remote sensing

Article On the Applicability of Galileo FOC Satellites with Incorrect Highly Eccentric Orbits: An Evaluation of Instantaneous Medium-Range Positioning

Jacek Paziewski ID , Rafal Sieradzki and Pawel Wielgosz * ID

Institute of Geodesy, University of Warmia and Mazury in Olsztyn, 10-719 Olsztyn, Poland; [email protected] (J.P.); [email protected] (R.S.) * Correspondence: [email protected]

Received: 20 December 2017; Accepted: 26 January 2018; Published: 30 January 2018

Abstract: This study addresses the potential contribution of the first pair of Galileo FOC satellites sent into incorrect highly eccentric orbits for geodetic and surveying applications. We began with an analysis of the carrier to noise density ratio and the stochastic properties of GNSS measurements. The investigations revealed that the signal power of E14 & E18 satellites is higher than for regular Galileo satellites, what is related to their lower altitude over the experiment area. With regard to the noise of the observables, there are no significant differences between all Galileo satellites. Furthermore, the study confirmed that the precision of Galileo data is higher than that of GPS, especially in the case of code measurements. Next analysis considered selected domains of precise instantaneous medium-range positioning: ambiguity resolution and coordinate accuracy as well as observable residuals. On the basis of test solutions, with and without E14 & E18 data, we found that these satellites did not noticeably influence the ambiguity resolution process. The discrepancy in ambiguity success rate between test solutions did not exceed 2%. The differences between standard deviations of the fixed coordinates did not exceed 1 mm for horizontal components. The standard deviation of the L1/E1 phase residuals, corresponding to regular GPS and Galileo, and E14 & E18 satellite signals, was at a comparable level, in the range of 6.5–8.7 mm. The study revealed that the Galileo satellites with incorrect orbits were fully usable in most geodetic, surveying and many other post-processed applications and may be beneficial especially for positioning during obstructed visibility of satellites. This claim holds true when providing precise ephemeris of satellites.

Keywords: Galileo; GNSS; RTK; satellite positioning

1. Introduction Galileo—the first European global navigation satellite system providing worldwide positioning, navigation and timing services—has been under extensive development since the early 2000s. The first two experimental satellites—GIOVE-A and GIOVE-B—were launched in 2005 and 2008, respectively. The satellites were the part of the Galileo System Test Bed (GSTB) [1]. After the initial delay of the programme, in recent years we can observe acceleration of the system development. The final constellation will comprise 30 satellites in total, evenly spread on three medium earth orbits including 24 operational plus two spare satellites per plane defining 24/3/1 Walker constellation [2,3]. At present (October 2017) the Galileo constellation consists of 18 satellites; however, this includes one with “not unusable”, two with “testing” and one with “not available” status. The current constellation consists of satellites belonging to in-orbit validation (IOV) and full operational capability (FOC) phases. The former phase, which has already been accomplished, used four satellites launched in 2011 and 2012 to validate the system. The latter comprises operational satellites launched from 2014 onwards.

Remote Sens. 2018, 10, 208; doi:10.3390/rs10020208 www.mdpi.com/journal/remotesensing Remote Sens. 2018, 10, 208 2 of 19

On 22 August 2014, the first two FOC satellites (GSAT0201-E18 and GSAT0202-E14), also named Doresa and Milena, respectively, were unintentionally injected into a wrong orbit. The failure was caused by a technical problem—specifically, by an interruption of propellant supply to the thrusters. On the next day, it was announced that the actual inclination of these satellites’ orbits is ~5◦ lower than the nominal one. Furthermore, the eccentricity of the orbit reached 0.29, which is much higher than the nominal one of 0.0002. Therefore, these satellites were in December 2014 and March 2015 moved by a series of correction manoeuvres into an improved, but still highly eccentric, orbit. This, however, consumed a significant amount of the on-board fuel. Afterwards, the satellites started transmission of the navigational signals [4]. Selected parameters of the actual and nominal E14 & E18 Galileo orbits are listed in Table1. The open question is the potential contribution of the first pair of FOC satellites to the Galileo services and applications. Due to format restrictions of the orbital parameters, E14 and E18 satellites are not included in the broadcast navigation message. Specifically, actual deviations of the semimajor axis and eccentricity exceed the nominal values by far over the limit. Accepting the premise that the maximum value of the eccentricity applied to the broadcast navigation message is 0.03125, the actual value exceeds the limit and reaches the level of 0.16. The nominal value of the semimajor axis (29,600 km) deviates by a value of 1620 km, which also exceeds the limit of 87 km. These facts seem to prevent the application of the E14 & E18 satellites to real-time solutions. Notwithstanding this, the satellites’ observations may be applied to post-processing applications, since several GNSS analysis centres provide post-mission products such as satellite clock corrections and orbits. As former studies showed, the quality of such E14 & E18 orbits may be considered as not worse than that of nominal FOC and IOV satellites [5]. Moreover, the eccentricity of the satellite orbits offers several possibilities for scientific applications including general relativity studies. It is recognised that an elliptic orbit of a satellite causes a periodic modulation of the gravitational redshift [6]. This phenomenon may be investigated by taking advantage of the high stability of the on-board H-maser clocks and the high eccentricity of the E14 & E18 orbits [7]. Furthermore, satellite observations may be used in a number of post-mission surveying, geodetic, and geodynamics applications, which is, in a sense, the goal of this paper.

Table 1. Selected parameters of E14 and E18 Galileo FOC satellites’ orbits [8].

GSAT0201 (5-Doresa) GSAT0202 (6-Milena) PRN Number/NORAD IDNominal Orbit E18/40128 E14/40129 Launch Date 22 August 2014 22 August 2014 Signal Transmission Date 29 November 2014 17 March 2015 Semi-major axis (km) 29,599.8 27,978 27,978 Eccentricity 0.0001 0.15601 0.15167 Revolution period (h) 14.08 12.97 12.97 Inclination (◦) 56 49.775 49.874 Minimum orbital height (km) 23,220 17,382 17,382 Maximum orbital height (km) 23,240 25,818 25,818

Since the initial phases of the Galileo program, the observational data were applied and analysed in several ways. This includes the signal analysis and positioning performance. The former studies of Galileo signals were devoted to phase and code noise, multipath, and cross-correlation [9–13]. The latter issue, applied to both single-system and multi-constellation single-point positioning, was investigated in [14–18]. Moreover, at this point we should acknowledge several studies devoted to precise positioning including both absolute (PPP) and relative (RTK) algorithm development and performance assessment. Example of single-system and combined PPP results may be found in [19–23], while the application of GIOVE and IOV Galileo signals to RTK was examined in [13,24]. In [25], single-frequency RTK positioning was analysed; in [26] selected methods for GPS + Galileo signals integration were studied and assessed, while [27] was devoted to Galileo IOV + FOC. At this point, it should be noted that the aforementioned studies did not include Galileo E14 and E18 satellites. Remote Sens. 2018, 10, 208 3 of 19

Moreover, most of these studies, based on real signals, were also limited to close-range RTK—single short baselines. Therefore, in order to extend knowledge in this field, in this paper we analyse the potential use of Galileo satellites with highly eccentric orbits in medium-range instantaneous RTK positioning. Nowadays, RTK positioning is considered a highly effective and reliable method of precise coordinate determination and so is a standard in many commercial and scientific applications. However, the starting point, which was a single-baseline single-system RTK positioning, suffered from several disadvantages such as limited baseline length and longer time to fix during higher ionosphere activity. Within the last decades, several advances in the RTK algorithms were introduced. These led to the development of the network-RTK mode, utilising atmospheric corrections derived from active reference networks. Taking advantage of these new algorithms, it was possible to extend the distance between reference sites and user receivers, and thus extend the service coverage area. This resulted in so-called wide area RTK, with baseline length up to dozens and even hundreds of kilometres (see [28–31]). Simultaneously, to support Positioning, Navigation and Timing applications (PNT), unprecedented interest was directed to algorithm and methodology development for combining multi-constellation signals. Several contributions were devoted not only to algorithm development and assessment [26,32], but also to characterisation of the inter GPS-Galileo system biases both in precise relative (RTK) and absolute methods (PPP) [33–37]. Thus, the RTK method can be considered as under extensive development and being used for a growing number of applications. The main objective of this paper is to evaluate the applicability of the E14 & E18 satellites to precise GNSS positioning. In this contribution we focus on relative kinematic positioning as an instantaneous solution in multi-baseline mode. The prerequisite of precise relative positioning is the correct ambiguity resolution. As expected, reliable single-epoch ambiguity resolution is obviously challenging [38–41]. On the other hand, such an approach is resistant to cycle-slips, and may be beneficial for better assessing the established and compared positioning scenarios. To present a comprehensive study, in the following section we start with the analysis of code and phase signals noise, with special attention paid to E14 & E18 satellites. Such analysis may be beneficial for establishing, e.g., an advanced stochastic model of positioning [42]. The characteristic of stochastic properties is followed by presentation of the observation model of multi-constellation relative kinematic positioning. Furthermore, the performance of the instantaneous multi-station medium-range positioning is assessed using single-system or combined GPS + Galileo dual-frequency data. The computations were performed using GNSS data processing software developed at the University of Warmia and Mazury in Olsztyn. In the last section, a summary and conclusions are provided.

