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1 Citation: Zhang Baocheng Teunien Peter J.G. Odik Denni. 2. A Novel Un-differenced PPP-RTK Concept. The Journal of Navigation. 64 (S): pp. S8-S9. Additional Information: If you wih to contact a Curtin reearcher aociated with thi document you may obtain an addre from Copyright 2 The Royal Intitute of Navigation Alternate Location: Permanent Link: The attached document may provide the author' accepted verion of a publihed work. See Citation for detail of the publihed work.

2 A Novel Un-differenced PPP-RTK Concept B.C. Zhang P. J.G. Teunien 2 3 D. Odik 2 (: Intitute of Geodey Geophyic Chinee Academy of Science Wuhan China) (2: GNSS Reearch Centre Curtin Univerity of Technology Perth Autralia) (3: Delft Intitute of Earth Obervation Space Sytem Delft Univerity of Technology The Netherl) ( b.zhang@whigg.ac.cn; p.teunien@curtin.edu.au) In thi contribution a novel un-differenced (UD) (PPP-RTK) concept i.e. a ynthei of Precie Point Poitioning Network-baed Real-Time Kinematic concept i introduced. In the firt tep of our PPP-RTK approach the UD GNSS obervation from a regional reference network are proceed baed upon re-parameteried obervation equation correction for atellite clock phae biae (interpolated) atmopheric delay are calculated provided to uer. In the econd tep thee network-baed correction are ued at the uer ite to retore the integer nature of hi UD phae ambiguitie which make rapid high accuracy uer poitioning poible. The propoed PPP-RTK approach wa teted uing two GPS CORS network with inter-tation ditance ranging from 6 to km. The firt tet network i the northern China CORS network the econd i the Autralian Perth CORS network. In the tet of the firt network a dual-frequency PPP-RTK uer receiver wa ued while in the tet of the econd network a low-cot ingle-frequency PPP-RTK uer receiver wa ued. The performance of fat ambiguity reolution the high accuracy poitioning of the PPP-RTK reult are demontrated. KEY WORDS. GNSS. 2. PPP-RTK. 3. Integer Ambiguity Reolution. 4. Satellite Phae Bia.. INTRODUCTION. Precie Point Poitioning (PPP) Network-baed Real-Time Kinematic (NRTK) are two repreentative technique for high accuracy Global Navigation Satellite Sytem (GNSS)-baed poitioning (Kouba Heroux 2; Wuebbena et al 25). Baed on obervation from a t-alone GNSS receiver the IGS precie orbit clock product PPP poitioning accuracy can reach cm- to dm-level for tatic or kinematic application (Bree et al 29). However due to the fact that PPP-baed olution ue real-valued float ambiguitie i.e. non-integer un-differenced (UD) phae ambiguitie long convergence time are experienced (Zumberge et al 997). NRTK doe not have thi drawback a obervation from one of the (virtual) network reference tation are ued by the NRTK uer the virtual tation obervation contain the error correction that are derived from the reference network. Thi allow the NRTK uer to perform fat Integer Ambiguity Reolution (IAR) realie poitioning with accuracy at the cm-level uing only a few epoch of data (Vollath et al 2; Wu et al 28; Odik et al 2). A novel UD PPP-RTK concept which i a ynthei of PPP NRTK i propoed analyzed in thi paper ome of it tet reult performance aement are demontrated. There are two difference between our PPP-RTK concept thoe exiting one (for example Wuebbena et al 25; Zhang et al 26; Geng et al 2; Li et al 2). Firt the UD obervation rather than their ionophere-free combination are ued to directly provide the ionopheric correction. Secondly all the

