PPP-RTK PLATFORM PERFORMANCE BASED ON SINGLE-FREQUENCY GPS DATA

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1 PPP-RTK PLATFORM PERFORMANCE BASED ON SINGLE-FREQUENCY GPS DATA Dennis Odik *, Pete J.G. Teunissen, and Baocheng Zhang Reseach Fellow, GNSS Reseach Cente, Depatment of Spatial Sciences, Cutin Univesity, GPO Box U987, Peth WA 85, Austalia; Tel: ; d.odik@cutin.edu.au Pofesso, GNSS Reseach Cente, Depatment of Spatial Sciences, Cutin Univesity, GPO Box U987, Peth WA 85, Austalia; Tel: ; Delft Institute of Eath Obsevation and Space Systems, Delft Univesity of Technology, PO Box 558, GB Delft, The Nethelands; p.teunissen@cutin.edu.au Reseache, Institute of Geodesy and Geophysics, Chinese Academy of Sciences Wuhan 77, P.R. China cham@whigg.ac.cn KEY WORDS: GPS, Pecise Point Positioning (PPP), PPP-RTK, ambiguity esolution, high-pecision positioning ABSTRACT: As an impovement ove conventional PPP, Real-Time Kinematic Pecise Point Positioning (PPP-RTK) is a pomising technique fo high-pecision (cm-level) caie-phase based emote sensing platfom positioning. The key to obtain these vey pecise positions is that the use should be able to esolve the ambiguities in the phase data to thei intege values, as then his phase data stats to act as if they wee vey pecise code data. In ode to do so, the use needs to apply coections to his GPS data. In addition to coections fo the satellite clocks and ionospheic delays, as with conventional PPP, cucial to estoe the integeness of the ambiguities is that the PPP-RTK use needs appopiate coections fo the satellite phase hadwae biases. In ou appoach these coections ae detemined by a egional netwok of CORS stations. To povide the most pecise coections to the PPP-RTK use, the coections should be based on a solution in which the netwok ambiguities ae esolved to thei intege values. Futhemoe, in ou appoach the ambiguity-fixed netwok ionospheic delays ae intepolated to the appoximate use location. So fa vey fast -even instantaneous- PPP-RTK intege ambiguity esolution pefomance has been epoted based on dual-fequency GPS data. Howeve, the technique becomes moe attactive when it can be applied to uses that opeate with low-cost mass-maket single-fequency eceives as well. In this contibution we demonstate that ou PPP-RTK appoach can be applied to these uses without any modification. Results ae pesented of the pefomance of single-fequency PPP-RTK fo both a high-gade and a low-gade GPS eceive. The conclusion eads that single-fequency PPP-RTK intege ambiguity esolution is feasible, even using a low-cost eceive: following an initialization time of less than 5 minutes the coect integes can be esolved in eal-time, thus poviding cm-level positioning.. INTRODUCTION The technique of Pecise Point Positioning (PPP) is based on GPS caie phase and code (eudo-ange) obsevations of a single eceive, employing coections fo, among othes, satellite obits, clocks and ionospheic delays obtained fom a woldwide netwok of GPS stations, fo example the pemanent GPS netwok of the Intenational GNSS Sevice (IGS). PPP was intoduced by Zumbege et al. (997) and the attainable instantaneous pecision fo a single-fequency use who employs global coections is typically at the level of a few dm (Bee and Tibeius, ). The key to fast and cm-level PPP lies in esolving the ambiguities that ae pesent in the phase data to intege values. Unfotunately, with the standad PPP technique this is not possible, because the ambiguities cannot be sepaated fom the satellite hadwae biases in the phase and code data. In this contibution we will pesent an appoach that allows the single-eceive use to pefom intege ambiguity esolution within shot time spans and consequently enable high-pecision positining. This PPP-RTK appoach is like standad PPP based on applying coections fo satellite clocks and ionospheic delays, but cucial to enable ambiguity esolution ae coections fo satellite phase biases, and these should have an appopiate definition. These coections should be estimated simultaneously fom a CORS netwok and tansmitted to uses. Advantage of ou PPP-RTK appoach is that it is not only suitable fo dual-fequency uses, but also fo uses employing low-cost single-fequency eceives. Although dual-fequency uses can do without ionospheic coections, these ae essential to speed up intege ambiguity esolution fo single-fequency uses; without ionospheic coections single-fequency PPP-RTK would suffe fom vey long

