A Pseudolite-Based Positioning System for Legacy GNSS Receivers

Transcription

1 Sensos 2014, 14, ; doi: /s Aticle OPEN ACCESS sensos ISSN A Psedolite-Based Positioning System fo Legacy GNSS Receives Chongwon Kim 1, Hyongmin So 2, Taikin Lee 3 and Changdon Kee 1, * School of Mechanical and Aeospace Engineeing and the Institte of Advanced Aeospace Technology, Seol National Univesity, Daehak-dong, Kwanak-g, Seol , Koea; nan772@sn.ac.k Agency fo Defense Development, The 3d R&D Institte-4, ADD, Yseong P.O. Box 35-3, DAEJEON , Koea; hyongmin.so@gmail.com Senso System Reseach Cente, Koea Institte of Science and Technology, Hwaang-o 14-gil 5, Seongbk-g, Seol , Koea; taikin@kist.e.k * Atho to whom coespondence shold be addessed; kee@sn.ac.k; Tel.: ; Fax: Received: 2 Decembe 2013; in evised fom: 17 Mach 2014 / Accepted: 18 Mach 2014 / Pblished: 27 Mach 2014 Abstact: The ephemeis data fomat of legacy GPS eceives is impope fo positioning stationay psedolites on the gond. Theefoe, to tilize psedolites fo navigation, GPS eceives mst be modified so that they can handle the modified data fomats of the psedolites. Becase of this poblem, the pactical se of psedolites has so fa been limited. This pape poposes a psedolite-based positioning system that can be sed with nmodified legacy GPS eceives. In the poposed system, psedolites tansmit simlated GPS signals. The signals se standad GPS ephemeis data fomat and contain ephemeis data of simlated GPS satellites, not those of psedolites. The se of the standad fomat enables the GPS eceive to pocess psedolite signals withot any modification. Howeve, the position otpt of the GPS eceive is not the coect position in this system, becase thee ae additional signal delays fom each psedolite to the eceive. A post-calclation pocess was added to obtain the coect eceive position sing GPS eceive otpt. This e-estimation is possible becase it is based on known infomation abot the simlated signals, psedolites, and positioning pocess of the GPS eceive. Simlations sing geneated data and live GPS data ae condcted fo vaios geometies to veify the poposed system. The test eslts show that the poposed system povides the desied se position sing psedolite signals withot eqiing any modifications to the legacy GPS

2 Sensos 2014, eceive. In this initial stdy, a psedolite-only indoo system was assmed. Howeve, it can be expanded to a GPS-psedolite system otdoos. Keywods: GPS; psedolite; indoo navigation 1. Intodction Ove the past few decades, thee have been a nmbe of stdies on Global Navigation Satellite Systems (GNSS). Many people aond the wold nowadays tilize GNSS eceives on mobile devices fo vaios kinds of applications. With the spead of location-based sevices and applications, the need fo position infomation has gown even in places whee GNSS signals ae not available, sch as indoos, in montainos o ban canyons, and in othe GNSS shadow aeas. Many stdies have been done to incease the availability of GNSS in these challenging envionments [1 3]. A psedolite is a GNSS-like signal geneato and tansmitte that can be sed as an additional signal soce to agment GNSS. Using psedolites has many advantages ove othe methods [4 6]. Employing mltiple psedolites, it is even possible to develop an independent positioning system whee the GNSS signals do not each. Howeve, thee ae some dawbacks to sing psedolites in positioning systems, inclding the following [7]: (1) Nea/fa poblem (2) Phase noise (3) Receive modifications This stdy focses on the eceive modification poblem. The eceive modification poblem efes to the need to modify GNSS eceive hadwae o fimwae to acqie accate data sing a psedolite-based positioning system. In a psedolite-based system, only GNSS eceives developed fo special ses can calclate thei own positions, becase the psedolite positions cannot be deliveed in ephemeis fomat. Theefoe, legacy GNSS eceives sch as those in smatphones o mobile devices cannot be sed with psedolite signals. To ovecome this poblem, a stdy was done that sggested a modified navigation message to delive a psedolite s position infomation [8]. The modification is simple yet ticky. Psedolites cheat the GPS eceives by filling in some ephemeis paametes with paticla nmbes to make the eslting coodinates independent fom time and fixed at eqied vales. Howeve, the scale facto and the nmbe of data bits sed in GPS ephemeis data fomat is limited [9]. Theefoe, it is impossible to make the psedolite position pefectly independent fom time, and the accacy and pecision of the psedolite position emains limited. This pape poposes a new positioning system fo psedolite signals that does not eqie any modification of legacy GPS eceives. The poposed system ses psedolites which geneate each channel signal of the GPS simlato and legacy GPS eceive withot any modification. The se position is estimated sing the otpt of the legacy GPS eceive and the infomation abot psedolites and simlated GPS satellites. Section 2 shows the limits of expessing psedolite positions in GPS ephemeis fomat. Section 3 poposes a new positioning algoithm sing psedolite signals. The