3 correction can be obtained in one go i.e. no tep-wie proceing procedure are required thu the conitency amongt different type of correction can be aured. Two ditinct part in the implementation of our PPP-RTK approach are. Firt the UD obervation are proceed at the network level. After eliminating the rank deficiencie with re-parameterization or S-bai choice (De Jonge 998) the network parameter can be etimated in real-time with a Kalman-filter or recurive leat quare. Once the network ambiguitie are uccefully reolved the ambiguity-fixed (biaed) atellite clock (biaed) atellite phae biae the (interpolated) ionopheric delay for the uer location will be aved ready for ending to the PPP uer that are within the network region. Secondly after correcting their obervation with the network correction the PPP uer can perform IAR poitioning ut a they do in the cae of NRTK. In the following ection we firt derive the obervation equation of our PPP-RTK approach pecial attention i given to rank defect parameter etimability. Subequently the performance of the PPP-RTK approach will be teted it capability for fat IAR high accuracy uer poitioning i demontrated. 2. THE PPP-RTK CONCEPT. In thi ection the full-rank obervation equation of our PPP-RTK concept are given. Thi i done for data proceing of both the network the uer ite. Although the work preented in thi contribution only ued ingle- dual-frequency GPS data the propoed PPP-RTK concept i alo applicable to multi-frequency multi-gnss application. In the following ub-ection we firtly dicu the network obervation equation then the uer obervation equation. 2.. Network Proceing. For a receiver-atellite pair r the UD carrier phae code obervation equation on frequency can be given a (Teunien Kleuberg 998): E( ϕ ) = ρ μ I + λ N + φ φ r r r r r E( p ) = ρ + μ I + b b r r r r () ϕ r where E(.) denote the expectation operator p r denote the phae code obervable repectively ρ = l + τ + dt dt r r r r l i the um of all the frequency-independent item r i the receiver-atellite range τ r the lant tropopheric delay dt r dt are the receiver atellite clock error repectively I r i the (firt-order) lant ionopheric delay on the L frequency 2 2 = 2 N r ( μ λ / λ μ.6469) i the integer phae ambiguity λ the wavelength of frequency φ r φ b are the frequency-dependent phae biae while r b are that of their code counterpart. Note that all the bia term are in unit of meter. For the purpoe of implifying our equation in the following ection the following aumption for the network proceing are made: The network conit of n tation ( r = n ) all the tation track the ame m atellite ( = m ) on the L L2 frequencie ( = 2 );

4 The geometric range of the receiver to the atellite l r i known from the known poition of the reference tation the atellite provided by the IGS precie orbit. For practical purpoe the flexibility of our approach we now dicu the approach for the following two cae: ) the atellite clock information i provided externally i.e. it i available to the uer 2) the atellite clock information i not available thu it mut be provided by the regional network When Satellite Clock Are Available. The atellite clock given below are aumed known from an external ource e.g. from IGS dt = dt + μ b b 2 I 2 μ2 μ2 Then the code obervation equation expreed in Equation () can be reformulated r r I r r (2) E( p l + dt ) = τ + dtr + μ I (3) p In Equation (3) all the code biae originating from r dt I are aborbed by the etimable receiver clock the lant ionopheric delay. Their re-parameteried form are therefore given a: μ dt = dt + b b Ir = Ir ( B Br) μ2 2 r r r r2 μ2 μ2 (4) B = b2 b where the B = b b r r2 r are the atellite receiver Differential Code Biae (DCB) repectively (Sardon Zarraoa 997; Yuan Ou 2). Similarly the network phae obervation equation can be obtained after the ame re-parameteriation: E( ϕ l + dt ) = τ + dt μ I + λ N + φ φ (5) r r I r r r r r Due to the oppoite ign of the ionopheric group phae delay the code biae within dt r I r cannot be cancelled a in the code obervation expreed in Equation (3). Hence the re-parameteried phae biae are given a: μ b b μ φ μ b b μ φ 2 r r2 r = φr + Br μ2 μ2 2 2 = φ + B μ2 μ2 N r Due to the linear dependence between φ r φ f there would be a rank defect of ( n+ m) in the deign matrix of Equation (5). One poible olution to thi problem i to chooe per frequency the φ phae biae of the firt receiver (here ) the ambiguitie from the firt atellite to all involved