2 convegence times. Moeove, it is doubtful whethe ambiguity esolution would still make sense, since the float pecision would aleady be good enough afte a sufficiently long time span. In this pape the PPP-RTK concept is demonstated based on coections detemined fom a egional CORS netwok with inte-station distances of less than km. Advantage of such a elatively dense egional netwok is that the ionospheic coections can be detemined much moe pecise than using a global netwok and this should benefit single-fequency applications. It is assumed that the egional netwok povides coections fo satellite clocks, phase biases and ionospheic delays, but not fo satellite obits. These should be computed by the use by employing the IGS obit infomation. The pape is set up as follows. Section eviews the GPS phase and code obsevation equations, while Section discusses the CORS netwok coections that enable both PPP and PPP-RTK. Results of the pefomance of both techniques based on single-fequency GPS data collected with both a high-gade and a low-cost eceive ae given in Section. A special focus in this section is on the possible tempoal stability of the satellite phase biases. Section 5 ends the pape with conclusions.. BETWEEN-SATELLITE DIFFERENCED GPS PHASE AND CODE OBSERVATION EQUATIONS Let us assume a eceive tacking multi-fequency GPS phase and code data. Since the focus of this pape is on the satellite-dependent effects, ou stating point is fomed by the between-satellite diffeences (SD) of the lineaized phase and code obsevation equations fom which all eceive-specific unknowns ae emoved, in units of distance: T E(, ) ( u ) x( dt, ) ı M, () T E( p, ) ( u ) x( dt d, ) ı whee the diffeences ae fomed between satellite s and a chosen pivot satellite, denoted using the supescipt p: ( ) () s ( ) p. It is assumed that the positions of the satellites ae known. In these obsevation equations E ( ) denotes the mathematical expectation,, and p, the obseved-minus-computed SD obsevables fo phase and code espectively on fequency, u the SD eceive-satellite line-of-sight vecto, x the (incemental) eceive coodinates, dt the SD satellite clock eo,, and d, the SD satellite phase and code hadwae biases, ı the SD ionospheic delay with ( / ) its fequency-dependent coefficient, the zenith topospheic delay (ZTD), with the SD mapping function, the wavelength, and M,, ( ) t N, the SD phase ambiguity that consists of the initial phases of satellite, ( t), plus an intege SD ambiguity N,, both in units of cycle. All clock eos and hadwae biases ae given in units of distance. Both phase and code data ae assumed to be a pioi coected fo effects such as hydostatic toposphee, phase cente offsets, phase wind-up, solid eath tides, ocean loading, etc. Moe details on these coections can be found in (Kouba and Héoux, ).. CORS-BASED SINGLE-FREQUENCY PPP AND PPP-RTK In this section the coections ae discussed that need to be estimated fom a GPS CORS netwok in ode fo a use to cay out PPP as well as PPP-RTK. Fo PPP-RTK it is shown that using satellite phase bias coections with appopiate definition the ambiguities fo the use become intege.. Regional CORS Netwok Coections The egional CORS GPS netwok pocessing is based on keeping the positions fixed of both eceives (since these ae pecisely known), as well as of the satellites (fom IGS obit infomation). Unknown netwok paametes ae then, in tems of between-satellite single diffeences: satellite clocks, satellite phase biases, ZTDs, ionospheic delays and phase ambiguities. Since the netwok model is not of full ank, the netwok paametes ae only estimable as combinations of paametes in ode to emove the netwok s ank deficiency. Hee we will show ou cuent choice fo the combination of these netwok paametes. The estimable satellite clock paametes fom the egional netwok can be shown to be a function of the tue satellite clocks, plus the code biases on L and L, and the ZTD of the netwok s pivot eceive (Odik et al., ): dt, IF ( dt d, d, ) dt d, DCB () It is emaked that the tems between backets coespond to the ionosphee-fee satellite clocks as povided by the IGS that ae applied in standad PPP, i.e. dt, IF dt d, d,. Ou egional-based satellite clock poduct is howeve biased by the ZTD of the netwok s pivot eceive, since fo egional CORS netwoks ZTDs ae not estimated fo each eceive, but elative to the pivot eceive of the netwok. Futhemoe, the so-called