3 Sensos 2014, system concept and detailed algoithms ae descibed. Simlation eslts will be pesented in Section 4. The test was pefomed sing simlated measements and live GPS L1 data with additional manal delays. The eslts show that an accate position can be obtained sing the poposed algoithm withot any eceive modification. Fo convenience, the GPS L1 signal with C/A code was assmed ding the stdy. 2. Ephemeis Paamete fo Psedolites Befoe switching to a psedolite-based positioning system, it makes sense to check fo the possibility of expessing psedolite positions sing GPS ephemeis paametes. Table 1 gives the definitions of the obital paametes sing typical Kepleian obital paamete teminology, and it also lists the elevant ephemeis paamete types. Legacy GPS eceives detemine GPS satellites obits sing these paametes [9]. The paametes ae two s complements with the sign bit (+ o ) occpying 1/ 2 the MSB. Exceptions to this le ae e, A, and t oe. Table 1. Selected ephemeis paamete of GPS L1 signal. Ephemeis Scale Facto Definition No. of Bits Data (LSB) Units M 0 Mean anomaly at efeence time Semi-cicles n Mean motion diffeence fom compted vale Semi-cicles/sec e Eccenticity Dimensionless 1/ 2 A Sqae oot of the semi-mao axis Metes 1/2 0 Longitde of ascending node of obit plane at weekly epoch Semi-cicles i 0 Inclination angle at efeence time Semi-cicles Agment of peigee Semi-cicles Rate of ight ascension Semi-cicles/sec i Rate of inclination angle Semi-cicles/sec The nmbe of bits and scale factos of GPS ephemeis paamete ae designed fo GPS satellites with adii of appoximately 26,000 km. In ode to employ GPS ephemeis fomat fo psedolites located on Eath, shold be identical to the otation ate of the Eath, which is e 5 ad/s [9]. Becase this is ot of the ange defined fo, which has 24 bits and a scale facto of , it is impossible to expess accate psedolite positions on the Eath sing GPS ephemeis data fomat. Theefoe, the ephemeis fomat fo GPS is not sitable fo psedolites on the gond. Howeve, legacy GPS eceive can only pocess the ephemeis fomat of GPS. Theefoe a new method is needed to tilize psedolites with legacy GPS eceives. 3. Psedolite-Based Positioning System fo Legacy GNSS Receives In this section, the poposed psedolite-based positioning system will be descibed System Configation The poposed system is composed of fo main pats: the psedolites, the data seve, the efeence station, and the se teminal. Fige 1 illstates the total system configation.