5 receiver (here N r N ) the ambiguitie from the firt receiver to all viible atellite (here ) a S-bai (Teunien et al 2). Then the network phae equation can be expreed a: E( ϕ l + dt ) = τ + dt μ I + λ N + φ φ (6) r r I r r r r r φ = φ φ λ where r r r N φ = φ + λ N Nr = Nr N r. Thu in Equation (6) N r we can find the integer double differenced (DD) ambiguitie. To avoid poible additional rank defect the lant tropopheric delay τ r in both Equation (3) (6) can be further parameteried: τ = mf T (7) r r r where Tr i the tation-wie Zenith Tropopheric Delay (ZTD) mf r i a mapping function. To ummarie when the atellite clock information i available from an external ource the PPP-RTK network proceing of the phae code data can be baed on the following et of full-rank re-parameteried obervation equation: E( p l + dt ) = mf T + dt + μ I E( ϕ l dt ) mf T dt μ I λ N φ φ r r I r r r r r r+ I = r r+ r r + r + r When Satellite Clock Are Unavailable. When the external atellite clock are not available they can be derived from a regional reference network. In thi cae the network obervation equation need to accommodate the additional unknown additional (near) rank defect. Thee rank defect are due to the linear dependence between the atellite clock receiver clock the near linear dependence between the atellite clock the ZTD mapping function. Thi problem can be olved by chooing the clock ZTD of the firt receiver to be the S-bai. Then the final full-rank obervation equation of the network become: ( ) = E p + r lr mfr Tr dt r dti + μ Ir E( ϕ l ) = mf T + dt dt μ I + λ N + φ φ r r r r rr I r r r (8) where T r = Tr T dt i the etimable ZTD I = dti dt+ mf T dt r = dtr dt are the redefined atellite receiver clock repectively. The network correction that are provided to the PPP uer include dt I φ which are eential for the uer fat IAR in PPP the interpolated I r which alo help to improve the performance of IAR (Yuan et al 28a; Yuan et al 28b; Li et al 2). Although not teted in thi contribution the ZTD from the network proceing method can be alo ued to facilitate the uer PPP-IAR. The network proceing trategy preented above can be ued in both real-time pot-proceing mode.

6 2.2. PPP Proceing. In the previou ection it wa dicued that the ionopheric delay i.e. in Equation (4) derived from the network proceing need to be interpolated in the patial domain for generating the ionopheric delay correction at the PPP uer approximate poition. Several interpolation method can be ued for thi purpoe the Kriging method (Jarlemark Emardon 998) wa elected in thi reearch. The covariance function elected for the ue of thi method i a imple linear function of the inter-tation ditance. The reulting interpolated ionopheric delay can be expreed a: n u = r r r = I f I E I I B B μ ( u ) = u ( u) 2 (9) I r where fr i the coefficient of the interpolation ubcript u denote the uer I u i the ionopheric delay of the uer receiver u to the atellite B i the atellite DCB which i free from the interpolation proce B u i the interpolated DCB for the PPP uer. After applying the network-baed correction the elimination of rank defect the linearied PPP-RTK obervation equation become: ( + ) = μ Δ + E p u lu dti u xu mfu Tu+ dtu + μ Iu E( ϕ l + dt + φ ) = μ Δ x + mf T + dt μ I + λ N + φ ( E Iu ) = Iu ΔBu μ2 u u I u u u u u u u u () l Where u i the approximate geometric range μu i the unit vector of the geometric range from the atellite to the uer receiver Δxu denote the vector increment of the receiver poition the form of T u dt I u u ( u u) term B B B are imilar to thoe in the network equation ee Equation (8). The Δ = in Equation () tem from the difference between the interpolated ionopheric delay I u the etimable ionopheric delay I u. N Obviouly in Equation () u φ u are linear dependent it reulting rank defect could be eliminated by chooing per frequency the firt atellite ingle differenced (SD) ambiguity N u a the λ N + φ S-bai. After u u in Equation () i replaced with the full-rank obervation equation for PPP uer can be obtained. λ N + φ where u u φ = φ + λ N u u u

