Accuracy Improvement of DGPS for Low-Cost Single-Frequency Receiver Using Modified Flächen Korrektur Parameter Correction

International Journal of Geo-Information

Article Accuracy Improvement of DGPS for Low-Cost Single-Frequency Receiver Using Modiﬁed Flächen Korrektur Parameter Correction

Jungbeom Kim 1, Junesol Song 1, Heekwon No 1, Deokhwa Han 1, Donguk Kim 1, Byungwoon Park 2,* and Changdon Kee 1,*

1 School of Mechanical and Aerospace Engineering and Institute of Advanced Aerospace Technology, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Korea; [email protected] (J.K.); [email protected] (J.S.); [email protected] (H.N.); [email protected] (D.H.); [email protected] (D.K.) 2 School of Aerospace Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Korea * Correspondence: [email protected] (B.P.); [email protected] (C.K.); Tel.: +82-02-3408-4385 (B.P.); +82-02-880-1912 (C.K.)

Academic Editor: Wolfgang Kainz Received: 17 June 2017; Accepted: 18 July 2017; Published: 20 July 2017

Abstract: A differential global positioning system (DGPS) is one of the most widely used augmentation systems for a low-cost L1 (1575.42 MHz) single-frequency GPS receiver. The positioning accuracy of a low-cost GPS receiver decreases because of the spatial decorrelation between the reference station (RS) of the DGPS and the users. Hence, a network real-time kinematic (RTK) solution is used to reduce the decorrelation error in the current DGPS system. Among the various network RTK methods, the Flächen Korrektur parameter (FKP) is used to complement the current DGPS, because its concept and system configuration are simple and the size of additional data required for the network RTK is small. The FKP was originally developed for the carrier-phase measurements of high-cost GPS receivers; thus, it should be modified to be used in the DGPS of low-cost GPS receivers. We propose an FKP-DGPS algorithm as a new augmentation method for the low-cost GPS receivers by integrating the conventional DGPS correction with the modified FKP correction to mitigate the positioning error due to the spatial decorrelation. A real-time FKP-DGPS software was developed and several real-time tests were conducted. The test results show that the positioning accuracy of the DGPS was improved by a maximum of 40%.

Keywords: differential global positioning system; Flächen Korrektur parameter; FKP-DGPS; spatial decorrelation

1. Introduction The global positioning system (GPS), which was initially limited to military or surveying fields, has gradually been extended to ordinary industrial fields such as navigation and time synchronization. The types of GPS receivers are determined based on the performance required in each field, the price of the system, and the size of the market. For example, in the field of land surveying or bridge monitoring where high accuracy is required, high-end GPS receivers that support multi-frequency signals are used, including L1, which is the primary frequency, and L2 (1227.60 MHz), which is the secondary frequency. These receivers are used to estimate the ionospheric errors and are capable of receiving pseudorange and carrier-phase measurements. In the field of safety-of-life (SoL) service for aviation or maritime, GPS receivers that are capable of receiving L1 pseudorange and carrier-phase measurements are used. In the field of location-based service (LBS) or road systems, low-cost GPS