4 Sensos 2014, Fige 1. Illstation of poposed system Psedolites In this system, psedolites geneate simlated GPS L1 signals and tansmit them fo ses. The necessay infomation fo the simlation is povided by the Data Seve. Using the simlation scenaio, psedolites geneate one channel signal of the simlation scenaio. Fige 2 shows the stcte of the psedolites sed in this system. The CPU contols oveall components of the psedolite accoding to the simlation scenaio eceived fom the data seve. The Digitally Contolled Oscillatos (DCO) is the clock soce of the psedolite. By poviding contol inpts to the DCO, the timing of the tansmission of the psedolite signal can be contolled. Also, the timing of the signals of the plal psedolites can be synchonized by poviding pope contol inpts to each psedolite. Geneation of the clock contol inpt fo the synchonization of the psedolites will be descibed late. Fige 2. Psedolite stcte.

5 Sensos 2014, As descibed, the psedolites in this system do not povide any infomation abot themselves (psedolites) in thei signals. They st boadcast simlated GPS signals as thee wee no psedolites. The eason of sing this kind of psedolites is to make the legacy GPS eceive pocess the psedolite signals withot any modifications Refeence Station The efeence station whose position is accately known is needed fo the clock synchonization of the psedolites. It incldes a efeence GPS eceive to collect measements of the psedolite signals. The efeence station povides the data seve with these measements. Then the data seve geneates the clock contol inpts fo each psedolite Data Seve The data seve plays two main oles in this system. One is to povide the psedolites and the se teminal with necessay infomation. It gives the infomation abot the simlation scenaio to the psedolites so that each psedolite can geneate a simlated GPS signal. Also, it povides the se teminal with the infomation abot simlated GPS satellites and psedolites. The deliveed infomation inclde the positions of psedolites and simlated GPS satellites which ae eqied to the post-calclation modle. It also incldes the infomation abot the assignment of the psedolites and coesponding GPS satellites. Using this infomation, the se teminal distingish the psedolites sing PRNs of coesponding GPS signals. The data link between the data seve and the se teminal can be WiFi o any othe possible means. Fige 3. Contol Block Diagam of Psedolite Clock Synchonization [10]. The othe ole of the data seve is geneating clock contol fo the synchonization of the psedolites. Howeve, this pape will not descibe the synchonization of the psedolites in detatil, becase the synchonization can be achieved by sing an existing method. This pape follows the method sing a efeence station eceive to synchonize the clocks of psedolites [10]. Fige 3 shows the contol block diagam of the psedolite clock synchonization. Accoding to the pape, the elative clock eo of the psedolites can be calclated by diffeencing the caie phase measements of the maste psedolite and a slave psedolite, and sbtacting the known distance vales. Then the popely designed loop filte F(s) estimates the contol vale of each psedolite clock. The otpt of the DDS

6 Sensos 2014, (Diect Digital Synthesizing) is then contolled to eliminate the clock eo α of the TCXO of the slave psedolite. The expeiment eslts showed cm-level accacy in CDGPS positioning based on the clock synchonized psedolites Use Teminal The se teminal incldes a geneal legacy GPS eceive, a data commnication modle, and a post-calclation modle. The GPS eceive calclates a position sing psedolite signals. Howeve, this a pioi position is not coect, becase the simlated GPS signal incldes additional delays de to the se of psedolites while the eceive does not know the existence of the psedolites. The post-calclation modle e-pocesses this false otpt of the GPS eceive sing infomation abot GPS satellite positions and psedolite positions. The detailed algoithm of the post-calclation modle will be descibed late. Fige 4 illstates the stcte of the se teminal. A smatphone is a good example of a se teminal, as it incldes a GPS eceive and data link. A platfom to adapt the post-calclation algoithm is also pepaed. Fige 4. Block diagam of se teminal Use Algoithm Concept In this system, psedolites simlate GPS signals eceived at a paticla eceiving point R, and each psedolite coesponds to the simlated GPS satellite. If the distances between the se teminal and each psedolite ae identical, as in Fige 5a, the otpt of the GPS eceive in the se teminal becomes the eceiving point R. The GPS eceive egads the eceived signals tansmitted fom not the psedolites bt the GPS satellites, as shown in Fige 5b, and the additional signal delay d 0 de to the se of psedolites becomes an additional common bias that does not affect the position eslt. If the distances between the se teminal and each psedolite ae diffeent fom each othe, as in Fige 6a, the otpt of the GPS eceive in the se teminal will also diffe fom the eceiving point. Fom the pespective of the GPS eceive, the signals fom Satellite 1 ae delayed by d0 d1, and signals fom Satellite 2 ae delayed by d0 d2. Theefoe, the otpt of the GPS eceive is neithe the eceiving point R no the se position.

