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Research on time difference detectionalgorithm based on combination of GNSSand PPPJun Yang1, Ziwen Zhang2*, Yijun Liu2, Zuoteng Xu2, Haowen Chen2, Wende Zhang2 and Yuqiang Chen3

Abstract

With the gradual increase in the number of GNSS systems and the improvement of functions, in addition to the single-system navigation and timing service, the integrated navigation and positioning service among multiple systems canprovide users with more accurate and stable positioning results, arousing more attention from the workers in GNSSfield. Compatibility and interoperability among different systems has become a trend in the development of GNSS.Compatibility and interoperability between systems require a uniform time scale. Therefore, the measurement andforecasting of time deviations in GNSS systems is particularly important. This paper first studies the multi-system fusionlocation model and proposes an adaptive GNSS fusion PPP algorithm based on parameter equivalent reduction. Then,the method of fusion PPP is used to monitor the time difference of GNSS. Finally, the effectiveness of the improvedalgorithm and time difference monitoring method is verified by practical examples.

Keywords: GNSS, PPP algorithm, Pseudo-time difference, Time difference monitoring

1 IntroductionThe official launching of China’s Beidou second-generationsatellite navigation system indicates that the number of glo-bal satellite navigation and positioning systems (GNSS) cur-rently providing services has increased from two to three.The number of GNSS working satellites has exceeded 70. Inthe next 5 to 10 years, with the completion of the EU Galileosystem, the total number of GNSS satellites will exceed 100,and the vast majority are modern multi-frequency oper-ational satellites. GNSS has entered a new chapter ofmulti-constellation and multi-frequency [1]. With themodernization of GNSS, the timing accuracy of multi-systemintegrated navigation positioning is also increasing. The de-velopment characteristics of GNSS have also gradually chan-ged from the single GPS positioning model that initiallyfocuses on post-processing relative positioning to themulti-system GNSS fusion absolute positioning with fastreal-time and high-frequency observations. Among them,the rapid and flexible precision point positioning technology

(PPP) is undoubtedly one of the most promising applicationtechnologies [2].The accuracy and stability of real-time fast positioning

will be greatly improved by using the fusion and posi-tioning of GNSS multi-system. In recent years, the re-search results of GNSS fusion PPP both at home andabroad are more abundant, mainly concentrated in the[3] GPS/GLONASS fusion. For example, Dr. Kuang ofJPL proposed that the precision orbit of GLONASS sin-gle star or constellation could be determined based onthe space-time system of the GPS system, and the orbitdetermination accuracy of GLONASS satellite was in-creased to 15 cm level by this method. Based on the glo-bal dual mode receiver, Ignacio realizes the joint orbitdetermination method of GPS and GLONASS and ana-lyzes the signal delay of the multi-mode system in differ-ent receivers in detail. Based on the ROCK lightpressure model, ESA established the GLONASS on-orbitsatellite solar photovoltaic model. These research resultsmainly demonstrate the accuracy and reliability advan-tages brought by fusion positioning and seldom involvethe fusion algorithm itself and the distribution of thecontribution ratio between different systems [4].

© The Author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link tothe Creative Commons license, and indicate if changes were made.

* Correspondence: [email protected] of Information Engineering, Guangdong University of Technology,Guangzhou 510006, ChinaFull list of author information is available at the end of the article

Yang et al. EURASIP Journal on Wireless Communications and Networking (2019) 2019:114 https://doi.org/10.1186/s13638-019-1416-2

http://crossmark.crossref.org/dialog/?doi=10.1186/s13638-019-1416-2&domain=pdfhttp://creativecommons.org/licenses/by/4.0/mailto:[email protected]