ISPRS Int. J. Geo-Inf. 2017, 6, 222; doi:10.3390/ijgi6070222 www.mdpi.com/journal/ijgi ISPRS Int. J. Geo-Inf. 2017, 6, 222 2 of 21 receivers that support the L1 single-frequency signal are used, the accuracy of which is approximately 5 m. As the price of the low-cost GPS chipsets has fallen below US one dollar and smartphones have become increasingly popular, the applications of global navigation satellite system (GNSS), such as car navigation, geo-tagging, and LBS, are likely to increase dramatically [1]. As the low-cost L1 single-frequency GPS receivers dominate most of the GPS market [2], there is a strong interest in enhancing their accuracy. Many types of augmentation systems have been developed for low-cost GPS receivers. Among them, the differential global positioning system (DGPS) is the most representative augmentation system. DGPS services have been established worldwide. They can be divided into so-called local-area DGPS (LADGPS) services for small areas, such as a country, and wide-area DGPS (WADGPS) services for larger areas such as an entire continent or even worldwide [3]. A single reference station (RS) in a LADGPS at a known location can estimate a range of error corrections for each GPS satellite in view. These error corrections are then broadcasted to users nearby an RS. By applying these corrections to the received signals, a user can typically improve the accuracy up to a range of 1–3 m [4]. However, as the distance between the user and the RS increases, the range decorrelation increases, thus reducing the accuracy. The positioning accuracy [3,4] reduces largely because of the spatial decorrelation such as ephemeris error and ionospheric and tropospheric delays. Furthermore, if a user moves away from the RS of the LADGPS while receiving the corrections, the error due to the spatial decorrelation cannot be ignored. In this case, it is possible to receive corrections from another RS that is getting closer while moving, but the discontinuity of the position can occur. To extend the service area using a few geosynchronous equatorial orbit (GEO) satellites and overcome the error due to the spatial decorrelation, the WADGPS has been proposed. This system is used to obtain a meter-level accuracy over a large region while using a fraction of the number of RSs. The general approach is to divide the total pseudorange error into its components and estimate the variation in each component over the entire region [5–7]. Hence, the accuracy does not depend on the proximity of the user to a single RS, such as that in the LADGPS [5]. However, the corrections regarding the ionospheric delay are broadcasted at maximum intervals of 300 s [8]. Although the intervals vary in different operating nations such as wide-area augmentation system (WAAS, USA), European geostationary navigation overlay service (EGNOS, Europe), and MTSAT satellite augmentation system (MSAS, Japan), the user needs to wait for a long time to receive all the corrections of the WADGPS. In addition, because the WADGPS has been developed for aviation, the constraint regarding the 40–50◦ elevation angle is not a major problem; however, it may be a major obstacle for users in urban and mountainous areas while receiving the signals from the GEO satellites. In other words, if a signal is interrupted while receiving corrections, the user needs to wait when the correction data are not being received. Hence, an effective and reasonable augmentation system is required to compensate for the error due to the spatial decorrelation even in the cases of long baselines while receiving the correction via separated communication from the LADGPS. A network real-time kinematic (RTK) solution is used to reduce the decorrelation error in a Carrier-phase DGPS system. Among the various network RTK methods, the Flächen Korrektur parameter (FKP), which is a suitable methodology to complement the current DGPS using an one-way communication environment, is also useful to complement the current LADGPS. KODGIS and NAWGIS services operated by the ASG-EUPOS in Poland are examples of systems to improve the low-cost receiver using the network RTK solution, which is very rare in other countries or infrastructures. While the KODGIS generates DGPS correction directly for the user’s location based on the virtual reference station (VRS) concept, the NAWGIS generates DGPS correction for strictly defined points (the geometric centers of the station network are for northern and southern Poland) based on the VRS concept to compensate for the spatial decorrelation error of the DGPS [9,10]. To provide the service, it uses a proprietary message from the radio technical commission for maritime (RTCM) for the solution. Thus, exclusive users who made a contractor with the operator support the system. The proprietary message of the NAWGIS (message ISPRS Int. J. Geo-Inf. 2017, 6, 222 3 of 21 type 59) has been recently moved to the reserved message for private use in the RTCM version 2.3, and mass market low-cost receivers such as u-blox series do not support the private message. In this study, we propose a user-oriented FKP-DGPS algorithm as a new augmentation system by integrating the conventional LADGPS correction with the modified FKP correction. This system combines the existing LADGPS and FKP infrastructures, and subsequently, generates a new correction to be provided to the low-cost GNSS receivers based on the RTCM standard. It does not require a special infrastructure for the FKP-DGPS and follows the current standards. Thus, any LADGPS user can compensate for the spatial decorrelation error by itself. In addition to solving the spatial-decorrelation problem in the LADGPS, it can be a solution for the signal corruption of the WADGPS correction from the satellite based augmentation system (SBAS) GEO satellite. Because it is difficult to ensure a stable service for land users based on the SBAS corrections, this study focuses on the ground infrastructure that provides the LADGPS service; herein, the DGPS referred is the LADGPS. The remainder of this paper is organized as follows. Section2 describes the spatial decorrelation of the LADGPS and introduces a method of reducing its influence using a modified FKP correction with the help of mathematical analysis. Section3 focuses on the method of developing a real-time FKP-DGPS algorithm using the modified FKP correction; moreover, the method of applying the calculated FKP-DGPS correction to a low-cost L1 single frequency GPS receiver is presented. Section4 shows the results of the static and dynamic user tests conducted to confirm the improvement in the accuracy obtained through the developed algorithm. Finally, the performance of the developed algorithm in determining the reduced positioning errors with sufficient coverage area is verified through the test results.

2. DGPS and FKP

2.1. DGPS and Spatial Decorrelation GPS is a widely known navigation system providing accurate, continuous, worldwide, three-dimensional position, velocity and time information. The positioning accuracy of the low-cost L1 single-frequency GPS receivers is generally about 5 m to 10 m because many sources of possible errors reduce the positioning accuracy [5]. In the space segment, GPS satellite orbit and clock errors exist. In addition, while a signal is being transmitted from a GPS satellite to a user, the atmospheric effects such as ionospheric and tropospheric delays may alter the travel time of the GPS signal. In the user segment, multipath error and noise exist. Except for the errors induced in the user segment, other errors, which are characteristic of the spatial correlation, can be fairly eliminated using the correction from the RS of the DGPS. In other words, the RS of the DGPS, which is positioned at a known location that was previously surveyed, can estimate the errors in its GPS signals and broadcast the correction data to nearby users. Figure1 shows the range errors between the RS and the users considering only the atmospheric effects. Even if there are common errors in the measurements, they cannot be exactly equal because of the spatial decorrelation. As the separation of the user from the RS increases, the difference in the ionospheric and tropospheric delay between the two sites increases. Table1 lists the different errors depending on the separation based on recent studies [11,12].

Table 1. Quantity of spatial decorrelations [12].

Delay Average Maximum Ionospheric 4 m 40 m Tropospheric 2 m 16 m Ephemeris <0.25 m <0.25 m ISPRS Int. J. Geo-Inf. 2017, 6, 222 3 of 21

In this study, we propose a user-oriented FKP–DGPS algorithm as a new augmentation system by integrating the conventional LADGPS correction with the modified FKP correction. This system combines the existing LADGPS and FKP infrastructures, and subsequently, generates a new correction to be provided to the low-cost GNSS receivers based on the RTCM standard. It does not require a special infrastructure for the FKP-DGPS and follows the current standards. Thus, any LADGPS user can compensate for the spatial decorrelation error by itself. In addition to solving the spatial-decorrelation problem in the LADGPS, it can be a solution for the signal corruption of the WADGPS correction from the satellite based augmentation system (SBAS) GEO satellite. Because it is difficult to ensure a stable service for land users based on the SBAS corrections, this study focuses on the ground infrastructure that provides the LADGPS service; herein, the DGPS referred is the LADGPS. The remainder of this paper is organized as follows. Section 2 describes the spatial decorrelation of the LADGPS and introduces a method of reducing its influence using a modified FKP correction with the help of mathematical analysis. Section 3 focuses on the method of developing a real-time FKP–DGPS algorithm using the modified FKP correction; moreover, the method of applying the calculated FKP–DGPS correction to a low-cost L1 single frequency GPS receiver is presented. Section 4 shows the results of the static and dynamic user tests conducted to confirm the improvement in the accuracy obtained through the developed algorithm. Finally, the performance of the developed algorithm in determining the reduced positioning errors with sufficient coverage area is verified through the test results.