7 Sensos 2014, Althogh the otpt of the GPS eceive is not the desied one, it contains some infomation abot the delays d 1, and d 2. Theefoe, sing the otpt position of the GPS eceive and the infomation abot simlated GPS satellites and psedolites obtained fom the data seve, it is possible to estimate d 1 and d 2 and se this infomation to e-estimate the desied se position. Fige 5. (a) A psedolite-based navigation system with identical tavel time fo both signals (2-D case); (b) Position eslt as given by the GPS eceive in the se teminal (2-D case). Fige 6. (a) A psedolite-based navigation system with diffeent tavel times fo each signal (2-D case); (b) Position eslt given by a GPS eceive in the se teminal (2-D case) Psedolite-Based Positioning Algoithm fo Legacy GNSS Receives In this section, the poposed se algoithm will be descibed with detailed fomlas. Fige 7 illstates the th psedolite and se teminal.

8 Sensos 2014, Fige 7. Illstation of th psedolite and se teminal (Simlated and Real Simation). R : position vecto of the th psedolite R : position vecto of the se d : distance between the se and the th psedolite e ˆ : nit vecto fom the se to the th psedolite R : position vecto of the GPS satellite simlated by the th psedolite R : position vecto of the eceiving point fo the simlated signal d : distance between the eceiving point and the GPS satellite simlated by the th psedolite e : nit vecto fom the eceiving point to the GPS satellite simlated by the th psedolite ˆ Positioning Pocess of GPS Receive The legacy GPS eceives in the se teminal estimates the se position sing psedolite signals. The psedoange measement fo the th psedolite can be expessed as Eqation (1): (1) d d T I T B whee T is the simlated topospheic delay of the th GPS signal, I is the simlated ionospheic delay of the th GPS signal, and T is the topospheic delay of the th psedolite signal. B is the clock bias of the GPS eceive, and is the themal noise. This stdy assmes that T, I, and T ae eithe negligible o ae eliminated by the model. The psedoange measement model is ths simplified into Eqation (2): (2) d d B Eqation (2) is the measement model fo te sitation. Howeve, the GPS eceive does not know the existence of psedolite. Theefoe the measement model sed by the GPS eceive will follow the geneal psedoange measement model as Eqation (3): d B R R B (3),

9 Sensos 2014, d is the distance between the th GPS satellite and the se, B is the clock bias of the, eceive, and is themal noise. If a pioi estimations of the se position and clock bias ae established so that ˆ T xˆ R ˆ, B T, the estimated psedoange measement shold be as follows: ˆ R Rˆ Bˆ (4), ˆ The psedoange measement esidal can be calclated by sbtacting Eqation (4) fom Eqation (3): ˆ ˆ ˆ R R, R R, B B ˆ (5) Lineaization is pefomed at cent estimation: ( ) ( ) ( ) ˆ ˆ R, R, B B ˆ R, B R ˆ B ˆ, R, B R, e ˆ, 1 B (6) Fo m satellites, m eqations ae detemined in the same way, and a matix eqation is constcted: 1 1 ˆ 1 e, 1 R, B eˆ 1 m m m, x H H x The eo state can be estimated by the Least Sqae Soltion [11]: 1 T ˆ T ˆ T T, xˆ R B H H H (8) (7) Next, state vaiables ae pdated: xˆ xˆ xˆ xˆ, old, old xˆ (9) These pocesses ae epeated ntil the state conveges. The conveged state may be expessed as T ˆ T xˆ ˆ, cvg R,, cvg B, cvg. This is the otpt of the GPS eceive and the a pioi position fo the post-calclation modle Estimation of Measements fom GPS Receive Otpt The post-calclation modle have to estimate the se position sing the otpt of the legacy GPS eceive. If the GPS eceive in the se teminal povides psedoange measements, the eceive otpt position can be ignoed and the desied se position can be calclated sing the otpt measement. Howeve, some legacy GPS eceives and some mobile devices that ae eqipped with