1.1 Related workAlthough the study of GNSS in the time and frequencydomain has been more than 30 years old, the study oftime difference monitoring between systems using theGNSS technology method is still at a preliminary stageof research. With the gradual improvement of China’sCOMPASS system, it becomes more and more urgent torealize the compatibility and interoperability betweenthe system and other GNSS systems [5]. At present,there are not many open researches on the time differ-ence monitoring of GNSS systems at home and abroad,mainly focusing on GPS and Galileo and GPS andCOMPASS. In recent years, the number of availableGNSS systems and the number of available satellites hasgradually increased, and real-time high-frequency dataof terrestrial receivers have been widely used. In thiscontext, for real-time mass data under multi-modeGNSS systems, if the traditional PPP fusion algorithm isused, all the GNSS observations are unified to form theobservation equation for unified solution, and the com-putational load is bound to increase exponentially. Atthe same time, this kind of overall solution is also diffi-cult to realize the adjustment of the weights of the adap-tive contribution between different systems, whichaffects the operational efficiency and precision and reli-ability of the fusion PPP positioning [6].The GNSS fusion sequential PPP algorithm based on

the principle of parameter equivalence reduction cansolve the abovementioned overall problem of low effi-ciency. This algorithm decomposes the multi-mode PPPintegral fusion solution into individual single-system in-dependent parallel solutions. The equations of the over-lapped parametric equations among different systemsare equivalently reduced by using the normal equationsconstructed by the single system, and the fusion solu-tions can be directly obtained by superposition. Themain advantage of the new algorithm is to improve itscomputational efficiency. With the increase of the num-ber of fusion systems, the computational load of trad-itional algorithms increases exponentially, and the newalgorithm could improve it to a linear growth. Inaddition, this paper also proposes an adaptive fusionmethod that balances the contribution weight ratios ofdifferent systems by using the posttest difference factor.Finally, the effectiveness and accuracy of the proposedalgorithm are verified by the comparison of actual dataoperation time and dynamic and static positioning tests.

2 Methods2.1 Single-system PPP algorithm based on parameterreductionThe parameters in the single-system observation equa-tion are divided into two categories. The classified

observation equation can be written as the followingblock matrix form:

V ¼ A1X1 þ A2X2‐L; P ð1Þ

Among them, X1 is a parameter that changes withtime and mainly refers to the receiver clock offset par-ameter in PPP. X2 is a parameter that does not changeover time and mainly refers to coordinate parameters,tropospheric parameters, and ambiguity parameters inPPP. What needs to be explained here is that the coord-inate parameters between epochs during dynamic PPPpositioning are also changed. It is not possible to carryout inheritance directly, and it can be forecasted by fil-tering the state equation [7].The partitioned equation obtained by formula (1) is as

follows:

B11 B12B21 B22

� �X1X2

� �¼ C11

C22

� �ð2Þ

wherein B11 ¼ AT1 PA1, B12 ¼ AT1 PA2, B21 ¼ BT12, B22 ¼ AT2PA2, C11 ¼ AT1 PL, C22 ¼ AT2 PL.Carry out the equivalent reduction of the parameters

of formula (2) and it could be obtained that:

B11 B120 B2

� �X1X2

� �¼ C11

R2

� �ð3Þ

wherein B2 ¼ B22−B21B−111B12, R2 ¼ C22−B21B−111C11.For formula (3), X2 is solved by the second formula,

and then X1 is returned through the first formula, that is

B2X2 ¼ R2 ð4Þ

B11X1 ¼ C11−B12X2 ð5Þ

That is, the single system PPP recurrence calculationformula for the ith epoch can be obtained as follows:

B̂i2 ¼ Bi2 þ B̂

i−12

R̂i2 ¼ Ri2 þ R̂

i−12

X2 ¼ B̂i2� �−1

R̂i2

X i1 ¼ Bi11� �−1

Ci11−Bi12X2

� �QX2 ¼ B̂

i2

� �−1

QX i2 ¼ Bi11−B

i12 B

i22 newð Þ

� �−1Bi21

� −1;

Bi22 newð Þ ¼ B̂i2 þ Bi21 Bi11

� �−1Bi12

8>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>:

ð6Þ

Through the recursive calculation of formula (12), thesingle-system static PPP sequential solution based onparameter reduction can be realized.