2. Analysis of Signal Power and Noise It can be expected that varying the height of E14 and E18 satellites should influence satellite signal strength and may lead to some modifications of its stochastic properties. Thus, in this work the positioning performance was preceded by evaluation of phase and code observational noise for GPS and Galileo measurements, with special attention to E14 and E18 satellites. In order to ensure full coverage of elevation angle domain by observations, raw data with 1 s interval were processed during a period of two weeks (3–16 October 2017). The noise analysis involved stations used subsequently for evaluation of precise positioning, i.e., BYCE, CHLE, IAWA and OLSZ. The experiment was based on data collected at four sites in Poland (Figure1). All these sites are equipped with Trimble NETR9 receivers. Three of them are equipped with geodetic TRM115000.00 antennas, whereas the last one (OLSZ) uses a choke-ring TRM59900.00 antenna. Remote Sens.Remote2018 ,Sens.10, 2082018, 10, x FOR PEER REVIEW 4 4of of 19 19

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FigureFigure 1. Baselines 1. Baselines andstations and stations processed processed in thein the experiment. experiment.

2.1. Signal2.1. Power Signal Power Figure 1. Baselines and stations processed in the experiment. It is wellIt knownis well known that the that observational the observational noise noise is basically is basically related related to to the the powerpower of the satellite satellite signal at the receiver, and the stochastic properties of GNSS data can be described as a function of signal2.1. at Signal the receiver, Power and the stochastic properties of GNSS data can be described as a function of this indicator [43,44]. Furthermore, it was also confirmed that the carrier to noise density ratio (C/N0) this indicator [43,44]. Furthermore, it was also confirmed that the carrier to noise density ratio (C/N0) forIt BDS-IGSOis well known and thatGEO the satellites, observational which arenoise characte is basicallyrised by related a much to higherthe power altitude, of the is satellite3–4 dB-Hz for BDS-IGSOsignallower at thethan and receiver, common GEO satellites, and BDS-MEO the stochastic which satellites are properties characterised[45,46]. ofThus, GNSS the by data starting a much can bepoint higher described of the altitude, investigations as a function is 3–4 dB-Hzgivenof lowerthis thanin indicator this common section [43,44]. BDS-MEO is the Furthermore, analysis satellites of theit was [carrier45 also,46]. confto Thus, noirmedise thedensity that starting the ratio carrier point for E14 to of noise and the E18density investigations satellites ratio (C/N0)registered given in this sectionfor atBDS-IGSO different is the analysis andaltitudes. GEO of Forsatellites, the this carrier purpose, which to noiseare we charactecomputed densityrised ratio5-min by foramean much E14 values higher and E18of altitude, C/N0 satellites at twois 3–4 registeredfrequencies, dB-Hz at differentlowerE1 altitudes. thanand E5a, common Forfor all this BDS-MEO FOC purpose, Galileo satellites satellites. we computed [45,46]. Subsequently, Thus, 5-min the meanthestarting reference values point level of the C/N0 of investigationsC/N0 at for two common frequencies, given ones in this section is the analysis of the carrier to noise density ratio for E14 and E18 satellites registered E1 and E5a,was fordetermined all FOC Galileo through satellites. averaging Subsequently, in 10° bins theof referenceelevation levelangle. of The C/N0 summary for common of these ones at different altitudes. For this purpose, we computed 5-min mean values of C/N0 at two frequencies, was determinedcomputations through for averagingtwo selected in 10 stations,◦ bins of IAWA elevation and angle. OLSZ The (two summary top and of two these bottom computations panels, E1 and E5a, for all FOC Galileo satellites. Subsequently, the reference level of C/N0 for common ones for two selectedrespectively), stations, is given IAWA in Figure and OLSZ2. According (two topto the and results, two bottomit can be panels,confirmed respectively), that registered is C/N0 given wasvalues determined depend throughon the varying averaging radius in of 10° highly bins ecce of ntricelevation orbits. angle.At high The elev summaryations, where of satellitesthese in Figure2. According to the results, it can be confirmed that registered C/N0 values depend on computationswere practically for two at minimalselected altitudesstations, (~17,000–18,000IAWA and OLSZ km), (two C/N0 top increased and two from bottom 1 and panels, 5 dB-Hz. the varyingrespectively),Interestingly, radius is of given at highly the in first Figure eccentric frequency 2. According orbits. (Figure At to 2, highthe left results, column), elevations, it can strong be where confirmed discrepancies satellites that betweenregistered were practically results C/N0 for at minimalvaluessatellites altitudes depend E14 (~17,000–18,000 on and the E18 varying are observed, radius km), C/N0of whereas highly increased ecce at E5antric (right from orbits. 1column) andAt high 5 dB-Hz.they elev areations,Interestingly, consistent where to satellites each at the other first frequencywereand (Figurepractically equal 2about, left at column),minimal2.5 dB-Hz. altitudes strongThis divergence discrepancies(~17,000–18,000 was dete between km),cted C/N0 at resultsall increasedstations for satellitesand from seems 1 and E14 to be5 and dB-Hz. related E18 areto observed,Interestingly,the whereas different at at powerthe E5a first (rightof frequency E1 signal column) emitted(Figure they by2,are leftboth consistentcolumn), satellites. strong toAt eachlow discrepancies elevations other and the equalbetween enhancement about results 2.5 of for dB-Hz.C/N0 This divergencesatellitesdid not E14 exceed was and detected E18 2 dB-Hz are observed, at in all all stations cases. whereas Furthermore, and at seems E5a (right tothe be signalcolumn) related strength they to the are values different consistent registered power to each at of maximalother E1 signal and equal about 2.5 dB-Hz. This divergence was detected at all stations and seems to be related to emitted byheight, both which satellites. was similar At low to elevations the nominal the one enhancement of Galileo orbit, of C/N0are coincident did not with exceed average 2 dB-Hz C/N0 in the different power of E1 signal emitted by both satellites. At low elevations the enhancement of C/N0 all cases.pattern Furthermore, obtained the for signalremaining strength satellites. values The registered common difference at maximal between height, levels which of C/N0 was similarfor both to did not exceed 2 dB-Hz in all cases. Furthermore, the signal strength values registered at maximal the nominalstations one (~3 of dB-Hz) Galileo seems orbit, to are be connected coincident with with different average antenna C/N0 type. pattern The results obtained for sites for BYCE remaining and height,CHLE, which equipped was similar the same to asthe IAWA, nominal not one included of Galileo here, orbit,are generally are coincident consistent with with average the latter. C/N0 satellites.pattern The obtained common for differenceremaining betweensatellites. The levels common of C/N0 difference for both between stations levels (~3 of dB-Hz) C/N0 for seems both to be connectedstations with (~3 differentdB-Hz) seems antenna to be connected type. The with results different for sites antenna BYCE type. and The CHLE, results equipped for sites BYCE the sameand as IAWA,CHLE, not included equipped here, the same are generallyas IAWA, not consistent included with here, the are latter.generally consistent with the latter.