7 The ource of atellite clock etimate dt I in Equation () i either the IGS clock etimate dt I or the regional network-baed atellite clock etimate dt I which depend on the trategy adopted in the network proceing a dicued in ection Baed upon both type of atellite clock the uer PPP-RTK obervation equation can be cat into a unified frame a given by Equation (). Note however that the interpretation of the etimable parameter T dt u u are different in the two cae: when provided from IGS the reult of dt I the T u dt u are in the IGS frame; while when calculated from the regional network the etimate of dt I T dt u u can only be relative to the T dt that have been aborbed by dt I. In our cae tudie dicued in the next ection the atellite clock parameter are aumed to be unavailable they were etimated from the regional network. 3. CASE STUDIES. Baed on the two CORS network one in northern China the other in Perth Wetern Autralia our PPP-RTK approach wa teted. The performance of the network proceing the fat IAR capability for both dual- ingle-frequency PPP at the uer end are demontrated. 3.. Northern China CORS: Dual-frequency PPP. Thi CORS network i a medium-cale network coniting of 4 tation with inter-tation ditance ranging from 6 to km ee Figure. Trimble GPS data on two frequencie: L L2 (L-L2-C-P2) on 29th April 29 with 3 ec ampling rate were collected. Figure. The configuration of the northern China CORS network coniting of 4 reference tation (triangle) the BDAG tation (circle) i the uer tation Network Proceing Reult. Our network proceing trategy i characteried a follow. The tard deviation of the UD phae code obervation were et to 3 mm 3 cm repectively. All the obervation were weighted according to their elevation the elevation cut-off angle of 5 degree wa ued. A Kalman-filter wa ued for the real-time data proceing. The reidual ionopheric ZTD

8 tropopheric delay are modeled a a rom walk proce; the clock error are modeled a white noie while the DD integer ambiguitie are treated a contant. For both network-iar uer-iar the LAMBDA method wa ued (Teunien 995; Teunien et al. 996). For the validation of the integer ambiguity reult the fixed-failure rate FFRatio tet wa ued (Teunien Verhagen 2). The epoch-wie full IAR wa tarted after the filter epoch (5 min) initialiation. The float ambiguitie correponding to newly rien atellite were only conidered for reolution after 6 epoch (3 min) filtering. Panel (a) of Figure 2 how the reult of ambiguity reolution with a ucce rate of about %. The epoch with wrongly fixed ambiguitie are correponding to the period during which the atellite were frequently riing etting a revealed in panel (b). Ratio ratio threhold (a) Number of atellite (b) 6 Figure 2. IAR reult for the northern China CORS: panel (a) FFRatio tet- threhold value veru time; panel (b) number of tracked atellite veru time

9 L atellite phae biae [cycle] (a) L2 atellite phae biae [cycle] (b) Interpolated ionopheric delay [m] (c) - Interpolation error [m] (d) Figure 3. Proceing reult of the northern China CORS network: panel (a) & (b): L & L2 atellite phae biae (in unit of cycle) repectively; panel (c) & (d): interpolated ionopheric delay their error (in unit of meter) repectively. Different color correpond to different atellite Figure 3 how the network proceing reult. In the two upper panel of thi figure the etimated dual-frequency phae biae are hown for each atellite continuou arc. The two lower panel of Figure 3 how the interpolated ionopheric delay their error/accuracy. Thee error etimate are obtained from comparing the interpolated delay with the reference value of the ionopheric delay at BDAG (uer) which could be derived from pot-proceing the GPS data of the network together with BDAG. Note that mot of the interpolation error/accuracy at BDAG i le than dm for all the atellite except thoe in ome period when the ionophere wa in diturbed condition (i.e. 2:-3: ) Dual-frequency PPP Reult. During the tatic PPP proceing the epoch-wie interpolated ionopheric delay were ued a peudo obervation whoe tard deviation were et to dm to account for the interpolation error.

10 .2 (a) Fixed poitioning catter 2 (b) Float poitioning catter. Meter Meter -. STD North:.3 cm STD Eat:.9 cm STD Up: 5. cm STD North: 2. dm STD Eat:.8 dm STD Up: 4.2 dm -2 Epoch for IAR (c) Figure 4. Dual-frequency PPP-RTK poitioning for the uer tation BDAG within the northern China CORS network: panel (a) (b): fixed & float poitioning catter repectively; panel (c): number of epoch needed for ucceful IAR veru time of the day Figure 4 how the dual-frequency PPP-RTK performance at the BDAG location. The bottom panel indicate that the number of epoch needed for ucceful IAR i alway le than 3 (5min) mot of the time even under (5min). The correponding accuracy of the ambiguity-fixed poitioning (with repect to the known ground-truth) i about cm 5 cm for the horizontal vertical component repectively while the accuracy of the ambiguity-float poitioning i in the range of 2-4 dm Perth CORS: Single-frequency PPP. The Perth CORS network conit of 6 tation with inter-tation ditance in the range of 6-8 km ee Figure 5. The dual-frequency (L-L2-C-P2) Trimble NetR5 GPS data collected on 23rd October 2 with the 3 ec ampling rate wa elected for the tet of the network proceing while the ingle-frequency (C-L) UBlox GPS data wa ued for the tet of the uer PPP proceing. The configuration of the network the uer tation are diplayed in Figure 5. The tet reult are hown in Figure 6.

