ubplot (a), the hitogram ha a total of 88 ample and 4 bin of width.5 n. The empirial normal PDF, determined by the empirial mean (.64 n) and the empirial tandard deviation (.4 n) of α 5 Critial value thee ample, i depited a a red urve. In ontrat to what we ee from ubplot (a) of Fig. 4, the onformity between the hitogram and the empirial normal PDF beome more evident. Moreover, ine thee BR-DCB etimate are more homogeneou in their formal preiion the hitogram i le aymmetri. With repet to the QQ plot depited in ubplot (b), the linearity of green roe onfirm the normal ditribution of the ample a well. Probability Quantile of input BR DCB Mean =.6 Empirial STD =.57 (a). CUT DOY Data Hitogram Empirial Normal PDF alileo BR DCB (n) (b). QQ Plot Quantile of N(.6,.57) Fig. 4 Panel (a): The hitogram of time-wie etimate of alileo BR-DCB referring to day and reeiverpair of CUT-CUT: 354 ample and 4 bin of width.5 n, and the empirial theoretial normal ditribution (red urve) baed on the mean (.6 n) and empirial tandard deviation (.57 n) of the ample. Panel (b): QQ plot of ample veru normal ditribution N.6,.57 ( ) Probability Quantile of input BR DCB Mean =.64 Empirial STD =.4 (a). CUT DOY 7 Data Hitogram Empirial Normal PDF PS BR DCB (n) (b). QQ Plot Quantile of N(.64,.4) Fig. 5 Panel (a): The hitogram of time-wie etimate of PS BR-DCB referring to day 7 and reeiver-pair of CUT-CUT: 88 ample and 4 bin of width.5 n, and the empirial theoretial normal ditribution (red urve) baed on the mean (.64 n) and empirial tandard deviation (.4 n) of the ample. Panel (b): QQ plot of N.64,.4 ample veru normal ditribution ( ) Poible dependeny of BeiDou BR-DCB etimate upon atellite type A inferred from (5), the BeiDou BR-DCB would beome dependent on atellite type, provided that the

6 dual-frequeny ode ISTB are preent and in the meantime differ from eah other. We will verify thi finding here by mean of invetigating the oniteny between the DWA etimate of EO/ISO/MEO BR- DCB retrieved for two reeiver-pair, involving not only the CUT-CUT3 of mixed type (Trimble-Javad, ISTBaffeted), but the CUT-CUT of ommon type (Trimble- Trimble, ISTB-free) a well. We further remark that, with repet to CUT-CUT3, the empirial value of dualfrequeny BeiDou ode ISTB aoiated with any two atellite type are already made available by [8] (f. Table 5 therein), thu offering u an opportunity to quantitatively validate (5). Daily weighted average (n) EO ISO MEO CUT CUT3 BeiDou BR DCB differene amount to -. n (-.6 m), whih i very loe to the differene between the empirial value of dual-frequeny ISO-MEO ode ISTB (- m) a reported in [8]. However, in ontrat to the other two time erie, the time erie of EO BR-DCB (dotted blak line) i found to have a ontant offet of roughly.45 n (3.5 m), whih deviate lightly from the differene between the empirial value of dual-frequeny EO-MEO (EO-ISO) ode ISTB (9 m) a reported in [8]. Therefore, one hould be aware that the BeiDou ode ISTB may lead to inonitent EO/ISO/MEO BR-DCB in their DWA etimate. Daily weighted average (n) CUT CUT BeiDou BR DCB EO ISO MEO Day of Year 3 Fig. 6 The daily weighted average etimate of CUT- CUT3 (Trimble-Javad) BeiDou BR-DCB in 3: EO reult (blak dotted line), ISO reult (red dotted line) and MEO reult (green dotted line) T Coniteny teting of CUT CUT3 BeiDou BR DCB EO ISO EO MEO ISO MEO N.5α (,) Day of Year 3 Fig. 7 Three tet tatiti T (blak/red/green dotted line) ued to diagnoe the oniteny between CUT- CUT3 EO/ISO/MEO BR-DCB (f. Fig. 6). Critial value N.5 α (,) (magenta line) omputed uing level of ignifiane α = 5% We how in Fig. 6 the DWA etimate of EO/ISO/MEO BR-DCB retrieved for CUT-CUT3. It follow that, the time erie of ISO BR-DCB (dotted red line) i generally in good agreement with that of MEO BR-DCB (dotted green line). The mean value of their Critial value Day of Year 3 Fig. 8 The daily weighted average etimate of CUT- CUT (Trimble-Trimble) BeiDou BR-DCB in 3: EO reult (blak dotted line), ISO reult (red dotted line) and MEO reult (green dotted line) With the ue of (9), we tet whether the direpany between any two of the time erie given in Fig. 6 i tatitially ignifiant or not. For eah day we ompute three tet tatiti T and preent their abolute value T in Fig. 7. Alo, a erie of ritial value N.5 α (,) =.96 remaining ontant over all 6 day are depited a a magenta line. From thee finding we onlude that for reeiver-pair CUT-CUT3 the DWA etimate of EO BR-DCB are eentially different from that of ISO/MEO BR-DCB. Quite imilar to Fig. 6, we how in Fig. 8 the DWA etimate of EO/ISO/MEO BR-DCB retrieved for the other reeiver-pair CUT-CUT that i found to be free from BeiDou ode ISTB. In thi ae, we ee that three time erie agree fairly well with one another, whih ugget good oniteny between EO/ISO/MEO BR-DCB etimate for CUT-CUT. Thi finding i further verified by the tatitial hypothei teting reult preented in Fig. 9, in whih the omputed value of all T are well below.96 with quite rare exeption. The diuion above would enable u to draw a preliminary onluion. When retrieving the BeiDou BR- DCB for reeiver-pair of mixed type, one hould take peial are of the effet due to the ode ISTB that may be preent. Provided that the dual-frequeny ode ISTB deviate ignifiantly from eah other, it then require one