2. DGPS and FKP

2.1. DGPS and Spatial Decorrelation GPS is a widely known navigation system providing accurate, continuous, worldwide, three-dimensional position, velocity and time information. The positioning accuracy of the low-cost L1 single-frequency GPS receivers is generally about 5 m to 10 m because many sources of possible errors reduce the positioning accuracy [5]. In the space segment, GPS satellite orbit and clock errors exist. In addition, while a signal is being transmitted from a GPS satellite to a user, the atmospheric effects such as ionospheric and tropospheric delays may alter the travel time of the GPS signal. In the user segment, multipath error and noise exist. Except for the errors induced in the user segment, other errors, which are characteristic of the spatial correlation, can be fairly eliminated using the correction from the RS of the DGPS. In other words, the RS of the DGPS, which is positioned at a ISPRS Int.known J. Geo-Inf. location2017 ,that6, 222 was previously surveyed, can estimate the errors in its GPS signals and 4 of 21 broadcast the correction data to nearby users.

Figure 1. DGPS concept and spatial decorrelation. Figure 1. DGPS concept and spatial decorrelation.

The errors due to the spatial decorrelation can be expressed using the following equations. First, the pseudorange measurements of the user and RS are given below.

i i i i i i i i ρu = R + δR − Ru · eu − b + Iu + Tu + Bu + εu j j j j j j j j ρu = R + δR − Ru · eu − b + Iu + Tu + Bu + εu (1) i i i i i i i i ρr = R + δR − Rr · er − b + Ir + Tr + Br + εr j j j j j j j j ρr = R + δR − Rr · er − b + Ir + Tr + Br + εr

The superscripts i and j denote the ith and jth GPS satellites, respectively, and the subscripts u and r denote the user and RS, respectively. In addition, R, e, b, B, I, T, δR, and ε are the position, line of sight vector, satellite clock bias, receiver clock bias, ionospheric delay, tropospheric delay, ephemeris i j i j error, and noise, respectively. By subtracting between two satellites single differences ( ∇ ρu, ∇ ρr), the double-difference measurement is obtained as follows.

i j h i i i j j j i i j u∆r ∇ ρ = R + δR · eu − R + δR · eu − Ru · eu − eu i j i j i j + Iu − Iu + (Tu − Tu) + ∇ εu (2) h i i i j j j i i j − R + δR · er − R + δR · er + Rr · er − er i j i j i j − Ir − Ir − Tr − Tr − ∇ εr

As explained previously, the measurement of the user apart from the RS includes the spatial decorrelation errors. Hence, considering the decorrelation errors (δI, δT), the relationship between the common errors can be expressed as follows.

i i i i i i i Iu = Ir + δI , Tu = Tr + δT −r ∆uTmodel j j j j j j j (3) Iu = Ir + δI , Tu = Tr + δT −r ∆uTmodel where δI, δT are the components of the ionospheric and tropospheric delays, respectively, due to the spatial decorrelation between the user and the RS. In addition, the subscript “model” denotes the value that is calculated using a tropospheric model. Several errors can be appropriately determined using various models such as the Klobuchar model for ionospheric delay and a simple model for the tropospheric delay. In particular, the tropospheric delay can be approximated using the model because the tropospheric refraction arises from the predictable component [13]. Hence, assuming that the user and the RS use the tropospheric model to eliminate the tropospheric error in their ISPRS Int. J. Geo-Inf. 2017, 6, 222 5 of 21 measurements, the relationship of the tropospheric delay can be expressed using the above equation. Because the ephemeris error is less affected by the spatial decorrelation compared to the ionospheric and tropospheric delays, as listed in Table1, it can be ignored in this mathematical analysis along with the noise. By substituting Equation (3) into Equation (2), we obtain the following equation.

i j i i j j i j i j u∆r ∇ ρ = R ·u ∆re − R ·u ∆re − Ru · eu + Ru · eu + Ru · eu − Ru · eu i j i j i i j (4) + ∇ δT −r ∆u ∇ Tmodel + ∇ δI

Finally, the errors due to the spatial decorrelation in the double-difference measurement are conﬁrmed. Hence, it is reasonable to conclude that the position accuracy reduces because of the spatial decorrelation.