3 Diffeential Code Bias (DCB) can be ecognized, which is defined as DCB d, d, (Schae, 999). Essential to the pefomance of single-fequency uses is futhemoe that the netwok should povide the use with ionospheic coections. Fo standad PPP these can be obtained fom a Global Ionospheic Map, but fo a dense egional CORS netwok a moe sophisticated ionospheic poduct can be geneated: the ionospheic delay intepolated at the appoximate use location fom the netwok ionospheic delays (Odik et al., ): ı ı DCB () with ı the ionospheic delay intepolated fom the netwok ionospheic estimates. Simila to the satellite clock paamete, in the estimable ionospheic paamete the DCB shows up. To enable intege ambiguity esolution fo the PPP use the CORS netwok should povide coections fo the satellite phase bias paametes, defined as follows (Odik et al., ):, M, (, d, DCB ) () The between-satellite phase bias paamete is in fact a combination of the tue between-satellite phase bias,, biased by a combination of the satellite code biases on L and L (though d, and DCB ), plus the (non-intege) ambiguity of the netwok s pivot eceive ( M, ). We finally emphasize that the netwok paametes should be tansmitted to the uses, afte the netwok ambiguities ae fixed to integes, such that the use has the disposal of coections with the best possible pecision.. PPP Based on Regional Netwok Coections With the netwok coections identified, the single-fequency obsevation equations fo egional PPP can be given as: T E(,, ) ( u ) x M, (5) T E( p, p, ) ( u ) x with the phase and code obsevables now coected fo the ionosphee-fee satellite clocks and intepolated ionospheic delays fom the CORS netwok, see Eqs. () and ():, dt, IF ı () p, dt, IF ı The estimable ZTD fo the PPP use is elative to the netwok s pivot station:. Consequence of coecting the phase data in this way is that the estimable ambiguity tem becomes: M, M, (, d, DCB ) (7) Fom this equation it can be clealy seen that the estimable ambiguity paamete is not an intege.. PPP-RTK Based on Regional Netwok Coections We will now show that intege ambiguity esolution fo the PPP use becomes possible when coecting his phase data using the netwok s satellite phase biases. The obsevation equations emain exactly the same as in Eq. (5), as well as the coected code obsevables, howeve the coection to be applied to the phase obsevable becomes:, dt, IF, ı (8) p, dt, IF ı As consequence, the satellite phase bias coection, will eliminate the phase-code bias tem (, d, DCB ) in the biased ambiguity tem, see Eq. (7), such that the estimable phase ambiguity paamete becomes a combination of the between-satellite ambiguities of the PPP eceive and the between-satellite ambiguities of the netwok s pivot eceive, i.e.: M, M, M, N, N, N, (9) which is a double-diffeenced ambiguity and thus intege. The estimable PPP ambiguity has become a double diffeence because of the ambiguity infomation of the netwok s pivot eceive hidden in the satellite phase bias coection. High-pecision PPP based on intege ambiguity esolution can now be ealized using the following stepwise appoach: (i) Float solution: the use solves the model (5) applying the PPP-RTK coections as given in Eq. (8) using standad least-squaes; the position solution then coesponds to a egional PPP solution (ii) Intege ambiguity

4 esolution: the float ambiguity solution is input to the LAMBDA method (Teunissen, 995) to esolve the double-diffeenced integes; (iii) Fixed solution: If the intege solution can be accepted, a egional PPP-RTK solution is computed based on model (5) with the ambiguities held fixed.. RESULTS OF CORS-BASED PPP AND PPP-RTK In ode to test the pefomance of ou PPP-RTK concept we detemined coections fom a egional CORS netwok and applied these to single-fequency use data. The CORS netwok is depicted in Figue and consists of fou stations of the GPS Netwok Peth in Westen Austalia, a pivately opeated CORS netwok. The fou stations ae at distances of about km and ae all equipped with the same Timble NetR5 eceives. The location at Cutin Univesity Bentley campus (CUT) was assigned as (static) ove station. At this station, GPS data wee collected using two eceives: a high-gade dual-fequency Timble NetR9 eceive, plus a low-gade single-fequency u-blox AEK-T eceive. Fo all CORS netwok stations dual-fequency phase and code obsevations have been collected above a cut-off elevation of deg duing the full day of Octobe with a sampling inteval of sec. 5 km ROTT TORK MIDL satellite clock [m] x epoch [ sec] 9 satellite clock [m] x epoch [ sec] 9 CUT MDAH iono delay [m] epoch iono delay [m] epoch Figue : (Left) CORS netwok (yellow tiangles) used fo geneating the PPP(-RTK) poducts fo use location CUT (black tiangle). (Right) Examples of ambiguity-fixed satellite clock and intepolated ionospheic delay estimates fo full acs of PRNs and duing Octobe, whee an epoch inteval is sec is used. In the gaphs the satellite s elevation is plotted as well.. Results