7 to onider the dependeny of BeiDou BR-DCB upon atellite type. On the other hand, one an afely introdue atellite type independent BeiDou BR-DCB for reeiverpair of ommon type. T Coniteny teting of CUT CUT BeiDou BR DCB EO ISO EO MEO ISO MEO N.5α (,) Day of Year 3 Fig. 9 Three tet tatiti T (blak/red/green dotted line) ued to diagnoe the oniteny between CUT- CUT EO/ISO/MEO BR-DCB (f. Fig. 8). Critial value N.5 α (,) (magenta line) omputed uing level of ignifiane α = 5% Daily weighted average (n) EO ISO MEO CUT CUT BeiDou BR DCB DOY Day of Year 3 Fig. The daily weighted average etimate of CUT- CUT (Trimble-Septentrio) BeiDou BR-DCB in 3: EO reult (blak dotted line), ISO reult (red dotted line) and MEO reult (green dotted line). Only after day 84, CUT tart to reeive ignal from BeiDou ISO and MEO atellite. The vertial red line indiate the day (74) when the firmware verion of CUT wa upgraded from 4.7 to 4.8 Analyi of inter-day variability in BR-DCB etimate Although we did not mention it yet, one may reognize from Fig. 6 that an abrupt hange our in the DWA etimate of CUT-CUT3 BeiDou BR-DCB before day 8, and from Fig. 8 that there i a trend in the time erie of CUT-CUT BeiDou BR-DCB etimate. We will attempt to eek for the poible reaon that aount for the ourrene of uh two phenomena. Before doing o, we preent in Table 3 the tatiti of the DWA etimate Critial value of 5 group of BR-DCB retrieved for all three reeiverpair over 3, in whih the empirial tandard deviation value would provide u an overall impreion on the inter-day variability of eah group of BR-DCB etimate. In general it follow from Table 3 that, with repet to a ommon ontellation, the BR-DCB etimate retrieved for two reeiver-pair of mixed type (in partiular CUT- CUT3) alway have larger empirial tandard deviation than thoe for reeiver-pair of ommon type (CUT- CUT), thu implying more evident inter-day variability. Moreover, in addition to CUT-CUT3, EO/ISO/MEO BR-DCB etimate retrieved for CUT-CUT alo manifet obviou direpany in their mean value, whih an alo be attributed to BeiDou ode ISTB. Similar to what one an ee from Fig. 6, DWA etimate of CUT-CUT BeiDou BR-DCB depited in Fig. alo exhibit an abrupt hange. Both BD-DCB hange our onurrently at day 75 and their atual ize are roughly.5 n and.4 n, repetively. One very likely fator aounting for thi may be identified a firmware verion upgrade undergone by reeiver CUT at day 74. The reaon for thi an be explained a follow. In general, the reeiver ode biae depend not only on the hardware, but alo on the digital ignal proeing that may hange with a firmware verion upgrade [9]. Interetingly, we notie that all group of CUT-CUT BR-DCB etimate eem to have no expliit repone to firmware verion upgrade of CUT. Conidering the fat that the other reeiver CUT wa alo upgraded at the ame day and both reeiver are of ommon type (f. Table ), the hange in their abolute DCB aued by imultaneou firmware verion upgrade would be idential and thu ould not manifet themelve in the retrieved BR-DCB etimate. Aording to the literature devoted to NSS (albeit PS-only) reeiver DCB tudie (e.g. [8, 9, 6, 33, 34]), the temperature i generally aknowledged a a predominant fator aounting for reeiver DCB variation. With thi in mind, we aume that the interday variability in DWA etimate of CUT-CUT BeiDou BR-DCB (f. Fig. 8) i a diret onequene of varying temperature at the reeiver ite. To verify our aumption, we depit in Fig. the time erie of CUT- CUT EO BR-DCB etimate (dotted blue line), together with that of daily maximum temperature (dotted red line) oberved by a weather tation deployed about 8 km away from our reeiver ite. We determine the Pearon orrelation oeffiient ( r ) between the two time erie to quantify their tatitial dependene. For a tatitial ample ize greater than, a i the ae here, the abolute value of r greater than.54 i rated ignifiant. Here the omputed Pearon r value i equal to.788 and the orreponding p-value for teting the null hypothei of no orrelation againt the alternative that there i a nonzero orrelation i fairly mall ( ). Thi how that both time erie are highly orrelated and it thu ugget that the inter-day variability in BR-DCB etimate i indeed due to the temperature effet.