2.2. Network RTK and FKP The positioning method based on the carrier-phase measurement is quite difficult because of the process of determining the integer ambiguity [14]. The spatial decorrelation affects the resolution of the integer ambiguity. Hence, many studies have been conducted on the spatial decorrelation and several network-RTK methods have been developed such as the VRS, master-auxiliary concept (MAC), and FKP. The VRS is the most widely used augmentation system worldwide. It provides an accurate, stable, and suitable service for static users. It can be used in all receivers wherein the RTCM message is employed. Moreover, the VRS has better performance than the other methods. However, a bidirectional communication is required because the corrections are transmitted only after receiving the position of the user [15]. Therefore, there is a privacy problem and it is unsuitable for dynamic users who are moving continuously and can go anywhere. In case of a system used in a local area such as precise farming, the correction received from the starting point may be continuously valid [16]. However, the performance deterioration due to the spatial decorrelation is inevitable for the user moving away from the starting point, and the correction from a new VRS point for the current user position should be updated to compensate for the decorrelation error, thereby leading to a VRS hand-over problem. The MAC has been developed to supplement the previously developed VRS and compensate for the drawbacks of the FKP with more accurate and stable positioning compared to the VRS and FKP. The MAC comprises a master RS and several auxiliary RSs. Each auxiliary RS sends its own measurements to the master, and the inter-station difference in the correction is used to estimate the required correction. This correction can be divided into dispersive (ionospheric) and non-dispersive (geometric) corrections for broadcast efficiency, and it can be modified for the low-cost GPS receivers. In addition, this solution can be applied with a one-way communication; thus, a user of a kinematic application can determine the position regardless of any interruption or discontinuity. However, the amount of data is somewhat high, and the method applied by the user is somewhat complicated [15]. The FKP is an “area-correction parameter” and it is one of the first methods that was developed to implement a network RTK. The FKP is used to calculate the coefficients of a polynomial surface, which models the correction difference referenced to the master station. These coefficients are horizontal gradients for the dispersive and non-dispersive errors, and are used to evaluate the error polynomial at the desired location. The user interpolates the corrections and applies them with the master station observations or corrections [15,17]. It helps broadcast coefficients that can express the error plane efficiently in a way described in Figure2. Thus, it is suitable for broadcasting corrections. Like the MAC, this solution can be applied with a one-way communication; thus, a user of a kinematic application can determine the position regardless of any interruption or discontinuity. Although the decision made by the provider regarding the complexity of the model can influence the performance of the user, and the accuracy of the FKP is less than that of other methods, the amount of data is small; moreover, the method applied by the user is simple [15,18]. Hence, in this study, we propose a new augmentation method to improve the accuracy of the current DGPS using practical and suitable FKP corrections for all the users described above. ISPRS Int. J. Geo-Inf. 2017, 6, 222 6 of 21 ISPRS Int. J. Geo-Inf. 2017, 6, 222 6 of 21

ISPRS Int. J. Geo-Inf. 2017, 6, 222 6 of 21

FigureFigure 2. 2.Linear Linear FKP FKP planes for for four four RSs RSs [19]. [19 ]. The range errors due to the spatial decorrelation in the space between the two RSs can be Theestimated, range errors as shown due to thein Figure spatial 3. decorrelation In other words, in the the space FKP between RS is theused two to RSs calculate can be estimated,the as showndistance-dependent in Figure3. In otherrange words,errors in the close FKP proximit RS is usedy to itself to calculate by comparing the distance-dependent the range errors of range errors innearby close RSs. proximity Subsequently, to itself it helps by comparing convert them the in rangeto error errors surfaces of nearbyand broadcast RSs. Subsequently, their first-order it helps linear approximated gradients as FKP corrections. Therefore, the users can eliminate the effects of convert them into error surfaces and broadcast their first-order linear approximated gradients as FKP the spatial decorrelation using the FKP correction. The FKP is less accurate than the VRS and MAC corrections.because Therefore, it simplifies the the users rangeFigure can errors eliminate 2. Linear into theFKP the first-order planes effects for four gradients. of theRSs [19]. spatial Nevertheless, decorrelation it can be using easily the FKP correction.modified The FKPfor pseudorange is less accurate measurements than the VRSin the and low-cost MAC L1 because single-frequency it simplifies GPS the receiver. range errorsThe into the first-orderparametersThe gradients.range of the errors FKP Nevertheless,due correction to the spatialshow it that candecorrelati the be horizontal easilyon in modifiedthe gradients space betweenforare pseudorangelinear the approximations two RSs measurements can beof in theestimated,the low-cost geometric L1as single-frequencyandshown ionospheric in Figure errors 3. GPS In in receiver. otherthe newords,ighborhood The the parameters FKPof the RS RS. is of Theused the geometric FKPto calculate correction gradient the show distance-dependent range errors in close proximity to itself by comparing the range errors of that thecontains horizontal the non-dispersive gradients are (eph linearemeris approximationsand troposphere residuals) of the geometricerrors whereas and the ionospheric ionospheric errors nearbygradient RSs. contains Subsequently, the dispersive it helps errors.convert The them geographical into error surfaces coordinates and broadcast, are theirthe ellipsoidalfirst-order in the neighborhood of the RS. The geometric gradient contains the non-dispersive (ephemeris linearcoordinates approximated of the corresponding gradients as RSFKP and corrections. the coordinates Therefore, of the the user users are can, .eliminate The corrections the effects can beof and tropospherethethen spatial written decorrelationresiduals) as follows. errorsusing the whereas FKP correction. the ionospheric The FKP is gradientless accurate contains than the the VRS dispersive and MAC errors. The geographicalbecause it simplifies coordinates the rangeϕr, λerrorsr are into the the ellipsoidal first-order coordinatesgradients. Nevertheless, of the corresponding it can be easily RS and the coordinatesmodified for of thepseudorange user are ϕmeasurements, λ. The corrections in the lo canw-cost be L1 then single-frequency written as follows. GPS receiver. The parameters of the FKP correction show that the horizontal gradients are linear approximations of the geometric and ionospheric errors in the neighborhood of the RS. The geometric gradient δρo = 6.37 · (No(ϕ − ϕr) + Eo(λ − λr) cos(ϕr)) contains the non-dispersive (ephemeris and troposphere residuals) errors whereas the ionospheric δρI = 6.37 · H · (NI (ϕ − ϕr) + EI (λ − λr) cos(ϕr)) (5) gradient contains the dispersive errors. The geographical coordinates , are the ellipsoidal = + ( − )3 coordinates of the correspondingH 1 16 RS0.53 and theel /coordinatesπ of the user are , . The corrections can be then written as follows.