11 Figure 5. Configuration of the Perth CORS network (triangle) the ingle-frequency PPP uer: UB (tar); the C i a dual-frequency receiver for forming a zero baeline with UB.8 Ratio Interpolated ionopheric delay [m] (a) (c) Satellite Number Interpolation error [m] (b) (d) Figure 6. Perth network proceing reult: panel (a) FFRatio tet- threhold value veru time; panel (b) number of tracked atellite veru time; panel (c) & (d) interpolated ionopheric delay at UB their error repectively. Different color correpond to different atellite

12 3.2.. Perth Network Proceing Reult. For the network data proceing the ame trategy a for the northern China network wa ued. Panel (a) in Figure 6 how the reult of ratio tet for network IAR with ucce rate roughly 257/2782 = 92.4%. The performance i lightly wore than that of the northern China network. Thi may be attributed to both the cale of the network the increae in the number of ambiguitie per epoch. To weight out the performance of ionophere interpolation the reference ionopheric delay at UB are derived from pot-proceing the dual-frequency GPS data from the reference network the C. Panel (d) in Figure 6 how the differencing value of the interpolated ionopheric delay thee reference from which the STD value calculated for the ionopheric interpolation preciion i.4 dm (Ciraolo et al 27) Single-frequency PPP Reult. The procedure etting were imilar a before but with the tard deviation of the peudo ionopheric obervable et to.4 dm..6 (a) Fixed poitioning catter 2 (b) Float poitioning catter.3 Meter Meter -.3 STD North: 3.2 cm STD Eat: 2.8 cm STD Up: 8.6 cm STD North: 2.5 dm STD Eat: 2.8 dm STD Up: 4.9 dm -2 Epoch for IAR (c) Figure 7. Reult of PPP-RTK at the ingle-frequency UB tation each panel ha the ame meaning a thoe in Figure 4 Similar to Figure 4 Figure 7 how the full IAR performance of the ingle-frequency PPP-RTK poitioning. From the bottom panel it can be een that the maximum number of epoch needed for IAR in PPP i le than 4 (2min) the averaging number of epoch needed for IAR i about (5min). The accuracie of the ambiguity-fixed poitioning in the horizontal component are in the range of 2-3 cm in the vertical direction i le than dm. In contrat the accuracie of the ambiguity-float poitioning in three component are in the range of 2-5 dm. 4. CONCLUSIONS. In thi contribution we decribed a novel PPP-RTK approach demontrate it potential for high accuracy poitioning which i due to the realied PPP-uer integer ambiguity reolution capabilitie. To emphaie the flexibility of our approach we alo how the data proceing method for the two the eae: with without atellite clock information provided externally.