of Regional CORS-Based Netwok Coections Fom the dual-fequency CORS netwok data pecise estimates fo satellite clock paametes, satellite phase bias paametes and intepolated ionospheic delays (fo location CUT) wee obtained afte netwok ambiguity esolution. Examples of estimates of the ambiguity-fixed satellite clocks and intepolated ionospheic delays ae shown in Figue fo full acs of and. It can be seen that both satellite clocks and ionospheic delays ae changing significantly in time. The tempoal behavio of the satellite phase biases, the paametes that enable PPP-RTK, is howeve much diffeent. Figue (left columns) depicts the ambiguity-fixed L satellite phase bias estimates fo the full day and fo all satellites in view by the netwok. Fo almost all satellites moe than one gaph is included, because duing a full day the same satellite can be tacked moe than once. It can be seen that the phase bias estimates seem to be quite stable duing the ac: the visible fluctuation is due to the noise in the estimates (seveal dm), but the moving aveage (depicted as the yellow cuve in each of the gaphs) only shows little fluctuation. If the satellite phase biases tun out to be sufficiently stable, they can be tansmitted to uses with a less fequent ate than at evey epoch. This tempoal stability of the satellite phase bias paametes has been futhe analyzed by means of statistical hypothesis testing. Pe satellite ac a null hypothesis ( H : E( ( i)) constant i, i.e. the satellite phase bias paamete is time-constant) is tested against an altenative hypothesis ( HA : E( ( i)) constant i, i.e. the satellite phase bias paamete is not time-constant). It can be shown that the test statistic coesponds to the oveall model test (Teunissen, ) of the model having as obsevations the satellite phase bias time seies pe ac and as unknown paamete the constant phase bias, incopoating the vaiance matices of the time-vaying phase biases obtained fom the netwok pocessing in the stochastic model. This oveall model test is not only executed based on all phase biases fo one ac, but stating fom the second epoch of the ac (note that at the fist epoch thee is no edundancy) as to demonstate the effect of accumulating the tempoal phase biases on the test outcomes. The oveall model test statistic has a cental F-distibution with the fist set of degees of feedom equal to the accumulated numbe of epochs minus (the edundancy) and the second set of degees of feedom set to infinity. The ight fou columns of Figue show the oveall model test outcomes (blue cuve), including citical values. In ode to see how sensitive the citical value is to the choice of significance level, the citical value is computed based on a significance level of. (ed cuve), as 9

5 well as fo a significance level of.5 (geen cuve). Fom the gaphs it can be seen that fo none of the satellite acs the test outcomes exceed both citical values. Fom this we may conclude that based on this dataset thee is no eason to assume that the phase bias paametes ae unstable in time duing the ac of a satellite. PRN PRN PRN PRN PRN 7 PRN PRN PRN PRN PRN PRN PRN PRN PRN PRN 7 PRN 8 PRN 9 PRN PRN PRN PRN PRN PRN PRN PRN 8 PRN PRN 7 8 PRN 8 PRN 8 8 PRN 7 PRN 8 PRN PRN 5789 PRN PRN PRN PRN 8 PRN PRN 7 8 PRN PRN 7 8 PRN PRN 7 8 PRN PRN PRN 9 8 PRN 8 PRN PRN 7 PRN PRN 8 PRN Figue : (Left) Ambiguity-fixed L satellite phase bias paametes pe satellite ac fo the full day of Octobe. The satellite phase biases (in blue) ae expessed in metes and fo each ac the moving aveage is plotted (in yellow). In each gaph the satellite s elevation is plotted as well (in deg; geen cuve). (Right) Test outcomes (blue) vs. citical value based on significance level of. (ed) and citical value based on significance level of.5 (geen) to test the stability of the satellite phase biases.. Results of Regional CORS-Based PPP and PPP-RTK In a next step the netwok coections ae applied to coect the use s high-gade and low-gade eceive data and pefom PPP and PPP-RTK. Fist the satellite clock paametes plus intepolated ionospheic delays ae used to enable egional-based PPP. Figue (left two columns) depicts the hoizontal position scatte solutions and vetical time seies obtained fom pocessing of the obsevation model (). The model is solved in a tuly epoch-by-epoch manne, whee the position and ambiguities ae solved fo each epoch, iespective of the solutions of othe epochs. The Noth-East-Up components ae obtained by compaing the position outcomes with known (gound-tuth) coodinates of station CUT. While the (empiical) hoizontal pecision of PPP with the high-gade eceive is at the