Figure 3. Broadcasted FKP correction information.

Figure 3. Broadcasted FKP correction information. Figure 3. Broadcasted FKP correction information.

ISPRS Int. J. Geo-Inf. 2017, 6, 222 7 of 21

The subscripts o and I denote the components of the geometric and ionospheric signals, respectively. In addition, N, E, el are the gradients in the north–south and east–west directions and elevation angle of the satellite at the user position, respectively [20,21]. These parameters are transmitted to the user through the network transport of the RTCM via the Internet protocol (NTRIP) in the form of an RTCM version 3.1 standard message. Based on the RTCM standard document, message type 1034 contains the FKP gradients and message type 1005 contains the station coordinates [21]. Regions where the users make use of the FKP service are such as many European countries including Germany, parts of America, Korea, Japan, and Australia [22]. The ephemeris error due to the spatial decorrelation is much smaller than the tropospheric delay. Hence, the correction used for the geometric errors can be used for the tropospheric delays. In addition, the sign of the correction for the ionospheric error should be reversed for the pseudorange measurements because the correction in Equation (5) is obtained for the carrier-phase measurements. Accordingly, Equation (5) is modiﬁed as follows.

δρo = δTFKP ' δT, δρI = −δIFKP ' δI (6)

The subscript FKP denotes the corrections made using the FKP messages. The residual errors due to the spatial decorrelation in Equation (4) could be then eliminated using the modiﬁed FKP corrections as follows.

i j i i j j i j i j u∆r ∇ ρ− R ·u ∆re − R ·u ∆re − Ru · eu + Ru · eu + Ru · eu − Ru · eu i j i j i i j (7) = ∇ δT −r ∆u ∇ Tmodel + ∇ δI i j i j i i j ' ∇ δTFKP −r ∆u ∇ Tmodel + − ∇ δIFKP

3. FKP-DGPS Algorithm

3.1. RTCM Version 2.3 The development of the real-time FKP-DGPS algorithm is based on the DGPS messages, which are broadcasted in the RTCM version 2.3 format through the NTRIP. The broadcasting information in the RTCM version 2.3 contains various messages regarding the DGPS correction and network RTK. Among the various messages, the low-cost GPS receiver requires several messages such as message types 1, 2, 3, and 9 to obtain the position of the DGPS more accurately, instead of only a standalone position [23,24]. Including the u-blox receiver, which is a typical low-cost GPS receiver, the commercial low-cost L1 single-frequency GPS receivers have an interface to receive the RTCM version 2.3 messages for the DGPS. Figure4 shows the structure of the message type 1 in the RTCM version 2.3. The structure comprises various information, such as pseudorange correction (PRC) and range-rate correction (RRC), which is expressed as pseudorange correction change rate in Figure4, issue of data (IOD), and user differential range error (UDRE). The DGPS correction for each satellite in message type 1 is approximately 40 bits except for the parity data, and it is usually broadcasted every second. The PRC is the main information for the DGPS, and we explain the method of integrating the modiﬁed FKP corrections with the PRC information of the message type 1 in Section 3.3. ISPRS Int. J. Geo-Inf. 2017, 6, 222 8 of 21 ISPRS Int. J. Geo-Inf. 2017, 6, 222 8 of 21

FigureFigure 4. 4. StructureStructure of of message message type type 1 1 in in RTCM RTCM version version 2.3. 2.3.

3.2.3.2. RTCM RTCM Version Version 3.1 3.1 [21] [21] TheThe development development of of the the real-time real-time FKP–DGPS FKP-DGPS al algorithmgorithm is is based on the FKP messages, which which areare broadcasted broadcasted in in the the RTCM RTCM version version 3.1 3.1 format format through through the the NTRIP. NTRIP. The broadcasting information inin the RTCMRTCM versionversion 3.1 3.1 contains contains various various messages messages regarding regarding the the GPS GPS observations observations and and network network RTK. RTK.Among Among the various the various messages, messages, message message type 1034 type contains 1034 contains the GPS the network GPS network FKP gradient FKP gradient message messagecomprising comprising geometric geometric and ionospheric and ionospheri gradientsc as gradients shown in as Table shown2. The in FKP Table information 2. The FKP per informationsatellite in the per message satellite type in the 1034 message is approximately type 1034 is 66 approximately bits except for 66 the bits parity except data, for andthe itparity is usually data, andbroadcasted it is usually at intervals broadcasted in the at rangeintervals of 10~15 in the s. range of 10~15 seconds.

TableTable 2. 2. StructureStructure of of message message type type 1034 1034 in in RTCM RTCM version 3.1. Data Field Data Type Number of Bits DataGPS Field Satellite ID Data unsigned Type int6 Number 6 of Bits GPS IssueGPS of Satellite data ephemeris ID (IDOE) unsigned bit(8) int6 86 GPS IssueN0: Geometric of data ephemeris gradient (IDOE) (North) bit(8) int12 12 8 N0: Geometric gradient (North) int12 12 E0:E0: Geometric Geometric gradient gradient (East) (East) int12 int12 12 12 NI:NI: Ionospheric Ionospheric gradient gradient (North) (North) int14 int14 14 14 EI: IonosphericEI: Ionospheric gradient gradie (East)nt (East) int14 int14 14 14 TotalTotal 66 66