10 Sensos 2014, GPS eceives does not povide these measements to the se. In these cases, the oiginal measements mst be estimated fom the otpt position of the GPS eceive. As descibed in Section 3.2, thogh the GPS eceive otpt calclated in Section does not give the coect position, it contains some infomation abot the oiginal measements. The measements fom the position otpt can be estimated via Eqation (10). Satellite position R is povided by the data seve: R Rˆ Bˆ (10),, cvg, cvg Final Estimation of the Use Position Using given psedoange measements, finally the post-calclation modle can estimate the se position. Fom Eqation (2), psedoange measements can be ewitten sing position vectos as in the following eqation: R R R R B (11) Again, an a pioi estimation of the state vecto as ˆ T xˆ R Bˆ is assmed. The estimated psedoange measements may then be descibed by Eqation (12): ˆ R R ˆ ˆ R R B ˆ (12) By sbtacting Eqation (12) fom Eqation (11), the psedoange measement esidal is calclated sing the following eqation: ˆ ˆ ˆ (13) Eqation (13) is lineaized at the a pioi estimation: R R R R B B ˆ ( ˆ R ) ( ˆ R B B) ( ) ˆ R R ˆ B ˆ R BB (14) R eˆ 1 B T The same eqations can be sed fo m psedolites: 1 1 eˆ 1 1 R m m B eˆ 1 m x H (15) H x The eo state is estimated by Least Sqae Soltion [11]: T 1 ˆ T ˆ ˆ T T x R B H H H (16)

11 Sensos 2014, The oiginal state is pdated sing estimated eo state: xˆ xˆ xˆ xˆ old old xˆ (17) The final estimation is obtained by epeating these pocesses ntil the states convege. The flow chat of the algoithm fo the post-calclation modle of the se teminal is illstated in Fige 8. Fige 8. Algoithm fo the Final Estimation of the Use Position. In Fige 8, blocks in the dashed box is exactly the same as the position estimation pocess of geneal GPS eceives except the nonlinea eqation sed in Eqation (12) (ed box). The diffeences ae coming fom the existence of the psedolites between the imaginay eceiving point and the se eceive antenna.

12 Sensos 2014, Simlation Reslts and Discssion Unfotnately, it was had to be eqipped with psedolites which opeates as a GPS simlato fo this system. Also we cold not make a hadwae GPS simlato by oselves. Theefoe, the only way to veify the system was the test sing simlated data. By the eslts, we tied to show the feasibility of the poposed new concept of the psedolite based navigation system. De to the easons above, the simlated data and SDR (Softwae Defined Radio) ae sed to veify the poposed system. The SDR sed in the veification is a platfom to test vaios eceive algoithms. The opeation of legacy GPS eceives also can be implemented in the SDR. In this pape, the SDR which is designed to opeate st as the legacy GPS eceives is sed fo the test. Theefoe, the se of the SDR instead of the legacy GPS eceive seems easonable. The est of this section shows some simlation eslts to veify the poposed system. Fist, a simlation is pefomed to show the feasibility of the algoithm. Second, the same test is caied ot nde poo geometies. Thid, a test sing live GPS signal is pefomed. Some manal delays de to the psedolites ae added to the live GPS measements in this test Feasibility Test The feasibility of the poposed algoithm is tested sing five simlated satellites and five coesponding psedolites. Fige 9 shows the pocede of the feasibility test. Fige 9. Simlation pocede. Fist of all, te vales ae povided fo the initial setting modle. The positions of simlated GPS satellites and psedolites ae shown in Fige 10. Fo convenience, the eceiving point is set at (0,0,0), and satellite positions ae set as they wee on the sphee of adis of 22,000 km centeed at the eceiving point. Local se positions wee set at (0,0,0) and (1,1,0). PDOPs fo GPS satellites and psedolites wee then calclated to be and , espectively.