Figure 2. Cont. Remote Sens. 2018, 10, 208 5 of 19 Remote Sens. 2018, 10, x FOR PEER REVIEW 5 of 19

FigureFigure 2. Carrier-to-noise 2. Carrier-to-noise density density ratio ratio of of the the Galileo Galileo E14E14 and E18 E18 signals signals on on different different frequencies frequencies as as functionfunction of satellite of satellite elevation elevation and and altitude altitude (two (two top top panels—IAWA,panels—IAWA, two two bottom bottom panels—OLSZ). panels—OLSZ). Black Black lines correspondlines correspond to average to average C/N0 C/N0 for for Galileo Galileo satellites satellites signals (E1 (E1 or or E5a) E5a) at atparticular particular station. station.

2.2. Code Measurement Noise 2.2. Code Measurement Noise The precision of code observations is generally limited by the combined influence of receiver Thenoise precision and site-specific of code observations multipath effect. is generally The aggregate limited byimpact the combinedof both these influence factors of receiveris usually noise and site-specificevaluated using multipath multipath effect. combinations, The aggregate which impact are formed of both from these dual-frequency factors is usually code evaluated and phase using multipathobservations combinations, [47]. Under which the areassumption formed from dual-frequency , the multipath codecombinations and phase for observationssatellite i and [47]. Underreceiver the assumption k can be writtenf1 > fas2, follows: the multipath combinations for satellite i and receiver k can be written as follows: 2 2 1 = −1+ + + + (1) , −1 , −1 , ,, ,, ,  2   2  = i − + i + i ≈ i + i + i MP1 Pk, f 1 2 λ f1 ϕk, f 2 λ f2 ϕk, f Mk,P, f ek,P, f Bk,MP1 (1) 21 = −µ − 1 +1 µ −−11 2 +1 +1 (2) , −1 , −1 , ,, ,, ,     where P andi φ are dual-frequency2µ i code and2µ phase observables,i respectively;i i λ is ithe signal MP2 = Pk f − λ f ϕk f + − 1 λ f ϕk f ≈ Mk P f + ek P f + Bk MP (2) wavelength; M, and2 µ denote− 1 multipath1 , 1 andµ noise− 1 effects affected2 , 2 code measurements;, , 2 , , 2 B is a, constant2 wherefactorP and includingϕ are dual-frequency ambiguity terms code and and hardware phase delay observables, biases (eliminated respectively; by theλ is subtracting the signal the wavelength; mean values of MP1 or MP2 time series for entire arc; and is the constant factor applied for conversion M and e denote multipath and noise effects affected code measurements; B is a constant factor including of the ionosphere delay on first frequency into that on second frequency according to the formula: ambiguity terms and hardware delay biases (eliminated by the subtracting the mean values of MP1 or MP2 time series for entire arc; and µ is the constant factor applied for conversion of the ionosphere delay on first frequency into that on second frequency according to the formula:

2 2 µ = f1 / f2 . (3) Remote Sens. 2018, 10, x FOR PEER REVIEW 6 of 19 Remote Sens. 2018, 10, 208 6 of 19 = ⁄ . (3) TheThe aboveabove equationsequations werewere appliedapplied toto generategenerate timetime seriesseries ofof dual-frequencydual-frequency multipathmultipath combinationscombinations for for all all observational observational arcs. arcs. For For this this purpose purpose we used we usedcode codeobservations observations C1C, C2W C1C, (GPS), C2W ◦ (GPS),C1X, C5X C1X, (Galileo) C5X (Galileo) and the and corresponding the corresponding phase phase data. data. Subsequently, Subsequently, their their RMSs RMSs in in 10° 10 bins ofof elevationselevations werewere computedcomputed separately for GPS, commoncommon Galileo, and satellites with eccentric orbits. TheThe resultsresults obtainedobtained forfor twotwo selectedselected stationsstations areare presentedpresented inin FigureFigure3 .3.

Figure 3. Variation of code noise and multipath with elevation at stations IAWA (top panel) and OLSZ Figure 3. Variation of code noise and multipath with elevation at stations IAWA (top panel) and OLSZ (bottom(bottom panel).panel).

With regard to results obtained for E14 and E18 satellites, one can conclude that the precision of With regard to results obtained for E14 and E18 satellites, one can conclude that the precision of their code observations is at the same level as for other Galileo satellites. Comparing only European their code observations is at the same level as for other Galileo satellites. Comparing only European satellites, the highest differences in elevation patterns did not exceed 3 cm and seem to be related to satellites, the highest differences in elevation patterns did not exceed 3 cm and seem to be related site-specific multipath effect. On the other hand, the results demonstrated significant distinctions to site-specific multipath effect. On the other hand, the results demonstrated significant distinctions between stations and systems. The former issue is a consequence of choke ring antenna installed at betweenOLSZ station, stations which and systems.allows improved The former multipath issue is ami consequencetigation. Thus, of chokeerrors ringof code antenna observables installed are at OLSZsignificantly station, lower which than allows at the improved IAWA site. multipath The improvement mitigation. at Thus, high elevations errors of code reaches observables about 10 arecm significantlyfor both Galileo lower (C1X) than atand the GPS IAWA (C1C) site. code The improvementsignals. Only at in high the elevationscase of C2W reaches observations about 10 cmis the for bothdecrease Galileo of code (C1X) observation and GPS (C1C) errors code for OLSZ signals. site Only much in thelower, case not of exceeding C2W observations 5 cm. Furthermore, is the decrease the ofresults code basically observation confirm errors that for the OLSZ precision site much of Galileo lower, code not observations exceeding 5 cm.outperforms Furthermore, those theof the results GPS basicallyones. RMS confirm values that of MP1 the precisionand MP2 ofcombinations Galileo code at observations high elevations outperforms for the European those of thesystem GPS are ones. at RMSthe level values of 0.19 of MP1 m, 0.16 and m MP2 (IAWA) combinations and 0.08at m, high 0.08 elevations m (OLSZ). for The the corresponding European system values are for atthe GPS level are of0.22 0.19 m, m,0.23 0.16 m mand (IAWA) 0.13 m, and 0.19 0.08 m, respectively. m, 0.08 m (OLSZ). The analysis The corresponding executed for valuesthe remaining for GPS sites are 0.22(BYCE m, 0.23and mCHLE) and 0.13showed m, 0.19 a similar m, respectively. precision Theof code analysis observations executed as for for the IAWA remaining station sites (see (BYCE Table and 2). CHLE)Analysing showed these a results, similar one precision can also of codeconclude observations that the precision as for IAWA of E5a station code (see measurements Table2). Analysing at sites thesewith common results, one antennas can also (BYCE, conclude CHLE, that theIAWA) precision is higher of E5a than code for measurements the E1 signal. at This sites improvement, with common antennasobserved (BYCE,for all three CHLE, cases, IAWA) varies is higherbetween than 0.02 for m theand E1 0.06 signal. m. This improvement, observed for all three cases, varies between 0.02 m and 0.06 m.

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Table 2. RMS of dual-frequency multipath combinationscombinations atat zenithzenith (m).(m).