Yang et al. EURASIP Journal on Wireless Communications and Networking (2019) 2019:114 Page 2 of 11

2.2 Multi-system fusion PPP algorithm based onparameter reductionFor multi-system fusion positioning, the fixed parame-ters X2 in the observation equations of each single sys-tem can be divided into two categories[8], namely X2= [Y1 Y2]

T. One is the overlapping parameters Y1 be-tween different systems, such as position and tropo-sphere parameters. The other is non-overlappingparameters Y2 that represent ambiguities and so on.Therefore, the B2 and R2 obtained by the reduction in

equation (4) is rewritten into the following block matrixform:

B2 ¼ M11 M12M21 M22� �

; R2 ¼ R11R22� �

ð7Þ

Formula (4) is written in the following matrix accord-ing to extension of Y1 and Y2:

M11 M12M21 M22

� �Y 1Y 2

� �¼ R11

R22

� �ð8Þ

It could be obtained from formula (8):

M1 0M21 M22

� �Y 1Y 2

� �¼ R1

R22

� �ð9Þ

wherein M1 ¼ M11−M12M−122M21 , R1 ¼ R11−M12M−122R22 .And then:

M1Y 1 ¼ R1 ð10ÞFor GPS, GLONASS, COMPASS, etc., the common

parameter in the parameters to be evaluated is Y1.Therefore, the results of the overlapping parameterequation (Eq. (10)) for each system can be obtained sep-arately. The equations are as follows:

MG1 Y 1 ¼ RG1 ; MR1Y 1 ¼ RR1 ; MC1 Y 1¼ RC1 ; ME1Y 1 ¼ RE1 ;…; ð11Þ

In the above formulae, the superscripts G, R, C, and Erepresent the GPS system, the GLONASS system, theCOMPASS system, and the GALILEO system, respectively.Therefore, the equation for solving the GNSS

multi-system fusion PPP solution is as follows:

Xmk¼1

Mk1Y 1 ¼Xmk¼1

Rk1 ð12Þ

Among them, M represents the number of satellitenavigation systems.After the value of Y1 is calculated, the value of Y2 can

be recovered by the formula (8) or (9); thus, the value ofX2 could be obtained and then recovery the value of X1,and then the fusion PPP is solved. The multi-systemPPP fusion formula for the ith epoch is as follows:

B̂i2 newð Þ ¼ B̂

i2 þ

Xmk¼1;k¿l

Mk1 0

0 0

264

375

R̂i2 newð Þ ¼ R̂

i2 þ

Xmk¼1;k¿l

Rk1

0

264

375

X2 ¼ B̂i2 newð Þ� �−1

R̂i2 newð Þ

Xi1 ¼ Bi11� �−1

Ci11−Bi12X2

� �QX2 ¼ B̂

i2 newð Þ

� �−1

QXi2 ¼ Bi11−B

i12 B

i22 newð Þ

� �−1Bi21

� −1;

Bi22 newð Þ ¼ B̂i2 þ Bi21 Bi11

� �−1Bi12

8>>>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>>>:

ð13Þ

In the equation (13),Pm

k¼1;k¿lMk1 and

Pmk¼1;k¿lR

k1 repre-

sents the sum of the normal equation observation matrixof systems other than the own system.

2.3 An adaptive PPP fusion algorithm based onposttesting error factorThe current three GNSS navigation systems are capableof providing four or more visual satellites for user navi-gation and positioning in real time or over the world.This provides us with a very valuable prior informationin the process of processing the fusion data. That is, asingle system can obtain independent overlapped param-eter values and their accuracy information, making theadaptive fusion PPP localization possible in dataprocessing.Therefore, in this paper, the adaptive factor is deter-

mined by using the posterior variance value of the over-lapping parameters obtained by the single system.The adaptive factor ak of the k system is set as follows:

ak ¼1=σ2xk 0 0 00 1=σ2yk 0 0

0 0 1=σ2zk 00 0 0 1=σ2Tk

26664

37775 ð14Þ

Among them, σ2xk , σ2yk, σ2zk and σ

2Tk are obtained

through multiplying the posterior variance σ20 of the sin-gle system by the diagonal elements of the correspond-ing parameter variance matrix Q. Formula (14) is aclassification adaptive factor form which is classified andadjusted according to different parameters. In actualwork, we can also directly take the square root of thesum of the variances of the four parameters to solve theoverall single factor. The calculation formula is asfollows:


ak ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiσ2xk þ σ2yk þ σ2zk þ σ2Tk