3.3.3.3. Real-Time Real-Time FKP–DGPS FKP-DGPS Algorithm [[25,26]25,26] UsingUsing the modified modiﬁed FKP corrections,corrections, shownshown in in Equations Equations (5) (5) and and (6), (6), the the PRC PRC in in message message type type 1 of1 ofthe the RTCM RTCM version version 2.3 2.3 can can be be described described as as follows. follows. PRC=+ PRC PRC PRCFKP−DGPSFKP− DGPS= PRCDGPS DGPS+ PRC FKP FKP PRC=−Δ−δδ T T I (8)(8) PRCFKP =FKPδTFKP FKP−r r∆u uTmodel − FKPδIFKP In other words, we decoded the received message type 1 and integrated the PRC in the In other words, we decoded the received message type 1 and integrated the PRC in the message message with the modified FKP corrections using the FKP gradient information typically with the modiﬁed FKP corrections using the FKP gradient information typically transmitted every transmitted every 10~60 s. In addition, the tropospheric delays are generated using the Niell 10~60 s. In addition, the tropospheric delays are generated using the Niell mapping function and mapping function and Saastamoinen tropospheric zenith-delay model, which are recommended in Saastamoinen tropospheric zenith-delay model, which are recommended in the RTCM standard the RTCM standard document. The integrated PRC of the FKP–DGPS is encoded in accordance document. The integrated PRC of the FKP-DGPS is encoded in accordance with the format of with the format of the original message type 1. the original message type 1. Figure 5 shows the process of the real-time FKP–DGPS algorithm. First, the user and correction data are acquired such as the DGPS correction in the RTCM version 2.3 and the FKP correction data in RTCM version 3.1. Using the collected data, the tropospheric delays are generated, and the FKP

ISPRS Int. J. Geo-Inf. 2017, 6, 222 9 of 21

Figure5 shows the process of the real-time FKP-DGPS algorithm. First, the user and correction

ISPRSdata areInt. J. acquired Geo-Inf. 2017 such, 6, 222 as the DGPS correction in the RTCM version 2.3 and the FKP correction9 dataof 21 in RTCM version 3.1. Using the collected data, the tropospheric delays are generated, and the FKP corrections areare calculatedcalculated as as explained explained previously previously using using Equations Equations (5) and (5) (8). and Finally, (8). itFinally, is necessary it is necessaryto encode theto encode generated the FKP-DGPS generated correctionFKP–DGPS in thecorrec formtion of messagein the form type of 1 inmessage the RTCM type version 1 in the 2.3 RTCMto directly version apply 2.3 it to thedirectly commercial apply it low-cost to the commercial L1 single-frequency low-cost GPSL1 single-frequency receiver. Thus, we GPS can receiver. acquire Thus,the FKP-DGPS we can acquire position the in FKP–DGPS real-time at position the output in real-time of the receiver. at the output of the receiver.

FigureFigure 5. 5. FlowFlow chart chart of of real-time real-time FKP–DGPS FKP-DGPS algorithm.

4. Test Results 4. Test Results

4.1. System System Configuration Conﬁguration Currently, the GPS-related correction information is being broadcasted in Korea by various agencies such as National Geographic Information Institute (NGII), Korea Astronomy and Space Science InstituteInstitute (KASSI),(KASSI), and and National National Maritime Maritime PNT PNT Ofﬁce Office (NMPO). (NMPO). Most Most of these of servicesthese services are widely are widelyused for used the RSsfor the operated RSs operated by NGII. by There NGII. are Ther moree are than more 50 RSsthan operated 50 RSs byoperated NGII asby described NGII as describedin Figure6 in, providingFigure 6, providing various services various suchservices as VRS,such as MAC, VRS, FKP, MAC, and FKP, DGPS. and DGPS. The RSs The are RSs used are usedto simultaneously to simultaneously broadcast broadcast the DGPS the (mountpoint: DGPS (mountpoint: DGPS_V2) DGPS_V2) and FKP correction and FKP (mountpoint: correction (mountpoint:FKP_V31) information. FKP_V31) information. Thus, several Thus, RSs several located RSs nearby located the nearby test users the test were users selected were selected to receive to receivethe corrections the corrections in the tests. in the tests.