GalileoGalileo GPSGPS GalileoGalileo E14E14 Galileo E18 E18 StationStation (Except(Except #14 #14 and and E18) E18) MMPP11 MMPP2 2 MPMP1 1 MMPP22 MMPP1 MMPP2 MMPP11 MPMP22 BYCEBYCE 0.20 0.20 0.21 0.21 0.16 0.16 0.14 0.14 0.16 0.13 0.16 0.13 0.13 CHLECHLE 0.21 0.21 0.22 0.22 0.19 0.19 0.13 0.13 0.17 0.13 0.18 0.13 0.13 IAWAIAWA 0.22 0.22 0.23 0.23 0.18 0.18 0.15 0.15 0.20 0.20 0.16 0.16 0.19 0.17 0.17 OLSZOLSZ 0.13 0.13 0.19 0.19 0.08 0.08 0.07 0.07 0.07 0.08 0.07 0.08 0.08

2.3. Phase Measurement Noise The analysisanalysis ofof phase phase noise noise at at a particulara particular frequency frequency is usuallyis usually performed performed with with zero zero or ultra-short or ultra- baselines,short baselines, which which allows allows for elimination for elimination of short-term of short-term variations variations of atmospheric of atmospheric influence. influence. However, theHowever, stations the used stations in the used given in experiment the given experime belong tont active belong reference to active networks reference and networks are distant and from are eachdistant other from by each a few other tens by of a few kilometres. tens of kilometres. In such a In case such the a combinedcase the combined weighted weighted phase noise phase can noise be derivedcan be derived from single-station from single-station data using data triple-frequency using triple-frequency combinations. combinations. In our case itIn was our realised case it using was therealised difference using ofthe two difference ionosphere-free of two ionosphere-f combinationsree (DIF) combinations according (DIF) to the according following equationto the following [12,45]: equation [12,45]:       DIF ϕi , ϕi , ϕi = IF ϕi , ϕi − IF ϕi , ϕi k,f1 ,k,f2 ,k,f3 =k, f1 ,k, f2 −k, f1,k, f3  , , , , , , , (4) f 2 f 2 f 2 f 2 = 1 − 1 i − 2 i + 3 i (4) 2 2 2 2 λ f1 ϕk, f 2 2 λ f2 ϕk, f 2 2 λ f3 ϕk, f f1 − f2 f1 − f3 1 f1 − f2 2 f1− f3 3 = − , − , + , − − − − This triple-frequency combination combination theoretically theoretically el eliminatesiminates all all geometric geometric fa factorsctors and and influence influence of ofthe the first-order first-order term term ofof ionospheric ionospheric refraction. refraction. Thus Thus,, the the right right side side of of the the equation should containcontain aggregated weighted phase noise, constant factor including ambiguity term, hardware delay and inter-frequency biases The last parameterparameter was recognisedrecognised andand investigatedinvestigated in GLONASSGLONASS (due toto satellite individualindividual frequencies) frequencies) and and GPS GPS signals. signals. However, However, it was it was reported reported in [12 in,48 [12,48]] that forthat the for latter the systemlatter system such datasuch are data affected are affected by variations by variations of inter-frequency of inter-frequency bias, bias, which which have have to be to eliminated. be eliminated. In this work work triple-frequency triple-frequency combinations combinations were were created created taking taking advantage advantage of ofL1, L1, L2, L2,L5 and L5 and E1, E1,E5a, E5a, E5b E5bsignals signals of GPS of GPS and andGalile Galileoo systems, systems, respectively. respectively. The long-t The long-termerm variations variations associated associated with withinter-frequency inter-frequency bias, bias,also observed also observed in our in case, our case,werewere removed removed using using a fourth-order a fourth-order polynomial. polynomial. The Thefurther further algorithm algorithm of DIF of DIF combination combination data data processi processingng was was analogous analogous as as in in the the case case of multipath combinations. A summary of phase noise variations withwith elevationelevation angleangle isis presentedpresented inin FigureFigure4 4..

Figure 4. Variation of phase noise and multipath (DIF) with elevation at stations IAWA (left panel) Figure 4. Variation of phase noise and multipath (DIF) with elevation at stations IAWA (left panel) and and OLSZ (right panel). OLSZ (right panel).

Looking at these results, it can be observed that DIF phase noise for E14 and E18 is slightly lower Looking at these results, it can be observed that DIF phase noise for E14 and E18 is slightly lower (up to 1 mm) than for the other Galileo satellites. On the other hand, this improvement is detectable (up to 1 mm) than for the other Galileo satellites. On the other hand, this improvement is detectable only at selected elevations (mainly low) and is probably an effect of the lower multipath in these only at selected elevations (mainly low) and is probably an effect of the lower multipath in these cases. cases. At high elevations the differences do not exceed 0.3 mm and 0.1 mm at IAWA and OLSZ, respectively. The results from stations with better equipment prove that the level of phase noise for

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At high elevations the differences do not exceed 0.3 mm and 0.1 mm at IAWA and OLSZ, respectively. The results from stations with better equipment prove that the level of phase noise for both analysed satellites is the same as for the others. The comparison of RMS values for IAWA and OLSZ sites confirms that applying a choke ring antenna reduces the phase multipath in the entire elevation angle domain. As a consequence, RMS of DIF combination declines from 2.3 mm and 8.8 mm to 1.6 mm and 5.0 mm at high and low elevations, respectively. Unfortunately, OLSZ station did not record the third GPS frequency, and thus the discussed results are given for IAWA station only. Taking into account ionosphere-free combination coefficients, it can be expected that RMS of DIF for the GPS system should be higher, but only by about 5% (assuming the same precision at all frequencies). However, in the case of IAWA this deterioration is about 25%, suggesting that Galileo phase observations are less noisy. These findings need further investigation.

3. Instantaneous Multi-Constellation Relative Positioning: Methodology and Performance Our first goal in this section is to briefly present a multi-constellation geometry-based relative positioning model. This is followed by an empirical evaluation of the instantaneous positioning with a focus on the application of Galileo E14 and E18 satellites.

3.1. Loosely Combined Relative Positioning Model with Parameterised Ionospheric Delays Nowadays, there are several functional models for combined processing of multi-constellation signals in a relative mode with double-differences (DD) (see [26]). Basically, we can distinguish between two general approaches: intra-system and inter-system combination. The former uses separate pivot satellite for each constellation when forming double-differenced observables. Thus, the observational model is free from the DD observables formed across constellations. This methodology can be considered a classical approach, applied commonly to constellations with no overlapping frequencies. The latter approach, termed tightly integrated or tightly coupled, uses a single common pivot satellite for all constellations. As a result, in this positioning model there are both intra-system and inter-system DD observables (mixed). Such an approach can be especially beneficial in urban canyons with limited satellite visibility, due to a higher number of DD observables in comparison to the intra-system combination. When using the tight integration we do not lose one satellite as pivot per constellation. The prerequisite of application of the tight integration is the presence of common frequencies in combined constellation, such as L1/E1 and L5/E5a in GPS and Galileo [49]. This model can strengthen the solution; however, it requires handling of inter-system biases. Specifically, in the relative mode these biases are differential values (differential ISBs). As studies show, the phase and code differential ISBs may be considered stable [37]. This creates an opportunity for priori calibration of the biases and further correction of observations. As a result, inter-system phase ambiguities for overlapping frequencies may be fixed to their integer values. At this point we should also highlight the most recent contributions considering an inter-system model with no overlapping frequencies. A tightly combined GPS + BDS RTK model with real-time estimation of differential ISB was proposed in [50]. Nevertheless, as studies show, both tight and loose coupling may provide comparative performance, especially in the case of a high number of tracked satellites [26,50]. Thus, considering the above, in this study we apply an intra-system model for assessing the performance of the relative kinematic positioning with the use of Galileo E14 & E18 satellites. Over the last decades several approaches were recognised for modelling of the ionospheric delay in relative GNSS positioning. Their application mainly depends on the baseline length, state of the ionosphere, positioning mode or session length. Among others, one highly effective approach is the ionosphere weighted model, commonly applied for medium- and long-range RTK [38,39,51–54] as well as instantaneous positioning [40,55]. The ionosphere weighted model can be considered a generalised approach to ionosphere delay parameterisation, taking into account information on both a priori values of ionosphere delays and its stochastic properties. Thus, the estimated DD ionospheric delays are weighted in the model estimation process by the application of the pseudo-observables, which allows Remote Sens. 2018, 10, 208 9 of 19 for constraining parameters using a priori variance factors. Thanks to the above, it is possible to tune these parameters to the expected values of the factual double differenced ionospheric delays. If we, however, do not introduce a priori information of the ionosphere delays, the model can be labelled the ionosphere float. On the other hand, positioning supported with ionospheric corrections considered as errorless is commonly termed the ionosphere fixed model [56]. The latter approach is, however, not applied in this study, since we take advantage of ionosphere float model. The relative positioning model based on geometry with parameterised ionospheric delays is given in Equation (5). The equations are presented for dual frequency phase and code observables; however, the model may be extended for multi-frequency signals accordingly [32]:

 ij ij ij ij ij ij λ f ϕ = ρ + T − I + λ f N + e  1 kl, f1 kl kl kl 1 kl, f1 kl,ϕ, f1  ij ij ij ij ij  P = ρ + T + I + e kl, f1 kl kl kl kl,P, f1 ij ij ij ij ij ij (5) λ ϕ = ρ + T − µI + λ N + e  f2 kl, f2 kl kl kl f2 kl, f2 kl,ϕ, f2  ij ij ij ij ij  P = ρ + T + µI + e kl, f2 kl kl kl kl,P, f2 where λ is the signal wavelength, ϕ is the carrier phase observable in cycles, P is the code pseudorange, ρ denotes the geometric satellite to receiver range, N is the integer ambiguity, superscripts i, j and k, l states for satellites and stations, respectively, subscripts f 1 and f 2 correspond to the first and second applied frequencies, I is the ionospheric delay at the first frequency, e denotes multipath and observation noise. T is the tropospheric delay, the double differenced value of which can be denoted as:

ij  i j i j  Tkl = αkZTDk − αkZTDk − αl ZTDl + αl ZTDl , (6) where ZTD is the tropospheric total zenith delay and α is the troposphere mapping function coefficient. ZTDs may be introduced as known values derived from global tropospheric models (troposphere fixed model) or treated as constrained parameters whose a priori values are corrected via estimation of the corrections (troposphere-weighted model). Since the linearized equations are formed independently for each constellation, there are no inter-system DD observables. The vector of unknowns is expressed as follows:

h ij ij ij ij iT x = δXk, δYk, δZk, δXl, δYl, δZl, δZTDk, δZTDl, Nkl ... Nkl, Ikl ... Ikl , (7) where {δXk, δYk, δZk, δXl, δYl, δZl} are the corrections to a priori geocentric coordinates of the stations, n ij ij o {δZTDk, δZTDl} are the residual zenith tropospheric delays, Nkl ... Nkl denotes the set of phase n ij ij o ambiguities for selected DD intra observables and, finally, Ikl ... Ikl denotes the set of epoch-specific DD ionospheric delays. The final solution with resolved double-differenced ambiguities is performed via a four-step procedure: (1) the float solution; (2) the ambiguity resolution; (3) the ambiguity validation; (4) the fixed solution obtained via parameter update, taking into account fixed ambiguities from step (2). The details of the processing strategy are listed in Table3. Remote Sens. 2018, 10, 208 10 of 19

Table 3. Processing strategy and session summary.

Date and Time of Session 3–5 October 2017 00:00–24:00 UTC Baselines’ lengths 61–62 km GNSS constellations GPS & Galileo Observation types dual frequency phase and pseudorange Frequencies L1 & L2 (GPS), E1 & E5a (Galileo) Session length & solution Instantaneous (single-epoch) relative solution # of solutions per day 288 independent single-epoch solution per day (@300 s) a priori values from Modified Hopfield + GMF mapping Tropospheric delay mitigation function + tightly constrained estimation of the residual ZTD constrained estimation of DD first-order ionospheric delays Ionospheric delay mitigation (ionosphere float model) Elevation cut-off angle 10◦ Ephemeris Precise final from CODE (COM) [57] Observation weighting scheme Elevation-dependent Fixed to integers with M-Lambda [58] and validated with Ambiguities handling W-ratio [59] 0.2 m and 0.002 m for code and phase (E1/L1), respectively A priori standard deviation of undifferenced observations σL2 = σL1·λL2/λL1 σE5a = σL1·λE5a/λL1 least squares adjustment with a priori parameter constraining Estimation method (single-epoch)

3.2. Performance Assessment of Precise Positioning with Focus on E14 and E18 Galileo Satellites

3.2.1. Data Selection & Experiment Design As stated previously, the hypothesis of the applicability of E14 and E18 satellites to positioning was verified on the basis of a multi-baseline, single-epoch RTK solution. For this purpose, the mathematical model given in Section 3.1 was applied to dual-frequency observations (L1/L2 & E1/E5a). The distribution of stations and test baselines used in the experiment is presented in Figure1. We used one station as a simulated rover receiver (OLSZ), as well as three surrounding permanent stations serving as reference sites (IAWA, CHLE, BYCE), being a part of the VRSNet active reference network [60]. As a consequence, the baselines were of similar length and reached ~60 km. The observational data covered three days, 3–5 October 2017, and were sampled at 30 s intervals. All sites were occupied by Trimble NETR9 receivers. BYCE, IAWA and CHLE sites were equipped with TRM115000.00 antennas, while at OLSZ station a choke ring model TRM59900.00 was used. Due to the lack of antenna phase centre offset and variation models for the Galileo E5a, E5b, E5 and E6 signals, the correction values corresponding to GPS L2 signals were applied. We believe that this may have a small impact on the positioning results due to the use of Galileo E5a observables. Nevertheless, at this time there is no better solution to this problem. Several processing scenarios were established for the experimental verification of the hypothesis (see Table4). The first and second scenarios apply a single system: GPS or Galileo. The third scenario takes advantage of a combined model including Galileo satellites on incorrect orbits (E14 & E18). The last strategy is based on a combined solution; however, it excludes these two satellites. By analysing the results of the last two scenarios, we evaluated the impact of Galileo E14 & E18 on the performance of the precise positioning.

Table 4. Processing scenarios.

# Constellations 1. GPS 2. Galileo 3. Combined GPS + Galileo with E14 and E18 4. Combined GPS + Galileo without E14 and E18 Remote Sens. 2018, 10, 208 11 of 19

The performance assessment was based on several indicators of solution quality related to the ambiguity resolution—coordinate domains as well as observable residuals. The empirical ambiguity resolution success rate (ASR) was used for the evaluation of the ambiguity resolution process. This indicator was computed as a ratio of epochs with correctly fixed ambiguities with respect to the number of processed epochs. The quality of the fixed solution in the coordinate domain was based on the standard deviation (std) of coordinate residuals with respect to the target (reference) position. In the residual domain we characterised descriptive measures such as standard deviation. This description is also presented in residual histograms.

3.2.2. Geometry and Configuration of the Satellites during the Experiment Figure5 depicts the number of tracked satellites and corresponding PDOP values at Olsztyn during three days of processed data. The values are given for GPS and Galileo, as well as for a combined solution. As can be seen from the figure, the number of visible GPS satellites varied from five to 11; however, most of the time their number was in the range of 8–10. As a consequence, the PDOP values in most cases did not exceed the level of 2.5. This indicates relatively good conditions in terms of the geometric distribution of satellites. In the case of a combined solution, the PDOP values were obviously lower, in most cases below 2. On the other hand, judging on the basis of the number of Galileo satellites, oneRemoteRemote can Sens. Sens. expect 2018 2018, 10,a 10, significantx, xFOR FOR PEER PEER REVIEW deterioration REVIEW of the solution based solely on this constellation. With 11 11 of theof 19 19 current Galileo constellation, the number of satellites most of the time did not exceed six, but some periods accidentallyHowever,However, there there reached were were seven time time orintervals intervals eight (Figure when when 5the thesolid number number green of line).of satellites satellites However, equalled equalled there five werefive or or time less; less; intervalsthis this accounted accounted when theforfor 37% number 37% and and of 28% 28% satellites of of the the equalledtime, time, respectively. respectively. five or less; Thus, thisThus, accounted PDOP PDOP reached reached for 37% a asignificantly and significantly 28% of the higher higher time, level respectively.level than than in in Thus,thethe case case PDOP of of the the reached GPS GPS constellation. aconstellation. significantly For higherFor 25% 25% level of of the the than time, time, in thePDOP PDOP case for offor thethe the GPSGalileo Galileo constellation. system system was was For higher higher 25% of than than the time,5 5(Figures (Figures PDOP 5 5 forand and the 6). 6). Galileo Therefore, Therefore, system we we was can can higherconclude conclude than that that 5 (Figures the the geometric geometric5 and6). distribution Therefore, distribution we of of can the the conclude Galileo Galileo satellites thatsatellites the geometricaboveabove the the distributionarea area of of interest interest of the was Galileowas not not satellitesfavourable favourable above for for thepositioning, positioning, area of interest especially especially was not regarding regarding favourable the the for single-epoch single-epoch positioning, especiallymode.mode. regarding the single-epoch mode.