� �r ð15Þ

The subsequent example used in this paper is the sin-gle factor adjustment method shown in (15).The formula for solving the normal equation of the

adaptive fusion PPP overlap parameter can be obtainedas follows:

Xmk¼1

akMk1Y 1 ¼

Xmk¼1

akRk1 ð16Þ

Through the above equation, when carrying out thefusion positioning of different GNSS system, the size ofthe contribution of the system to the fusion solution canbe adaptively adjusted according to the single system’sinternal accuracy index, so as to avoid serious influenceon the fusion solution when a system is grossly poor.This improves the accuracy and stability of multi-systemfusion solutions.The parameter reduction method in this paper can be

extended to the research work of GNSS precision satel-lite clock error correction, non-differential baseline net-work adjustment, and GNSS multi-mode time differencemonitoring, which can effectively improve its work effi-ciency. The feasibility and accuracy of the fusion PPPmethod in this section for GNSS time difference moni-toring will be discussed below.

3 Monitoring and analysis of GNSS timedifference based on fusion PPP model3.1 Concept of GNSS time difference and conventionalmonitoring methodsThere is a system deviation between the time systems ofdifferent GNSS navigation systems, known as time dif-ferences. Taking the GPS/GLONASS time difference asan example, there is the following transformation be-tween GPST and GLOT:

GPST ¼ GLOTþ τcþ τuþ τg ð17ÞIn this, τc represents the time difference between the

GLOT and the UTC (SU). τu represents the time differ-ence between UTC (SU) and international UTC. τg rep-resents the time difference between international UTCand GPST. The time difference between GPST andGLOT is the sum of the above three.At present, the GPS’s broadcast ephemeris provides a

linear time difference conversion model coefficient fromGPST to UTC (USNO). The GLONASS broadcastephemeris provides a time difference between GLOTand UTC (SU). Therefore, as long as the time compari-son between UTC (USNO) and UTC (SU) is obtained,the GPS/GLONASS time difference can be obtained.

The time comparison between UTC (USNO) and UTC(SU) can be obtained by direct comparison of the masterstations or their comparison with international UTC orInternational Atomic Time (TAI). A brief process forobtaining a time difference through a time comparisontechnique at the end of the system is shown in the dia-gram in Fig. 1.The above time difference acquisition method has the

advantages of high precision and stable and reliable timedifference. It is one of the main ways to obtain the inter-national GNSS TDOA. However, this time difference ac-quisition method is usually performed on the maincontrol station of the GNSS navigation system, and itneeds to establish time comparison links between inter-national large time-frequency laboratories, and the oper-ation mode is not flexible enough. This also leads to theshortcomings such as poor real-time performance and thedifficulty of direct acquisition by the user, which restrictsits application in the actual navigation and positioning.Based on this, this section will construct a feasible

method for monitoring time difference directly in the cli-ent using a multi-mode receiver fusion PPP method. First,analyze the concept and nature of GNSS time differencerequired by the actual navigation and positioning user.

3.2 Concept of “pseudo-time difference” for navigationand positioning of usersFor the navigation and location users of the multimodereceiver, the most important contribution of the systemtime difference is to reduce the number of receiver clockparameters to be estimated, and then reduce the neces-sary satellite observations. Taking GPS/GLONASS as anexample, the receiver’s clock error parameter of GPS

system t̂Gr and the receiver clock error parameter of

GLONASS system t̂Rr , absorb the absolute device delay

error b and inter-frequency relative equipment delayerror δb on the respective system in addition to the realreceiver clock difference tGr and t

Rr under its own time

system. The specific formula expression is as follows [9]:

Fig. 1 Acquisition of time difference through GPS/GLONASS systemtime comparison


t̂Gr ¼ tGr þ bG þ δbG ð18Þ

t̂Rr ¼ tRr þ bR þ δbR ð19Þ

Subtract the left and right sides of (18) and (19) bytwo and it could be obtained that:

t̂sys ¼ t̂Gr −t̂rR¼tGr −tRr þ bG−bR� �þ δbG−δbR� � ð20Þ

The time difference t̂sys in the type (20) includesboth the real GPS/GLONASS system time differencetsysðtsys ¼ tGr −tRr Þ and the poor delay of the GPS/GLO-NASS device (bG − bR) + (δbG − δbR). The time differ-ence of this property is called the “pseudo-timedifference” of the receiver.It can be seen that the difference between the real time

difference tsys and pseudo-time delay difference t̂sys is theequipment time delay (bG − bR) + (δbG − δbR) betweenGPS/GLONASS system. If the equipment time delay sig-nal of the GPS system and GLONASS system in the re-ceiver is the same, then the pseudo-time difference isreal-time difference; otherwise, the two are not equivalent.