ISPRS Int. J. Geo-Inf. 2017, 6, 222 10 of 21

Figure 6. Reference Stations operated by NGII in Korea Figure 6. Reference Stations operated by NGII in Korea. 4.2. Preliminary Test 4.2. Preliminary Test Before improving the accuracy in the position domain using the FKP correction, a preliminary Beforetest was improving conducted on the the accuracy Figurerange 6.domain Reference in the and position Stations the te operated domainst data bywere usingNGII analyzed in theKorea FKP through correction, post-processing. a preliminary test wasThe conducteddata were collected on the rangefor an domainhour (2–3 and pm thein local test time) data wereon 24 analyzedSeptember through2013. As post-processing.the FKP RS, 4.2. Preliminary Test The dataYANP were station collected was selected for an which hour is (2–3 70 km pm east in localof INCH time) station on 24 as September user. As analyzed 2013. Aspreviously, the FKP RS, Before improving the accuracy in the position domain using the FKP correction, a preliminary YANPthe station divergence-free was selected hatch-filtered which is(N 70 = 1000) km eastdouble of-differenced INCH station (DD) as measurements user. As analyzed were used previously, and (7) testcan wasbe divided conducted into on two the casesrange suchdomain as theand residuthe testal dataerror were before analyzed applying through the FKP post-processing. corrections as the divergence-free hatch-ﬁltered (N = 1000) double-differenced (DD) measurements were used and andThe thatdata afterwere applying collected themfor an as hour . (2–3 pm in local time) on 24 September 2013. As the FKP RS, (7) can beYANP divided station into was two selected cases which such is as 70 the km residualeast of INCH error station before as applyinguser. As analyzed the FKP previously, corrections as α αρ=Δ∇ij −()R i ⋅Δ e i − R j ⋅Δ e j − Re ⋅ i + Re ⋅ j + Re ⋅ i − Re ⋅ j and thatthe after divergence-free applying them hatch-filteredur as β. (N ur= 1000) double ur-differenced uu uu (DD) measurements uu uu were used and (9) βα=−∇ij δ −Δ∇ iji +−∇ ij δ (7) can be divided into two()() casesTTFKP such r as u themodel residual error I FKP before applying the FKP corrections as and that afteri applyingj themi as i. j j i j i j α =u ∆r ∇ ρ − R ·u ∆re − R ·u ∆re − Ru · e + Ru · eu + Ru · e − Ru · eu As shown in Figure 7, the residual errors decreased ubecause of the positiveu effect of the FKP (9) i j αρ=Δ∇ij −()Ri i ⋅Δj ei i − R j ⋅Δ e j −i Re ⋅j i + Re ⋅ j + Re ⋅ i − Re ⋅ j β = α − ∇ δT ur−r ∆u ∇ urT ur+ − ∇ uuδI uu uu uu corrections. In addition, mostFKP of the rangemodel errors of each satelliteFKP were reduced by more than(9) 0.1 m βα=−∇()()ij δTT −Δ∇ iji +−∇ ij δ I and the maximum reduced error isFKP approximately r umodel 0.35 m FKP on PRN #8 (the smallest elevation angle) Asas listed shown in Table in Figure 3. This7, is the beca residualuse the smaller errors decreasedthe elevation because angle, the of higher the positive is the error effect due of to the the FKP corrections.As In addition,shown in Figure most of7, the residual range errors errors ofdecre eachased satellite because were of the reduced positive by effect more of thanthe FKP 0.1 m and spatialcorrections. decorrelation In addition, [27]. most of the range errors of each satellite were reduced by more than 0.1 m the maximumand the reducedmaximum error reduced is approximately error is approximately 0.35 m 0.35 on PRNm on #8PRN (the #8 smallest(the smallest elevation elevation angle) angle) as listed in Tableas3. listed This in is Table because 3. This the is smallerbecause the the smaller elevation the elevation angle, theangle, higher the higher is the is the error error due due to to the the spatial decorrelationspatial decorrelation [27]. [27].

(a) (b)

Figure 7. (a) DD residual errors without FKP correction, and (b) DD residual errors with FKP correction. (a) (b)

Figure 7. (a) DD residual errors without FKP correction, and (b) DD residual errors with FKP correction. Figure 7. (a) DD residual errors without FKP correction; and (b) DD residual errors with FKP correction.

ISPRS Int. J. Geo-Inf. 2017, 6, 222 11 of 21 ISPRS Int. J. Geo-Inf. 2017, 6, 222 11 of 21 Table 3. DD residual errors without and with FKP correction.

DD Residual Errors (RMSTable 1) 3. DD PRN residual #1 errors PRN without #4 and with PRN FKP #8 correction. PRN #11 PRN #17

DDElevation Residual Angle Errors (RMS 1) 49.9°PRN #1 PRN15.9° #4 PRN 14.3° #8 PRN 30.6° #11 PRN 43.3° #17 BeforeElevation Case ( Angle) 0.51 49.9 m◦ 0.3215.9 m◦ 0.6314.3◦ m 30.6 0.36◦ m 43.3 0.21◦ m AfterBefore Case Case() (α) 0.36 0.51 m m 0.11 0.32 m m 0.280.63 m m 0.36 0.37 m m 0.21 0.14 m m After Case (β) 0.36 m 0.11 m 0.28 m 0.37 m 0.14 m 1 Root mean square (RMS). 1 Root mean square (RMS). 4.3. Static Test 4.3. Static Test To confirm the improvement in the accuracy of the DGPS of the low-cost single frequency GPS To confirm the improvement in the accuracy of the DGPS of the low-cost single frequency GPS receiver using the modified FKP corrections in the position domain, static and dynamic user tests receiver using the modified FKP corrections in the position domain, static and dynamic user tests were conducted. First, the static test is introduced. were conducted. First, the static test is introduced. In theIn static the static test, test,Figure Figure 8a 8showsa shows the the u-blox u-blox LE LEA-6TA-6T evaluation evaluation kitkit selectedselected as as the the low-cost low-cost GPS GPS receiver,receiver, which which is one is one of of the the most popularpopular and and inexpensive inexpensive commercial commercial GPS receivers. GPS receivers. It can be It applied can be appliedfor for the the DGPS DGPS messages messages in the in RTCM the RTCM version version 2.3. The 2.3. static The userstatic is user located is located at Bldg. at 312 Bldg. in Seoul 312 in SeoulNational National University University in Korea. in Korea. In addition, In addition, to confirm to the confirm effect of thethe FKP effect corrections of the correspondingFKP corrections to correspondingthe baseline to lengths the baseline which is lengths the distance which between is the the distance user and between the RS, fourthe RSsuser (YANP, and the WNJU, RS, four YOWL, RSs (YANP,and WNJU, WULJ) YOWL, were selected and WULJ) which arewere at selected distances which of 50, 90,are 140,at distances and 225 kmof 50, south–east 90, 140, ofand the 225 user km south–eastin sequence, of the asuser shown in sequence, in Figure 8asb. shown in Figure 8b.

(a) (b)

FigureFigure 8. (a) 8. u-blox(a) u-blox LEA-6T LEA-6T evaluation evaluation kit, kit; and and (b (b) )Locations Locations of of reference stations. stations.