1818 3030 1616 2525 1414 1212 2020 1010 1515 8 8 6 6 1010 4 4 5 5 2 2 0 0 0 0 0:000:00 276 276 DOY DOY 12:00 12:00 24:00 24:00 12:00 12:00 24:00 24:00 12:00 12:00 24:00 24:00 FigureFigure 5.5. 5. NumberNumber Number ofof oftracked tracked tracked satellites satellites satellites (solid (solid (solid lines) lines) lines) and and and PDOP PDOP PDOP (dotted (dotted (dotted lines) lines) lines) corresponding corresponding corresponding to GPS-only to to GPS- GPS- constellation—red,onlyonly constellation—red, constellation—red, Galileo-only Galileo-only Galileo-only constellation—green, co constellation—green,nstellation—green, GPS +GPS GPS Galileo—magenta). + +Galileo—magenta). Galileo—magenta).

FigureFigure 6. 6. Histogram Histogram of of PDOP PDOP values values during during experime experimentalntal period. period. GPS GPS constellation—red, constellation—red, Galileo Galileo Figure 6. Histogram of PDOP values during experimental period. GPS constellation—red, constellation—green. Galileoconstellation—green. constellation—green.

FigureFigure 7 7presents presents sky sky plots plots of of th the eGalileo Galileo and and GPS GPS constellations constellations over over the the area area of of interest. interest. We We Figure7 presents sky plots of the Galileo and GPS constellations over the area of interest. We can cancan clearly clearly see see from from the the figure figure the the deviation deviation of of E1 E14 4and and E18 E18 altitudes altitudes from from the the nominal nominal values values (dark (dark clearlyblueblue lines). lines). see from While While the the figurethe nominal nominal the deviation alti altitudetude ofof of E14Galileo Galileo and E18satellites satellites altitudes reac reac fromheshes over theover nominal~23,200 ~23,200 km, values km, E14 E14 (dark and and blueE18 E18 satellitessatellites were were tracked tracked at at a asignificantly significantly lower lower he heightight above above the the Earth Earth (bel (belowow 18,000 18,000 km). km). Moreover, Moreover, whenwhen the the E14 E14 and and E18 E18 satellites satellites are are close close to to their their minimal minimal orbital orbital height, height, they they are are observed observed at at high high elevationelevation angles angles at at experiment experiment localisation. localisation. As As is is well well known, known, GPS GPS orbits orbits with with altitude altitude lower lower than than GalileoGalileo equal equal ~20,200 ~20,200 km, km, hence hence in in Figu Figurere 7 7they they are are marked marked with with azure. azure.

FigureFigure 7. 7. Sky Sky plots plots of of Galileo Galileo (dark (dark yellow), yellow), Galileo Galileo E14 E14 & & E18 E18 (dark (dark blue) blue) and and GPS GPS (azure) (azure) satellites satellites with with relationrelation to to its its altitude altitude over over OLSZ OLSZ station station during during the the test test period period (3, (3, 4, 4, 5 5October October 2017, 2017, from from left left to to right). right).

Remote Sens. 2018, 10, x FOR PEER REVIEW 11 of 19

However, there were time intervals when the number of satellites equalled five or less; this accounted for 37% and 28% of the time, respectively. Thus, PDOP reached a significantly higher level than in the case of the GPS constellation. For 25% of the time, PDOP for the Galileo system was higher than 5 (Figures 5 and 6). Therefore, we can conclude that the geometric distribution of the Galileo satellites above the area of interest was not favourable for positioning, especially regarding the single-epoch mode.

18 30 16 25 14 12 20 10 15 8 6 10 4 5 2 0 0 0:00 276 DOY 12:00 24:00 12:00 24:00 12:00 24:00 Figure 5. Number of tracked satellites (solid lines) and PDOP (dotted lines) corresponding to GPS- only constellation—red, Galileo-only constellation—green, GPS + Galileo—magenta).

Figure 6. Histogram of PDOP values during experimental period. GPS constellation—red, Galileo constellation—green.

Remote Sens.Figure2018 7, 10presents, 208 sky plots of the Galileo and GPS constellations over the area of interest.12 of We 19 can clearly see from the figure the deviation of E14 and E18 altitudes from the nominal values (dark blue lines). While the nominal altitude of Galileo satellites reaches over ~23,200 km, E14 and E18 lines).satellites While were the tracked nominal at altitude a significantly of Galileo lower satellites height reaches above overthe Earth ~23,200 (bel km,ow E1418,000 and km). E18 Moreover, satellites werewhen tracked the E14 at aand significantly E18 satellites lower are height close to above their the minimal Earth (beloworbital 18,000height, km). they Moreover,are observed when at thehigh E14elevation and E18 angles satellites at experiment are close to localisation. their minimal As orbitalis well height,known, they GPS areorbits observed with altitude at high lower elevation than anglesGalileo at equal experiment ~20,200 localisation. km, hence Asin Figu is wellre 7 known, they are GPS marked orbits with with azure. altitude lower than Galileo equal ~20,200 km, hence in Figure7 they are marked with azure.

Figure 7. Sky plots of Galileo (dark yellow), Galileo E14 & E18 (dark blue) and GPS (azure) satellites with relationFigure to7. itsSky altitude plots of over Galileo OLSZ (dark station yellow), during Galileo the test E14 period & E18 (3, (dark 4, 5 Octoberblue) and 2017, GPS from (azure) left satellites to right). with relation to its altitude over OLSZ station during the test period (3, 4, 5 October 2017, from left to right). 3.2.3. Performance Assessment of Instantaneous Positioning

We start the evaluation of the processing results with the ambiguity resolution domain. A GPS-based instantaneous solution results in a very high level of the ambiguity resolution success rate, from 97% to 99%. Therefore, no significant improvement triggered by the addition of the Galileo signals should be expected. The solution based on the Galileo-only constellation experienced a significantly lower success rate. ASR in this case did not exceed 33%, which may be attributed to the current Galileo constellation, and consequently, the number of tracked satellites resulting in high PDOP. A similar effect on short-baseline Galileo processing was found in other studies [27]. In that case, researchers indicated the important impact of the multipath effect and, therefore, applying multipath corrections resulted in a significant enhancement of the ambiguity fixing reliability. According to our results, we did not, in turn, notice a significant influence on the ambiguity resolution success rate caused by the application or elimination of two Galileo satellites with incorrect orbits. On the first day of the experiment we obtained the same level of this percentage (96%) for both multi-constellation solutions (scenarios #3 and #4). On the next days, this discrepancy was at an insignificant level (1–2%). Comparing the ambiguity success rate from the coupled solution including Galileo satellites with incorrect orbits (#3) with that from the solution excluding them (#4), we can judge that the signals from these satellites did not noticeably influence the quality of the ambiguity resolution process. In the following, the positioning results in coordinate domain are discussed. Table5 summarises the standard deviations of fixed solution derived for consecutive scenarios, whereas Figure8 shows the scatter plots of single-epoch coordinate residuals for a sample day (3 October 2017). The highest precision of coordinates was obtained with the use of a sole GPS constellation. In this case the standard deviation reached 0.9–1.2 cm, 0.6 cm, and 2.0–2.8 cm for the N, E and U components, respectively (Table5). The results are in agreement with previous studies where researchers indicated the higher accuracy of a single-constellation GPS-based solution than for combined ones using Galileo or BDS [61–63]. Looking at the Galileo-based solution, we can clearly see the deterioration of the precision of height component, since the std reached 5.5–6.6 cm on 3–4 October 2017 and 12.8 cm on the last day of the experiment. On the other hand, plane coordinates were determined with only a slightly lower precision with respect to the GPS-based solution. In these cases, the std of N, E components was in the range of 1.5–1.7 cm and 1.2–1.4 cm, respectively. Since higher deterioration was observed in the height component, this may indicate that poor satellite geometry is the main source of this phenomenon. Remote Sens. 2018, 10, 208 13 of 19