3.3 Acquisition of pseudo-time difference based on fusionPPP technologyFirst, the observational equations of the simplified fusionPPP are listed as follows:

PIF ¼ ρ̂þ ctr þ bP þ δbP þ ε PIFð Þ ð21ÞΦIF ¼ ρ̂þ ctr þ bΦ þ δbΦ þ N þ ε ΦIFð Þ ð22Þ

Among them, ρ̂ represents the geometric distance be-tween the station and the satellite after the correction ofthe atmospheric error and so on. tr represents the re-ceiver clock difference. The receiver’s code and phasedevice time delay is divided into two parts: one is thefixed time delay on the frequency bP and bφ, the other isthe relative device time delay between the frequency δbPand δbφ. For the phase observation, if the ambiguity par-ameter is a floating point solution, the fixed time delaybφ and relative time delay δbφ can be absorbed by theambiguity parameter, and there is no need to solve inthe actual navigation and location. For code observation,if the device delay is not corrected, it will be absorbedby the receiver clock error parameter, which will directlyaffect the absolute value of the receiver clock offset.Therefore, the absolute accuracy of the satellite clockdifference is determined by the code observation valuein the process of solving the actual satellite clock differ-ence. The phase observation value determines the rela-tive accuracy of the satellite clock difference calculation.At present, IGS organizations provide three types of

relative equipment delay correction products for codeobservations, also known as differential code deviation

correction products. It should be noted that in additionto DCB corrections for satellites announced in DCBproducts, DCB corrections on stations are also an-nounced. The measurement station DCB correction isoften overlooked in GNSS positioning, mainly because itcan be absorbed by the receiver clock skew and does notaffect the actual navigation positioning solution. How-ever, in time difference monitoring, this correction isvery important. It directly affects the magnitude of thereceiver clock difference and must be subtracted fromthe observation equation.DCB products with IGS can correct relative device de-

lays δbP between frequencies. However, absolute devicedelay bP cannot be eliminated. In other words, the timedifference obtained by using the fusion PPP method is nota true time difference, but a pseudo-time difference con-taining the poor delay of the absolute equipment betweensystems, which can be expressed by the following formula:

tsys ¼ tsys þ bGP −bRP� � ð23Þ

It can be seen from the above equation that when theabsolute device delays of different navigation systems arethe same, the fusion PPP gets the real system time differ-ence sequence. In fact, the absolute device delays of dif-ferent navigation systems in the same receiver aredifferent, and the phase difference can range from a fewnanoseconds to hundreds of nanoseconds.

4 ExperienceIn order to compare and verify the efficiency and accur-acy of this algorithm, the following two types of exam-ples are designed to verify it.

4.1 Comparison of operational efficiencyFirst, 1000 epoch observation data for the four naviga-tion systems GPS, GLONASS, COMPASS, and Galileowere simulated. Each system has ten observation satel-lites per epoch. Satellite replacement does not occurduring the observation period. The computational effi-ciency of multi-mode fusion PPP positioning based ontraditional algorithm and parameter reduction is calcu-lated respectively. Fusion static PPP location calculation ofsingle-system, dual-system, three-system, and four-systemis performed. The data processing carrier is based on ahigh-performance configuration computing computer.Both schemes use different numbers of GNSS systems forfusion PPP positioning. The computational time statisticsneeded to process 1000 epochs are shown in Fig. 3:As can be seen from Fig. 2, with the increase in the

number of GNSS fusion systems, the processing time oftraditional fusion algorithms increases exponentially, andthe computational burden increases with the same type.The parameter reduction algorithm proposed in this paper


shows a linear increase in processing time. With the wideapplication of multi-mode systems, the computational ef-ficiency of this algorithm is significantly higher than thetraditional algorithm.