13 Sensos 2014, The initial setting modle stoes each te vale to the pope vaiables. Using these vales, psedoange measements ae geneated accoding to Eqation (2). Topospheic and ionospheic delays ae assmed to be eliminated by the model o by othe methods. Fige 10. (a) Skyplot of simlated GPS satellites viewed fom the eceiving point (b) Local positions of psedolites and se. Additional Gassian andom noise is added to the measements. Vaiance of the measement noise is set to 1 mete fo all psedolites. Fige 11 shows the geneated psedoange measements fo each psedolite eceived by the Use #2. Fige 11. Geneated Psedoange Measements. The GPS eceive calclates the a pioi position sing geneated measements as if it wee the geneal legacy GPS eceive. The post-calclation modle ses this a pioi position, the te GPS satellite position, and the te psedolite position to e-estimate the final position. Instead of the data seve, necessay infomation ae povided to the post-calclation modle diectly in this

14 Sensos 2014, simlation. Fige 12a shows that the a pioi position of Use #1 calclated by the algoithm stated in Section is not biased. In this case, the distances fom all psedolites to the se ae the same. Theefoe, all psedolite signals ae sbect to the same delay, which affects only the clock eo, not the position meased. The hoizontal and vetical dms eos ae calclated to be m and m, espectively. Unlike Use #1, Use #2 got biased a pioi positions fom the GPS eceive, as shown in Fige 12b. The distances fom the psedolites to the se ae diffeent fom each othe in this case, and they affect the position eslts. Howeve, sing the poposed algoithm, the final position is estimated with easonable accacy. The hoizontal and vetical dms eos ae calclated to be m and m, espectively. The a pioi position of Use #2 has mch bias eo than that of Use #1. Howeve the eo vaiance is calclated as the same vale. Fige 12. (a) a pioi position fo se #1 (b) a pioi position fo se #2. As descibed in Section 3.3.2, thogh the GPS eceive otpt does not give the coect position, it contains some infomation abot the oiginal measements. The measements fom the position otpt can be estimated via Eqation (10). Fige 13 shows the diffeence between the oiginally geneated and e-estimated psedoange measements. The esidal vales ae affected by the geomety of the simlated GPS satellites and psedolites. Fige 13. Estimated Psedoange Measements.

15 Sensos 2014, Using the a pioi positions and the estimated psedoange measements, the final estimation of se position can be calclated as descibed in Section Fige 14 shows the a pioi and final position of Use #1 and Use #2. In the final estimation, the bias eo is eliminated fo not only the Use #1, bt also fo Use #2. The vales of the hoizontal and vetical dms and bias eos became smalle than those of the a pioi estimates. The eslts show that sing the poposed system, se position can be estimated despite eliance on psedolites combined with an nmodified legacy GPS eceive. The algoithm woks egadless of the existence of bias in the otpt of the GPS eceive. Howeve, it can be affected by the geomety of simlated GPS satellites and psedolites. In the next section, simlation eslts fo poo DOPs ae pesented. Fige 14. (a) Estimation eslts fo se #1 (b) Estimation eslts fo se # Poo Geomety Test Simlated GPS satellites neve have seveely poo geomety, becase simlation allows the satellite configation to be maniplated as necessay. Howeve, the geomety may become less than ideal if the eceive nexpectedly loses a psedolite signal coesponding to a GPS satellite. Theefoe, the poposed algoithm is tested fo cases involving poo GPS and psedolite constellation geomety. Once again, five GPS satellites sing five coesponding psedolites ae simlated. The simlation pocede and settings except the GPS satellites, psedolite, and se positions ae the same as the feasibility test. Fige 15 illstates the eslts fo good and bad GPS satellite geometies. Fo each case, the DOPs fo GPS ae and , espectively. The psedolite DOP is calclated to be With highe DOPs, the a pioi position gets wose, and the final position eo is also affected. Howeve, nlike the biased a pioi position, the final estimated position still matches the te position.