Looking at the precision of the solutions based on coupled GPS + Galileo signals, again we cannot detect any significant impact on the coordinate domain caused by signals from a pair of Galileo FOC satellites with incorrect orbits. The discrepancies between std of fixed coordinates did not exceed 1 mm for horizontal components, whereas in the case of height this difference reached 6 mm on 3 October (Table4). We, however, do not link this with the quality of E14 & E18 satellite signals, but with unfavourable Galileo satellites geometry. Having investigated the results in the ambiguity resolution and coordinate domains, the following analysis was based on the observation residuals. Here we focus on the residuals corresponding to dual-frequency phase signals. Close attention was paid to the observations of the Galileo E14 and E18 satellites. AtRemote this Sens. point 2018 we, 10, shouldx FOR PEER recall REVIEW that the residuals correspond to double-differenced observables. 13 of 19 dN [m] 0.05 0.1

0.025 0.05

0 0 -0.05 -0.025 -0.05 -0.1 00:00 09:00 18:00 -0.05-0.0250 0.0250.05 Scenario #1 dE [m] UTC 1

0.6

0.2

-0.2 0.05 -0.6 0.025

0 -1 00:00 06:00 12:00 18:00 -0.025 UTC -0.05 -0.05-0.0250 0.0250.05 Scenario #2 dE [m] 1

0.6

0.2

dN [m] -0.2 0.1

0.05 -0.6

0 -1

dN [m] -0.05 00:00 06:00 12:00 18:00 UTC -0.1 00:00 09:00 18:00 Scenario #3 UTC

1 1

0.6 0.6

0.2 0.2

-0.2 -0.2 0.1

-0.6 0.05 -0.6

-1 0 -1

dN [m] -1 -0.6 -0.2 0.2 0.6 1 -0.05 00:00 06:00 12:00 18:00 dE [m] UTC -0.1 Scenario #4 00:00 09:00 18:00 UTC Figure 8. Scatter plots of coordinate residuals obtained on 3 October 2017 for tested scenarios. Grey Figure 8. Scatterand green plots dots of represent coordinate float residuals and fixed obtained solutions, on respectively. 3 October 2017 for tested scenarios. Grey and green dots represent float and fixed solutions, respectively. Having investigated the results in the ambiguity resolution and coordinate domains, the following analysis was based on the observation residuals. Here we focus on the residuals corresponding to dual-frequency phase signals. Close attention was paid to the observations of the Galileo E14 and E18 satellites. At this point we should recall that the residuals correspond to double- differenced observables. As an example, Figures 9 and 10 show L1/E1 and L2/E5a phase residuals obtained on 3 October 2017. For better distinction, these values were depicted with separate colours for GPS, Galileo, E14 and E18 signals. Moreover, Figure 11 presents L1/E1 phase residuals in the function of satellite elevation and Figure 12 depicts elevation angle of the E14 and E18 satellites. In general, the figures did not reveal important differences in DD observable residuals between GPS, Galileo, E14 and E18 satellites. We did not recognise the outliers in the signals from the FOC satellites with incorrect orbits.

Remote Sens. 2018, 10, 208 14 of 19

Table 5. Empirical standard deviation (in cm) of the rover coordinates obtained in fixed solution.

GPS Galileo GPS + Galileo with E14 & E18 GPS + Galileo without E14 & E18 Satellites 3 October 2017 (276 DOY) N 0.9 1.5 1.2 1.1 E 0.6 1.2 0.8 0.8 U 2.1 5.5 2.9 2.3 4 October 2017 (277 DOY) N 0.9 1.7 1.2 1.1 E 0.6 1.4 0.8 0.8 U 2.0 6.6 2.5 2.5 5 October 2017 (278 DOY) N 1.2 1.9 1.3 1.3 E 0.6 1.3 0.9 0.9 U 2.8 12.8 3.3 3.4

As an example, Figures9 and 10 show L1/E1 and L2/E5a phase residuals obtained on 3 October 2017. For better distinction, these values were depicted with separate colours for GPS, Galileo, E14 and E18 signals. Moreover, Figure 11 presents L1/E1 phase residuals in the function of satellite elevation and Figure 12 depicts elevation angle of the E14 and E18 satellites. In general, the figures did not reveal importantRemote Sens. differences 2018,, 10,, xx in FORFOR DD PEERPEER observable REVIEWREVIEW residuals between GPS, Galileo, E14 and E18 satellites. We did 14 14 not ofof 1919 recognise the outliers in the signals from the FOC satellites with incorrect orbits. A more detailed analysis mayA bemore performed detailed on analysis the basis may of residuals’ be performed histograms on th ande basis selected of statisticalresiduals’ measures. histograms The and former selected are presentedstatistical in measures. Figure 13. TheThe latterformer were are given presented in Table in 6Figure. 13. The latter were given in Table 6.

FigureFigure 9. L19. L1L1 + E1 ++ E1E1 DD DDDD phase phasephase residuals residualsresiduals on onon 3October 33 OctoberOctober 2017. 2017.2017.

Figure 10. L2 + E5a DD phase residuals on 3 October 2017. FigureFigure 10. 10.L2 L2 + E5a+ E5a DD DD phase phase residuals residuals on on 3October 3 October 2017. 2017.

Figure 11. L1L1 ++ E1E1 DDDD phasephase residualsresiduals inin thethe functionfunction of satellite elevation angle on 3 October 2017.

Figure 12. ElevationElevation ofof thethe E14E14 andand E18E18 satellitessatellites inin thethe funcfunctiontion ofof thethe satellitesatellite altitudealtitude onon 33 OctoberOctober 2017.2017.

Table 6 summarises the results in the observation residuals domain obtained with scenario #3. Specifically, we give the values of the standard deviation of phase residuals obtained on the corresponding days of the positioning experiment. In addition,addition, FigureFigure 1313 visualisesvisualises thethe distributiondistribution of the phase residuals of the selected satellites and systems obtained on 3 October 2017.

Remote Sens. 2018, 10, x FOR PEER REVIEW 14 of 19 Remote Sens. 2018, 10, x FOR PEER REVIEW 14 of 19

A more detailed analysis may be performed on the basis of residuals’ histograms and selected statistical measures. The former are presented in Figure 13. The latter were given in Table 6.

Figure 9. L1L1 ++ E1E1 DDDD phasephase residualsresiduals onon 33 OctoberOctober 2017.2017.

Remote Sens. 2018, 10, 208 15 of 19 Figure 10. L2L2 ++ E5aE5a DDDD phasephase residualsresiduals onon 33 OctoberOctober 2017.2017.

FigureFigure 11. 11.L1 L1L1 + + E1+ E1E1 DD DDDD phase phasephase residuals residualsresiduals in inin the thethe function functionfunction of of satellite satellite elevation elevation angle angle on on 3 October3 October 2017. 2017.

Remote Sens. 2018, 10, x FOR PEER REVIEW 15 of 19

Table 6. Empirical standard deviation of phase observable residuals based on multi-baseline single- epoch solution (in mm).

GPS L1 GPS L2 Gal E1 E14 E1 E18 E1 Gal E5a E14 E5a E18 E5a 3 October 7.4 10.3 7.3 8.0 7.0 13.9 12.3 15.4

4 October 7.0 10.3 7.3 8.7 7.5 14.6 16.3 15.8 FigureFigure5 12.October 12.Elevation ElevationElevation of7.8 ofof the thethe E14 E14E14 10.3 and andand E18 E18E18 satellites satellitessatellites7.7 in inin the8.5 thethe function funcfunction6.5tion of ofof the thethe satellite14.6 satellitesatellite altitude altitudealtitude17.3 on onon 3 33 October 14.7 OctoberOctober 2017. 2017.2017.