6 dm level and at sub-m level fo the vetical component, the esults fo the low-gade eceive ae about a facto wose. This diffeence is due to the quality of the code data, which is a facto wose fo the ublox eceive compaed to the Timble eceive. The epoch-by-epoch PPP solutions ae known to be fully diven by these code data. PPP high-gade PPP low-gade PPP-RTK high-gade PPP-RTK low-gade Noth [m] std East:.m std Noth:.m mean East:.85m mean Noth:.5m Noth [m] std East:.5m std Noth:.7m mean East:.7m mean Noth:.m Noth [m].5 std East:.59m std Noth:.7m mean East:.5m mean Noth:.8m Noth [m].5 std East:.5 m std Noth:.7m mean East:.m.5 mean Noth:.9m std Up:.75m 5 std Up:. m. std Up:.m. std Up:.m mean Up:.m epoch [ sec] mean Up:.7m epoch [ sec].5.5 mean Up:.m epoch [ sec].5.5 mean Up:.m epoch [ sec] Figue : PPP and PPP-RTK positioning esults based on single-fequency GPS phase and code data. It is emaked that the PPP esults ae obtained by epoch-by-epoch kinematic pocessing, while those fo PPP-RTK ae based on accumulation of epochs. Fo the same high-gade and low-gade single-eceive data PPP-RTK was subsequently enabled by coecting the phase data fo the satellite phase biases. Fo these esults these have been tansmitted to the use at evey epoch. Due to the weakness of the single-fequency obsevation model (), instantaneous o epoch-by-epoch ambiguity esolution was not feasible; howeve ambiguity esolution was successful by accumulating epochs (based on the constancy of the ambiguities); fo the Timble eceive afte.5 min on aveage and afte min on aveage fo the ublox eceive. Afte ambiguity esolution, the hoizontal pecision of the kinematically solved fixed positions is at sub-cm level, while the vetical pecision is about cm, fo both types of eceives; see Figue (ight two columns). 5. CONCLUSIONS In this pape it has been shown that intege ambiguity esolution is possible fo single-eceive Pecise Point Positioning of platfoms. The obsevation model of this PPP-RTK method is intinsically the same as fo standad PPP ; the diffeence lies in the coections applied to the use s phase data. One can do standad PPP with coections fo among othes satellite clock and ionospheic delay estimated fom a CORS netwok; howeve the essential coection that enables intege ambiguity esolution is the satellite phase bias paamete, which is in fact a combination of the (tue) satellite phase bias, togethe with the (non-intege) ambiguity of the netwok's pivot station and dual-fequency satellite code biases. Ou data pocessing indicates that these satellite phase bias paametes seem to be elatively stable duing a satellite ac. Ou PPP-RTK appoach is not only suitable fo dual-fequency but also fo single-fequency applications. Results demonstate that single-fequency PPP ambiguity esolution is feasible, based on convegence times of less than 5 minutes, even using low-gade eceives. The kinematic position accuacy with the intege ambiguities fixed is at sub-cm level hoizontally, and at the level of a few cm in the vetical diection. ACKNOWLEDGMENTS This wok has been executed in the famewok of the Positioning Pogam Poect. ("New caie phase pocessing stategies fo achieving pecise and eliable multi-satellite, multi-fequency GNSS/RNSS positioning in Austalia") of the Coopeative Reseach Cente fo Spatial Infomation (CRC-SI). Pete J.G. Teunissen is the ecipient of an Austalian Reseach Council (ARC) Fedeation Fellowship (poect numbe FF8888). The CORS netwok data in this study has been povided by the GPS Netwok Peth. All this suppot is gatefully acknowledged. REFERENCES Bee, R.J.P. van, and C.C.J.M. Tibeius,. Real-time single-fequency pecise point positioning: accuacy assessment. GPS Solutions, DOI.7/s9--8-, 8 p. Kouba, J., and P. Héoux,. Pecise point positioning using IGS obit poducts. GPS Solutions, 5(), pp. -8. Odik, D., P.J.G. Teunissen, and B. Zhang,. Single-fequency intege ambiguity esolution enabled pecise point positioning. Submitted to Jounal of Suveying Engineeing. Schae, S., 999: Mapping and pedicting the Eath's ionosphee using the Global Positioning System, Ph.D. thesis, Astonomical Institute, Univesity of Bene, Switzeland. Teunissen, P.J.G., 995. The least-squaes ambiguity decoelation adustment: a method fo fast GPS intege ambiguity estimation. Jounal of Geodesy, 7, pp Teunissen, P.J.G.,. Testing theoy, an intoduction. Seies on Mathematical Geodesy and Positioning, Delft. Zumbege, J.F., M.B. Heflin, D.C. Jeffeson, M.M. Watkins, and F.H. Webb, 997. Pecise point positioning fo the efficient and obust analysis of GPS data fom lage netwoks. Jounal of Geophysical Reseach, (B), pp