16 Sensos 2014, Fige 15. (a) Reslts fo good DOP of GPS satellites (b) Reslts fo poo DOP of GPS satellites. To test fo even wose cases, poo psedolite geometies ae sed in addition to poo GPS geomety. Fige 16 illstates the eslts fo high psedolite DOPs. In each case, the DOPs fo the psedolites ae and , espectively. Fo the same a pioi positions, poo psedolite geomety makes the final estimation even wose. Again, nlike the biased a pioi positions, the final eslts match the te se positions. Fige 16. (a) Reslts fo poo DOP of psedolites (b) Reslts fo wose DOP of psedolites.

17 Sensos 2014, It can be assmed that any time a psedolite system is developed, the psedolites will be aanged in an effective configation. Howeve, if the se s GPS eceive loses some psedolite signals, the system will be left with poo geomety. Simlation eslts show that even when the geomety gets wose, the poposed algoithm woks with only a slight loss of accacy Test Using Live GPS Signals The poposed algoithm is then tested sing live GPS signals. De to a lack of available GPS-simlating psedolites, a live GPS L1 signal is sed instead of GPS-simlating psedolites. Live GPS signals wee collected sing a GP 2015 RF boad and an NI DAQ cad [12]. The aw data was stoed as a binay data file on a PC. The stoed data is then pocessed by a Softwae Defined Radio (SDR) developed by the Seol National Univesity GNSS Laboatoy [13]. The SDR otpt psedoange incldes the distance fom the GPS satellites to the GPS antenna, clock eos, topospheic and ionospheic delays, etc. The signal delay fom the psedolite to the se was manally geneated and added. This simlated psedoange was then sed to test the poposed algoithm. Fige 17 illstates the simlation pocede. Fige 17. Simlation pocede. Fo GPS satellites and fo coesponding psedolites ae sed in this test. The GPS and psedolite constellation is shown in Fige 18. To test fo diffeent geometies, se positions ae set to both (3,3,0) and (20,20,0) metes. The PDOP fo psedolites with espect to Use #1 and Use #2 ae and , espectively. The PDOP fo the GPS satellites is Test eslts fo each case ae illstated in Fige 19. Fo both cases, the GPS eceive otpt is biased. The amont of bias is geate when the geomety is poo. Howeve, the final estimated eslts place the ses in the coect positions. The hoizontal and vetical dms eos ae m and m fo Use #1. Fo Use #2, hoizontal and vetical dms eos ae calclated to be m and m.

18 Sensos 2014, Fige 18. (a) Skyplot of live GPS satellites (b) Local positions of psedolites and se. Fige 19. (a) Estimation eslts fo Use #1 (good DOP) (b) Estimation eslts fo Use #2 (poo DOP). 5. Conclsions One of the mao poblems inheent in psedolite-based positioning systems is the eceive modification poblem. De to this poblem, psedolites cannot be sed with geneal legacy GPS eceives. To esolve this poblem, this stdy poposed a psedolite-based positioning system that can be sed by nmodified legacy GPS eceives. The poposed system ses GPS-simlating psedolites whose signal can be pocessed by legacy GPS eceives. The position otpt of the GPS eceive is then epocessed sing the position infomation of the simlated GPS satellites and psedolites.