4.2 Static and dynamic accuracy test of fusion positioningIn order to further verify the correctness of the fusionPPP location algorithm and the effectiveness of the adap-tive factor, the measured GPS/GLONASS dual-system ob-servation data is used for calculation and analysis. Thedata comes from the global IGS tracking and monitoringnetwork, and 24 IGS stations equipped with GPS/GLO-NASS dual-mode receivers that are evenly distributed onthe European continental plate are selected for static PPPcalculation. The data sampling rate is 30 s. The total ob-servation period of data is 24 h.Two scenarios were designed for comparative analysis:

case 1, fusion PPP positioning based on parameter reduc-tion, and case 2, self-adaptive fusion PPP positioningbased on the posttest difference. Using the coordinates ofthe stations posted on the IGS website as “true values,”the deviation values of the positioning results of each sta-tion in N, E, and U directions were calculated, and theoverall RMS indicators corresponding to the deviationvalues of all stations were calculated. The statistics of devi-ations and RMS values of static PPP positioning resultsfor specific experiments are shown in Fig. 3.It can be seen from Fig. 4 that for a single-day solu-

tion, in the dual system fusion PPP positioning, the posi-tioning accuracy on the plane can reach the millimeterlevel. The accuracy of the elevation direction is alsomaintained at about 1 cm. This aspect shows good ob-servation conditions at the IGS tracking station. On theother hand, it also illustrates the high-precision featuresof current PPP technology. Scenario 1 uses only equal

weights to carry out the normal equation stacking andcannot reasonably assign the weight ratio relationshipbetween GPS and GLONASS observations. The resultingfusion location results and accuracy lie between the po-sitioning accuracy of the two single systems. The use ofa posterior misalignment for adaptive fusion positioning(case 4) solves this problem better and has the best posi-tioning accuracy.In addition, in order to further verify the effectiveness

and accuracy of the proposed algorithm in dynamic PPP lo-cation, a high-frequency IGS monitoring station equippedwith a GPS/GLONASS dual-mode receiver was selected fordynamic PPP calculation. The data sampling rate is 1 s, andthe total data observation duration is 5 h. Using the coordi-nates of the stations published on the IGS website as the“true value,” the sequence of deviations in the N, E, and U

Fig. 2 Time information of multi-system fusion PPP processingcarried out by two methods Fig. 3 Positioning result deviation and RMS value of case 1

Fig. 4 Positioning result deviation and RMS value of case 2


directions of the station’s dynamic positioning results wascalculated and the corresponding RMS values were calcu-lated. The statistics of the dynamic PPP positioning devi-ation sequence and the RMS index value for specificexperiments are shown in Fig. 5.It can be seen from Fig. 6 that whether it is equal-value

fusion PPP (case 1) or adaptive fusion PPP (case 2), the dy-namic positioning accuracy is better than the single-systemPPP positioning result. This shows that multi-system fusionpositioning has significant advantages for improving theaccuracy of dynamic positioning. When the observation

conditions are good, the positioning accuracy of the twoconditions is basically the same.In order to further analyze the validity of case 2 in the

presence of gross errors in observations, this article addsa phase error of 1 m to the first GPS satellite of eachepoch during the 10,000th to 12,000th epoch of dynamicstations. The observations after 10,000 epochs werecompared using case 1 and case 2. The positioning re-sults are shown in Fig. 7.The change in the ratio of the adaptive factor of GLO-

NASS to GPS of case 2 is shown in the following diagram.

Fig. 5 Dynamic positioning deviation and RMS value of case 1

Fig. 6 Dynamic positioning deviation and RMS value of case 2


From Figs. 7, 8, and 9, it can be seen that when thereis a rough difference between the observed values of asingle system, the location results of case 1 are ser-iously affected, and the situation 2 is less affected. Thereason is that when a single system experiences agross error in observations, the resulting single-systemtest posterior error will gradually become larger, sothat the adaptive factor of case 2 will be automaticallyadjusted to redistribute the fusion weight ratio rela-tionship of different systems and reduce the grosserror ratio and reduce the contribution of system nor-mal equations with gross errors to achieve the purposeof suppressing gross errors.