8 Table 3 Statiti of the DWA etimate of BR-DCB over 3: mean/empirial tandard deviation (n) Reeiver-pair PS BeiDou alileo EO ISO MEO CUT-CUT -3.63/ / / /.44.8/.5 (Trimble-Septentrio) CUT-CUT.5/ / /.9 -.6/..35/. (Trimble-Trimble) CUT-CUT3 (Trimble-Javad) -3.3/ / / / /.8. BR DCB veru daily maximum temperature 58 6 BR DCB veru daily maximum temperature CUT CUT EO BR DCB (n) BR DCB Temperature Day of Year 3 Fig. The daily weighted average etimate of CUT- CUT EO BR-DCB (blue dotted line) and the daily maximum temperature value (red dotted line) meaured by a weather tation deployed about 8 km away from the reeiver ite. The Pearon orrelation oeffiient between both time erie i.788 with a orreponding p-value of almot zero Reall that there exit three likely fator aounting for the reeiver DCB dependene on temperature: the antenna, the able and the reeiver hardware [8]. For our zero-baeline etup, the able an further be eparated into one antenna-plitter able ommonly hared by all the reeiver, a well a thoe plitter-reeiver able onneting the plitter to eah reeiver. One reaon for having temperature effet zero-baeline BR-DCB etimate might be aued by refletion in the able that depend on the antenna impedane and an lightly vary with temperature. Sine the radio frequeny path along the able to the two reeiver are not exatly idential, thee refletion would indue a different ode bia on both reeiver [9]. In thi ae, a both reeiver are of ommon type (Trimble NETR9), one would urmie that a large proportion of the effet due to the temperature on their BR-DCB etimate hould be largely anelled [35]. Thi may explain why in thi ae the peak-to-peak variation between the highet and the lowet BR-DCB etimate i only about.6 n Daily maximum temperature ( o C) CUT3 CUT PS BR DCB (n) BR DCB Temperature Day of Year 3 Fig. The daily weighted average etimate of CUT3- CUT PS BR-DCB (blue dotted line) and the daily maximum temperature value (red dotted line) meaured by a weather tation deployed about 8 km away from the reeiver ite. The time period indiated by the horizontal axi orrepond to day - of 3. The Pearon orrelation oeffiient between both time erie i.9 with a orreponding p-value of almot zero Similarly, Figure how the CUT-CUT3 PS BR-DCB etimate for the firt day of 3. Aide from that, the maximum temperature value at eah day i alo given. The Pearon r value determined for both time erie i a great a.9 orreponding to a p-value of zero. Thi again learly demontrate the effet of temperature upon the inter-day variability in another group of BR- DCB etimate. Moreover, the peak-to-peak variation of BR-DCB etimate now reahe roughly 3 n, poibly due to the fat that both reeiver are of mixed type. SUMMARY AND CONCLUSIONS In thi ontribution, we deribed a method for time-wie retrieval of BR-DCB employing ode meaurement imultaneouly olleted by two reeiver forming one zero-baeline from NSS ontellation tranmitting CDMA ignal. Thee time-wie etimate of the BR- DCB have therefore the ame high temporal reolution a the olleted NSS meaurement. We deribed two tatitial hypothei teting heme with the goal of teting, repetively, the intra-day tability of time-wie etimate of the BR-DCB and the oniteny between the DWA etimate of the EO/ISO/MEO BR-DCB Daily maximum temperature ( o C)

9 We arried out a field ampaign over an entire - year period (3) at the main ampu of Curtin Univerity in Bentley (Perth), during whih, dualfrequeny PS/BeiDou/alileo meaurement were olleted by four reeiver of three type onneted to one ommon antenna, with a ampling rate of 3 eond. We defined three independent reeiver-pair and for eah of them we retrieved the time-wie etimate of PS/EO/ISO/MEO/alileo BR-DCB. The main onluion drawn from analyzing thee BR-DCB etimate inlude: o For eah group of BR-DCB etimate, they are uffiiently table over a -day period; o For reeiver-pair of mixed type, poible