19 Sensos 2014, Seveal simlation tests wee condcted sing MATLAB to veify the poposed system. It was shown that the poposed system eslts in an accate se position, nlike the biased GPS eceive otpts. Even nde poo geometies of psedolites o simlated GPS satellites, the poposed algoithm sccessflly obtained ses positions. Becase GPS-simlating psedolites wee not available, live GPS signals wee sed to veify the system. Intentional delays wee added to the psedoange measements in ode to simlate the GPS signals tansmitted by psedolites and eceived by a local se s eceive. The eslts show that the algoithm woks well fo vaios psedolite geometies and coesponding simlated GPS satellite geometies. This pape poposed a new concept of the psedolite based navigation to ovecome the eceive modification poblem of the psedolite-based positioning systems. The feasibility of the system is shown by test eslts sing simlated data. In the fte, poposed system shold be tested by physically eal data sing eal GPS-simlating psedolites and geneal legacy GPS eceives. If this system concept mates, then psedolite-based indoo o otdoo navigation will be available fo many people with GPS eceives in thei smatphones. The only othe eqiement wold be an application that epocesses the otpt of the GPS eceive. Acknowledgments This eseach was sppoted by a gant fom Development of Wide Aea Diffeential GNSS, which is fnded by the Ministy of Oceans and Fisheies of the Koean govenment, contacted thogh SNU-IAMD at Seol National Univesity. Conflicts of Inteest The athos declae no conflict of inteest. Refeences 1. Godha, S.; Lachapelle, G.; Cannon, M. Integated GPS/INS System fo Pedestian Navigation in a Signal Degaded Envionment. In Poceedings of the ION GNSS, Foth Woth, TX, USA, Septembe Kee, C.; Jn, H.; Yn, D.; Kim, B.; Kim, Y.; Pakinson, B.W.; Langenstein, T.; Pllen, S.; Lee, J. Development of Indoo Navigation System Using Asynchonos Psedolites. In Poceedings of the 13th Intenational Technical Meeting of the Satellite Division of The Institte of Navigation (ION GPS 2000), Salt Lake City, UT, USA, Septembe 2000; pp Lashley, M.; Bevly, D.M.; Hng, J.Y. Pefomance analysis of vecto tacking algoithms fo weak GPS signals in high dynamics. IEEE J. Sel. Topics Signal Pocess. 2009, 3, Pakinson, B.W.; Spilke, J.J. Global Positioning System: Theoy and Applications; AIAA: Reston, VA, USA, 1996; Volme Stone, J.M.; LeMaste, E.A.; Powell, J.D.; Rock, S. GPS Psedolite Tansceives and Thei Applications. In Poceedings of the ION National Technical Meeting, San Diego, CA, USA, Janay 1999; pp

20 Sensos 2014, Wang, J. Psedolite applications in positioning and navigation: Pogess and poblems. J. Glob. Position. Syst. 2002, 1, Cobb, H.S. GPS Psedolites: Theoy, Design, and Applications; Stanfod Univesity: Stanfod, CA, USA, Rapinski, J.; Cellme, S.; Rzepecka, Z. Modified GPS/psedolite navigation message. J. Navig. 2012, 65, ICD, G. Navsta GPS Space Segment/Navigation Use Intefaces, Inteface Specification; IS-GPS-200E: El Segndo, CA, USA, Yn, D.; Kee, C. Centimete Accacy Stand-alone Indoo Navigation System by Synchonized Psedolite Constellation. In Poceedings of the 15th Intenational Technical Meeting of the Satellite Division of the Institte of Navigation (ION GPS 2002), Potland, OR, USA, Septembe 2002; pp Simon, D. Optimal State Estimation: Kalman, h Infinity, and Nonlinea Appoaches; Wiley: Weinheim, Gemany, Semicondcto, Z. Gp2015 GPS eceive RF font end datasheet. Febay Jeon, S.; So, H.; No, H.; Lee, T.; Kee, C. Development of Real-time Softwae GPS Receive Using Windows Visal C++ and USB RF Font-end. In Poceedings of the 2010 Intenational Technical Meeting of the Institte of Navigation, Long Beach, CA, USA, Janay 2001; pp by the athos; licensee MDPI, Basel, Switzeland. This aticle is an open access aticle distibted nde the tems and conditions of the Ceative Commons Attibtion license (