4.3 Short term stability of fusion PPP pseudo-timedifference resultsIn this section, the data of 14 GPS/GLONASS observa-tion stations in the IGS continuous tracking station net-work in the European region were uniformly selected foranalysis [10]. The data acquisition time is March 22,2012, the data sampling rate is 30 s, and the total obser-vation time is 24 h. The satellite orbit and clock differ-ence products are derived from the IAG productsprovided by the MCC Analysis Center under the IGSorganization. The GPS/GLONASS orbit of IAG productshas been classified into the ITRF framework, and thesatellite clock difference is kept under the respective

Fig. 7 Dynamic positioning deviation and RMS value of case 1 (with gross error)

Fig. 8 Dynamic positioning deviation and RMS value of case 2 (with gross error)


time system. The sampling rate of the track product is15 min, and the sampling rate of the clock differenceproduct is 5 min. All stations are equipped with dual fre-quency dual mode GNSS receivers. In order to comparethe difference in the result of the time difference be-tween the different receiver types, the station name andthe receiver type information are listed, as shown inTable 1:As you can see from Table 1, there are six kinds of re-

ceiver types in the 13 selected stations. There are six sta-tions in which the LEICA receiver is equipped. Fourstations are equipped with TRIMBLE receivers. Theother types of receivers have only one station configur-ation each. The mean and standard deviation of the timedifference sequence on all stations are counted, asshown in the Table 2:The standard deviation index of the time difference

sequence of different stations is compared, as shownin Fig. 10.

The Allen variance is used to calculate the single dayfrequency stability index of time difference sequences ofthe different station, such as 11.As can be seen from the graph in Figs. 10 and 11, the

result of the time difference sequence obtained by thesame type of receiver is relatively close, and the absolutedifference of the time difference is less than 20 ns. Thisis mainly due to the close proximity of the absolutehardware delay of the same type of receiver, so the timedifference sequence is relatively close. There is a largesystem error due to the difference of absolute hardwaredelay between different receivers[11]. The maximum

Fig. 9 Change of adaptive factor ratio in case 2

Table 1 Station name and the receiver type information

Station name Receiver type Station name Receiver type

CAGZ TPS E_GGD PENC LEICA CR × 1200

ONSA JPS E_GGD GANP TRIMBLE NETR8

GLSV NOV OEMV3 GRAS TRIMBLE NETR5

HERT LEICA CR × 1200 TLSE TRIMBLE NETR9

JOZ2 LEICA CR × 1200 ZIM2 TRIMBLE NETR5

LAMA LEICA CR × 1200 WTZZ JAVAD TRE_G3TH

MATE LEICA CR × 1200

Table 2 Mean and standard deviation of the time differencesequence (unit: nanosecond)

Station name Receiver type Mean Standard deviation

CAGZ TPS E_GGD − 448.257 0.423

ONSA JPS E_GGD − 464.486 0.286

GLSV NOV OEMV3 − 348.679 1.123

HERT LEICA CR × 1200 − 337.857 0.546

JOZ2 LEICA CR × 1200 − 353.536 0.475

LAMA LEICA CR × 1200 − 345.758 0.389

MATE LEICA CR × 1200 − 333.689 0.732

PENC LEICA CR × 1200 −345.785 0.598

GANP TRIMBLE NETR8 − 374.537 0.694

GRAS TRIMBLE NETR5 − 375.974 0.645

TLSE TRIMBLE NETR9 − 364.876 0.432

ZIM2 TRIMBLE NETR5 − 384.438 0.564

WTZZ JAVAD TRE_G3TH − 398.343 0.654


mean time difference is more than 130 ns. The result ofthe time difference sequence on all stations is very stablein 1 day. Most of the standard deviation of the time dif-ference sequence is better than 1 ns, and the averagestandard deviation is only 0.52 ns. This stable character-istic provides a good premise for the follow-up time dif-ference prediction and the application in navigation andpositioning[12]. The single-day frequency stability ana-lysis of the TDOA sequence shows that the single daystability index of the TDOA sequence obtained by thefusion PPP is about the magnitude of 10−14, and the

average frequency stability is 3.0 × 10−14. This shows thatit is feasible to use the fusion PPP method to monitorthe time difference of the system from the precision[13].