inoniteny between EO/ISO/MEO BR- DCB etimate may our, mainly due to the effet of BeiDou ode ISTB; o The DWA etimate of BR-DCB may exhibit an abrupt hange indued by reeiver firmware upgrade, whoe ize an range from.4 n to.5 n; o The variability in the DWA etimate of the BR-DCB over a -year period how a high orrelation with the daily maximum temperature variation at reeiver ite. ACKNOWLEDMENTS Thi work ha been exeuted in the framework of the Poitioning Program Projet. New arrier phae proeing trategie for ahieving preie and reliable multi-atellite, multi-frequeny NSS/RNSS poitioning in Autralia of the Cooperative Reearh Centre for Spatial Information (CRC-SI). Thi work wa alo partially funded by the CAS/KNAW joint reearh projet Compa, alileo and PS for improved ionophere modeling. The eond author i the reipient of an Autralian Reearh Counil (ARC) Federation Fellowhip (projet number FF88388). All thi upport i gratefully aknowledged. REFERENCES [] Hernández-Pajare, M., et al., The ionophere: effet, PS modeling and the benefit for pae geodeti tehnique. Journal of eodey,. 85(): p [] Jin, S. and A. Komjathy, NSS refletometry and remote ening: New objetive and reult. Advane in Spae Reearh,. 46(): p. -7. [3] Jakowki, N., et al., Ionopheri pae weather effet monitored by imultaneou ground and pae baed NSS ignal. Journal of atmopheri and olar-terretrial phyi, 5. 67(): p [4] Yiyan, Z., et al., Ionopheri anomalie deteted by ground-baed PS before the Mw7. 9 Wenhuan earthquake of May, 8, China. Journal of atmopheri and olar-terretrial phyi, 9. 7(8): p [5] Zakharenkova, I., et al., Anomalou modifiation of the ionopheri total eletron ontent prior to the 6 September 5 Peru earthquake. Journal of atmopheri and olar-terretrial phyi, 8. 7(5): p [6] Banville, S., et al., lobal and Regional Ionopheri Corretion for Fater PPP Convergene. Navigation, 4. 6(): p [7] Montenbruk, O., P. Steigenberger, and A. Hauhild, Broadat veru preie ephemeride: a multi-nss perpetive. PS Solution, 4. DOI:.7/ [8] Yang, Y., et al., Preliminary aement of the navigation and poitioning performane of BeiDou regional navigation atellite ytem. Siene China Earth Siene, 4. 57(): p [9] Bartolomé, J.P., et al., Overview of alileo Sytem, in ALILEO Poitioning Tehnology 5, Springer. p [] Spit, J. and R. Warnant, Total eletron ontent monitoring uing triple frequeny NSS: Reult with iove-a/-b data. Advane in Spae Reearh,. 47(): p [] Spit, J. and R. Warnant, Total eletron ontent monitoring uing triple frequeny NSS data: A three-tep approah. Journal of Atmopheri and Solar-Terretrial Phyi, 8. 7(5): p [] Hernández-Pajare, M., et al., The IS VTEC map: a reliable oure of ionopheri information ine 998. Journal of eodey, 9. 83(3-4): p [3] Kehin, M., A new algorithm for ingle reeiver DCB etimation uing IS TEC map. PS Solution,. 6(3): p [4] Sardón, E. and N. Zarraoa, Etimation of total eletron ontent uing PS data: How table are the differential atellite and reeiver intrumental biae? Radio Siene, (5): p [5] Coo, D.S., et al., Variability of PS atellite differential group delay biae. Aeropae and Eletroni Sytem, IEEE Tranation on, 99. 7(6): p [6] Li, Z., et al., Two-tep method for the determination of the differential ode biae of COMPASS atellite. Journal of eodey,. 86(): p [7] Zhang, B., et al., Extration of line-of-ight ionopheri obervable from PS data uing preie point poitioning. Siene China Earth Siene,. 55(): p [8] Coter, A., et al., Auray of PS total eletron ontent: PS reeiver bia temperature dependene. Radio Siene, 3. 48(): p [9] Bruyninx, C., P. Defraigne, and J.-M. Sleewaegen, Time and frequeny tranfer uing PS ode and arrier phae: onite experiment. PS Solution, (): p. -. [] Ciraolo, L., et al., Calibration error on experimental lant total eletron ontent (TEC) determined with PS. Journal of eodey, 7. 8(): p. -.

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