Table 6 summarisesL1/E1 the results in the observation residuals domainL2/E5a obtained with scenario #3. Specifically, we give the values of the standard deviation of phase residuals obtained on the corresponding days of the positioning experiment. In addition,addition, FigureFigure 1313 visualisesvisualises thethe distributiondistribution of the phase residuals of the selected satellites and systems obtained on 3 October 2017. relative frequency frequency relative

relative frequencyrelative

Figure 13. Histograms of phase residuals corresponding to L1/E1 and L2/E5a on 3 October 2017. Figure 13. Histograms of phase residuals corresponding to L1/E1 and L2/E5a on 3 October 2017. As we can see from Table 6, the standard deviation of the L1/E1 phase residuals, corresponding Tableto GPS, 6. Galileo,Empirical E14 and standard E18 signals, deviation were at of a phase comparable observable level, in residuals the range based of 6.5–8.7 on multi-baseline mm. Slightly single-epochhigher values solution were recognised (in mm). for residuals of double-differenced observables formed with the application of E14 satellites (up to 8.7 mm), whereas in the case of E18 signals these indicators were in the range of 6.5–7.5GPS L1 mm. GPS At the L2 same Gal time E1 the E14std E1for observables E18 E1 formed Gal E5a with E14Galileo E5a satellites E18 E5a other3 October than E14 & E18 7.4 were within 10.3 7.3–7.7 7.3mm. Accord 8.0ing to this, 7.0 we do not 13.9 see important 12.3 differences 15.4 between4 October residuals 7.0corresponding 10.3 to signals 7.3 of satellites 8.7 with incorrect 7.5 orbit 14.6 and others. 16.3 In the case 15.8 of 5 October 7.8 10.3 7.7 8.5 6.5 14.6 17.3 14.7 L2 and E5a frequencies, we found that the std of phase residuals was at a higher level with respect to L1/E1. This may be explained in two ways. First, the weighting scheme distinguishes the observable Tableweights6 summarisesbetween frequencies. the results Specifically, in the observation the weights residuals are correlated domain to obtainedthe ratio of with applied scenario #3. Specifically,frequencies with we respect give the to L1/E1 values [64]. of Therefore, the standard L2 and deviation E5a signals of are phase depicted residuals with lower obtained weights on the correspondingthan L1/E1. days This ofratio the is positioningobviously more experiment. significant In when addition, E1 & E5a Figure signals 13 visualisesare used than the in distribution the case of the phaseof L1 & residuals L2. Moreover, of the we selected should satellitesnote the lack and of systems official antenna obtained phase on 3centre October offsets 2017. and variations for E5a signals. In this case, corrections corresponding to L2 frequency are applied. For GPS signals As we can see from Table6, the standard deviation of the L1/E1 phase residuals, corresponding the std of L2 phase residuals equalled 10.3 mm, whereas this reached 14.6 mm in the case of Galileo to GPS, Galileo, E14 and E18 signals, were at a comparable level, in the range of 6.5–8.7 mm. Slightly satellite signals excluding E14 and E18. In the case of the latter satellites, the standard deviation of the E5a phase residuals of DD observables was in the range 12.3–17.3 mm. Judging on the basis of observable residuals, the FOC satellites with incorrect orbits did not stand out.

4. Summary and Conclusions This contribution evaluates the performance of the coupled Galileo + GPS instantaneous medium-range positioning, with special attention paid to the application of the Galileo FOC satellites—E14 & E18—launched into incorrect elliptic orbital planes. Therefore, the main goal of the paper was to investigate the potential capability of these satellites in surveying and geodetic applications. In the paper we provided both a methodology of coupled instantaneous medium-range positioning and experimental performance analysis. In the first part of the study, we focused on the analysis of the signal power and noise of Galileo E14 & E18 satellites, comparing the results to other GPS and Galileo satellites. It was confirmed that

Remote Sens. 2018, 10, 208 16 of 19 higher values were recognised for residuals of double-differenced observables formed with the application of E14 satellites (up to 8.7 mm), whereas in the case of E18 signals these indicators were in the range of 6.5–7.5 mm. At the same time the std for observables formed with Galileo satellites other than E14 & E18 were within 7.3–7.7 mm. According to this, we do not see important differences between residuals corresponding to signals of satellites with incorrect orbit and others. In the case of L2 and E5a frequencies, we found that the std of phase residuals was at a higher level with respect to L1/E1. This may be explained in two ways. First, the weighting scheme distinguishes the observable weights between frequencies. Specifically, the weights are correlated to the ratio of applied frequencies with respect to L1/E1 [64]. Therefore, L2 and E5a signals are depicted with lower weights than L1/E1. This ratio is obviously more significant when E1 & E5a signals are used than in the case of L1 & L2. Moreover, we should note the lack of official antenna phase centre offsets and variations for E5a signals. In this case, corrections corresponding to L2 frequency are applied. For GPS signals the std of L2 phase residuals equalled 10.3 mm, whereas this reached 14.6 mm in the case of Galileo satellite signals excluding E14 and E18. In the case of the latter satellites, the standard deviation of the E5a phase residuals of DD observables was in the range 12.3–17.3 mm. Judging on the basis of observable residuals, the FOC satellites with incorrect orbits did not stand out.

4. Summary and Conclusions This contribution evaluates the performance of the coupled Galileo + GPS instantaneous medium-range positioning, with special attention paid to the application of the Galileo FOC satellites—E14 & E18—launched into incorrect elliptic orbital planes. Therefore, the main goal of the paper was to investigate the potential capability of these satellites in surveying and geodetic applications. In the paper we provided both a methodology of coupled instantaneous medium-range positioning and experimental performance analysis. In the first part of the study, we focused on the analysis of the signal power and noise of Galileo E14 & E18 satellites, comparing the results to other GPS and Galileo satellites. It was confirmed that the signal power of E14 & E18 satellites was basically higher than the signals of other Galileo satellites (up to 53 dB-Hz). This was clearly related to their lower orbital altitude over the area of the test stations. On the other hand, analysis of observational noise did not reveal any differences between all the European satellites. The inter-system comparison of the noise (GPS and Galileo) proved that the precision of code measurement of the latter was significantly better. The same effect, though less pronounced, was also observed in triple-frequency combination of phase observations. Further analysis was based on the positioning experiment and considered ambiguity resolution and coordinate domains as well as observable residuals. We confirmed the high performance of the instantaneous medium-range positioning based on the GPS-only constellation, providing unobstructed visibility of the satellites. When adding in Galileo observations, we did not see an important change in the performance of the ambiguity resolution. Both solutions, GPS and GPS + Galileo, provided competitive rates of ambiguity resolution success, reaching up to 99%. On the basis of the two scenarios, one with and one without E14 & E18 satellites, we found that the Galileo satellites launched into eccentric orbital planes did not deteriorate the ambiguity resolution process. On the other hand, we experienced significant worsening in the ambiguity domain when the Galileo-only constellation was applied. We believe that this was caused by the current uncompleted constellation and thus poor geometry of the Galileo satellites over the experimental area. Having analysed the precision of the solutions based on the coupled GPS + Galileo constellation, we can conclude that the E14 & E18 satellites do not have any negative impact on the coordinate domain. The differences between the standard deviation of fixed coordinates did not exceed 1 mm for plane components, whereas in the case of height this difference reached 6 mm. According to the obtained results, again we do not see any increased observation residuals corresponding to signals of E14 and E18. The standard deviation of the L1/E1 phase residuals Remote Sens. 2018, 10, 208 17 of 19 corresponding to GPS, Galileo and E14 & E18 satellite signals were at a comparable level, in the range of 6.5–8.7 mm. Considering the above, precise positioning using Galileo satellites launched into incorrect orbital planes is feasible. Therefore, these satellites are applicable to most geodetic, surveying and many other solutions. This claim, however, holds true providing the precise ephemeris of the satellites.

Acknowledgments: The work in this contribution was supported by the National Science Centre, Poland: project No. 2016/23/D/ST10/01546. The GNSS observational data from CORS network were kindly provided by VRSNet Ltd., Poland. Author Contributions: Jacek Paziewski designed and performed the experiments, analysed the data and discussed the conclusions. Rafal Sieradzki performed and analysed the experiment given in Section2 and discussed the conclusions. Pawel Wielgosz supervised the investigations and discussed the conclusions. Conflicts of Interest: The authors declare no conflict of interest.

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