5 Results and discussionThe traditional multi-mode GNSS fusion precise single-point positioning algorithm has the disadvantages of lowefficiency and difficulty in satisfying the demand forhigh-accuracy real-time and high-frequency data[14]. Tosolve the above problems, this paper proposes an adap-tive GNSS fusion PPP algorithm based on parameter

Fig. 10 Standard deviation statistics for time difference sequences of different stations

Fig. 11 Frequency stability index of the time difference sequence of different stations


equivalence reduction. With the increase of the numberof fusion systems, the computing load of traditional al-gorithms is exponentially increasing. The new algorithmimproves it to a linear growth, which greatly improvesthe computational efficiency. The actual example verifiesthe effectiveness and accuracy of the improved algo-rithm. Secondly, this paper also studies the feasibilityand algorithm flow of GNSS time difference monitoringusing multi-system fusion PPP algorithm at the userend. Pseudo-time difference monitoring and forecastingwork has more important application value for naviga-tion and positioning users[15]. The real system time dif-ference has no practical significance for navigation users.

AbbreviationsGLONASS: GLObalnaya NAvigatsionnaya Sputnikovaya Sistema; GNSS: GlobalNavigation Satellite System; GPS: Global Position System; PPP: Point-to-PointProtocol; UTC: United Technology Corporation

FundingTechnology Platform Project of Guangdong Provincial Department ofEducation (2017GKTSCX104), Plan Project of Guangdong Science andTechnology (2014A010103002)

Availability of data and materialsThe datasets used and/or analysed during the current study are availablefrom the corresponding author on reasonable request.

Authors’ contributionsZZ carried out the time difference detection algorithm studies, participatedin the sequence alignment and drafted the manuscript. ZX and HC carriedout the Data test. JY and YL participated in the sequence alignment. WZparticipated in the design of the study and performed the statistical analysis.YC conceived of the study and participated in its design and coordination.All authors read and approved the final manuscript.

Authors’ informationZiwen Zhang, Male, Postdoctoral, 1987-11-25, Guangdong University ofTechnology.Major: High-precision satellite positioning, radar interferometry, deeplearning.Jun Yang, Male, postgraduate, Chongqing Vocational College ofTransportation.Main research direction: high-precision satellite positioning, radarinterferometry, deep learning.Yijun Liu, Male, Professor, Guangdong University of Technology.Major: High-precision satellite positioning, deep learning.Zuoteng Xu, Male, Master student, Guangdong University of Technology,Communication Engineering.Main research direction: Deep learning, computer graphics processing.Haowen Chen, Male, Master student, Guangdong University of Technology.Main research direction: Deep learning, computer graphics processing.Yuqiang Chen, Male, Professor, 1983-07-13, Gongguan Polytechnic.Main research direction: Satellite high-precision positioning, artificialintelligence.

Competing interestsThe authors declare that they have no competing interests.

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.

Author details1Chongqing Vocational College of Transportation, Chongqing 402247, China.2School of Information Engineering, Guangdong University of Technology,

Guangzhou 510006, China. 3Dongguan Polytechnic, Dongguan 523000,China.

Received: 29 December 2018 Accepted: 26 March 2019

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https://doi.org/10.1007/s10291-012-0254-z

AbstractIntroductionRelated work

MethodsSingle-system PPP algorithm based on parameter reductionMulti-system fusion PPP algorithm based on parameter reductionAn adaptive PPP fusion algorithm based on posttesting error factor

Monitoring and analysis of GNSS time difference based on fusion PPP modelConcept of GNSS time difference and conventional monitoring methodsConcept of “pseudo-time difference” for navigation and positioning of usersAcquisition of pseudo-time difference based on fusion PPP technology

ExperienceComparison of operational efficiencyStatic and dynamic accuracy test of fusion positioningShort term stability of fusion PPP pseudo-time difference results

Results and discussionAbbreviationsFundingAvailability of data and materialsAuthors’ contributionsAuthors’ informationCompeting interestsPublisher’s NoteAuthor detailsReferences

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