13 In our PPP-RTK approach the UD GNSS network obervation are proceed by olving a re-parameteried full-rank ytem of obervation equation. The re-parameteriation eliminate the ytem rank defect thereby etimable parameter in the network can be obtained. Thee etimable parameter include the SD (biaed) receiver clock the (biaed) atellite clock the (biaed) phae code intrumental delay the DD ambiguitie the SD ZTD the ionopheric model parameter. After network ambiguity i reolved the PPP-uer ue the relevant ambiguity-fixed network parameter (e.g. biaed atellite clock atellite phae bia interpolated ionopheric lant delay) in hi own etimation procedure which enable the PPP-uer to perform integer ambiguity reolution realie cm-level poitioning. Our PPP-RTK concept combine the merit of both PPP network-baed RTK. It performance i demontrated by the tet of two CORS network: one i a northern China network the other i a Wetern Autralia network near Perth. ACKNOWLEDGMENTS Thi work wa conducted in the context of the Autralian ASRP reearch proect Space Platform Technologie. Data from the Wet Autralian Network i kindly provided by GPS Network Perth. The author thank two reviewer Dr Suqin Wu Prof. Xiufeng He for their contructive comment. The econd author i the recipient of an Autralian Reearch Council (ARC) Federation Fellowhip (proect number FF88388). All thi upport i gratefully acknowledged. REFERENCES Bree R. J. P. Tiberiu C. C. J. M. Hauchild A. (29). Real time atellite clock in ingle frequency precie point poitioning. Proceeding of the ION GNSS 29 Savannah Georgia USA. Ciraolo L. Azpilicueta F. J. Brunini C. Meza A. Radicella S. M. (27). Calibration error on experimental lant total electron content (TEC) determined with GPS. Journal of Geodey 8-2. De Jonge P. J. (998). A proceing trategy for the application of the GPS in network. Netherl Geodetic Commiion. Geng J. Teferle F. N. Meng X. Dodon A. H. (2). Toward PPP-RTK: Ambiguity reolution in real-time precie point poitioning. Advance in pace reearch doi:.6/.ar Jarlemark P. O. J. Emardon T. R. (998). Strategie for patial temporal extrapolation interpolation of wet delay. Journal of Geodey Kouba J. Heroux H. (2). Precie point poitioning uing IGS orbit clock product. GPS Solution Li X. Zhang X. Ge M. (2) Regional reference network augmented precie point poitioning for intantaneou ambiguity reolution. Journal of Geodey Odik D. Verhagen S. Teunien P. J. G. Hernez-Paare M. Juan M. J. Sanz J. Samon J. Toaint M. (2). LAMBDA-Baed Ambiguity Reolution for Next-Generation GNSS Wide Area RTK. Proceeding of the 2 International Technical Meeting of the Intitute of Navigation San Diego California USA. Sardon E. Zarraoa N. (997). Etimation of total electron-content uing GPS data: how table are the differential atellite receiver intrumental biae? Radio Science Teunien P. J. G. (995). The leat quare ambiguity decorrelation adutment: a method for fat GPS integer ambiguity etimation. Journal of Geodey Teunien P. J. G. Kleuberg A. (998). GPS for Geodey 2nd edition. Springer-Verlag. Teunien P. J. G. Verhagen S. (29). The GNSS ambiguity ratio-tet reviited. Survey Review Teunien P. J. G. De Jonge P. J. Tiberiu C. C. J. M. (996). Volume of the GPS ambiguity earch pace it relevance for integer ambiguity reolution. Proceeding of the 996 9th International Technical Meeting of the Satellite Diviion of the Intitute of Navigation ION GPS-96. Part (of 2) Kana City MO USA. Teunien P. J. G. Odik D. Zhang B. C. (2). PPP-RTK: reult of CORS network-baed PPP with integer ambiguity reolution. Journal of Aeronautic Atronautic Aviation Vollath U. Deking A. Lau H. Pagel C. Wagner B. (2). Multi-bae RTK poitioning uing Virtual Reference Station. Proceeding of the ION GPS 2 Salt Lake City Utah USA. Wu S. Q. Zhang K. F. Silcock D. (28). An Invetigation of Performance Difference of Regional Atmopheric Model for Network RTK A Cae Study in Victoria. Proceeding of International Sympoium on GPS/GNSS 28 Tokyo Japan. Wuebbena G. Schmitz M. Bagge A. (25). PPP-RTK: Precie Point Poitioning uing tate-pace repreentation in RTK network. Proceeding of the ION GNSS 25 Long Beach California USA. Yuan Y. B. Ou J. K. (2). An improvement on ionopheric delay correction for ingle frequency GPS uer-the APR-I cheme. Journal of Geodey Yuan Y. B. Huo X. L. Ou J. K. Zhang K. F. Chai Y. J. Wen D. B. Grenfell R. (28a). Refining the Klobuchar ionopheric coefficient baed on GPS obervation. IEEE tranaction on aeropace electronic ytem Yuan Y. B. Tcherning C. C. Knuden P. Xu G. C. Ou J. K. (28b). The ionopheric eclipe factor method (IEFM) it application to determining the ionopheric delay for GPS. Journal of Geodey Zhang K. Wu F. Wu S. Rizo C. Robert C. Ge L. Yan T. Gordini C. Kealy A. Hale M. Ramm P. Amuen H.

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