The testThe was test wasconducted conducted for forapproximately approximately 12 12 h hfrom from 4 4April April 2017 2017 10:30 inin locallocal time time (UTC+09). (UTC+09). To obtainTo obtain the data the data from from the thefour four RSs RSs simultaneo simultaneouslyusly and and let let the the receivers operateoperate the the DGPS DGPS and and FKP–DGPS,FKP-DGPS, eight eight receivers receivers were were used used as as the the static user.user. In In the the test, test, an an RS RS receiver receiver of Trimble of Trimble NetR9 NetR9 and and thethe eight eight u-bloxu-blox receivers receivers were were connected connected to a Trimbleto a Trimble Zephyr Zephyr geodetic geodetic 2 antenna 2 asantenna shown as in Figureshown9. in FigureUsing 9. Using the measurements the measurements from the from NetR9 the and NetR9 Zephyr and antenna, Zephyr a preciseantenna, position a precise was determined.position was determined.Although Although the geodetic the antennageodetic reduces antenna the reduces noise level the of noise the u-blox level receiverof the u-blox compared receiver to the compared original to thepatch original antenna, patch itantenna, does not it reducedoes not the reduce bias error the bias due toerror the due spatial to the decorrelation, spatial decorrelation, which can which help can helpin distinguishing in distinguishing the bias the error bias from error the from noise-related the noise-related error. In addition,error. In Figureaddition, 10a showsFigure the 10a visible shows the visiblesatellites satellites in the skyin the during sky during the test. the Figure test. 10Figureb shows 10b the shows position the dilutionposition ofdilution precision of (PDOP).precision (PDOP).The geometryThe geometry of satellites of satellites affects the affects positioning the positioning accuracy and accuracy the dilution and factor the dilution (DOP) depends factor solely(DOP) on the geometry. Thus, the PDOP is normally presented with the positioning results in the ﬁeld of GPS depends solely on the geometry. Thus, the PDOP is normally presented with the positioning results error analysis [28]. in the field of GPS error analysis [28].

ISPRS Int. J. Geo-Inf. 2017, 6, 222 12 of 21 ISPRS Int. J. Geo-Inf. 2017, 6, 222 12 of 21 ISPRS Int. J. Geo-Inf. 2017, 6, 222 12 of 21

Figure 9. Configuration of the static test. FigureFigure 9. Configuration 9. Conﬁguration of ofthe the static static test. test.

(a) (b) (a) (b) Figure 10. (a) Skyplot in static test, and (b) PDOP during static test. FigureFigure 10. 10. (a)( Skyplota) Skyplot in instatic static test, test; and and (b) ( bPDOP) PDOP during during static static test. test. Figure 11 shows the horizontal and vertical position errors of the DGPS and FKP–DGPS results Figure 11 shows the horizontal and vertical position errors of the DGPS and FKP–DGPS results of theFigure WULJ 11 RS, shows which the is horizontallocated farthest and vertical from the position static user errors in ofthe the east-north-up DGPS and FKP-DGPS(ENU) coordinate. results of the WULJ RS, which is located farthest from the static user in the east-north-up (ENU) coordinate. Itof is the easily WULJ confirmed RS, which that is located the horizontal farthest from result the of static the userDGPS in theis slightly east-north-up biased(ENU) on the coordinate. left side. It is easily confirmed that the horizontal result of the DGPS is slightly biased on the left side. However,It is easily conﬁrmedthe horizontal that theresult horizontal of the FKP–DGPS result of the seems DGPS unbiased, is slightly but biased slightly on the noisy. left side. Furthermore, However, However, the horizontal result of the FKP–DGPS seems unbiased, but slightly noisy. Furthermore, the horizontalpositive effect result of ofthe the FKP FKP-DGPS correction seems can be unbiased, confirmed but from slightly the noisy.vertical Furthermore, result. The blank the positive in the the positive effect of the FKP correction can be confirmed from the vertical result. The blank in the verticaleffect of theresults FKP occurred correction when can be the conﬁrmed correction from data the are vertical not result.received The from blank the in theNGII vertical FKP resultsserver vertical results occurred when the correction data are not received from the NGII FKP server becauseoccurred of when the server-side the correction problem. data are The not data received in the from blank the are NGII exclu FKPded server from because the analysis. of the server-side because of the server-side problem. The data in the blank are excluded from the analysis. problem. The data in the blank are excluded from the analysis.

ISPRS Int. J. Geo-Inf. 2017, 6, 222 13 of 21 ISPRS Int. J. Geo-Inf. 2017, 6, 222 13 of 21 ISPRS Int. J. Geo-Inf. 2017, 6, 222 13 of 21

(a) (b) (a) (b)

(c) (c) FigureFigure 11. 11. (a(a)) DGPSDGPS horizontalhorizontal error (WULJ), (WULJ); ( (bb)) FKP–DGPS FKP-DGPS horizontal horizontal error error (WULJ), (WULJ); and and (c) FKP–DGPS and DGPS vertical errors (WULJ). (c)Figure FKP-DGPS 11. ( anda) DGPS DGPS horizontal vertical errors error (WULJ). (WULJ), (b) FKP–DGPS horizontal error (WULJ), and (c) FKP–DGPS and DGPS vertical errors (WULJ). Figure 12 shows the reason for the bias in the horizontal result of the DGPS on the west side. ConsideringFigureFigure 12 12 showsthe shows rotation the the reason reasonof the for forEarth, thethe biasbiasthe appearan in the ho horizontalrizontalce of satellites result result ofis of thein the DGPSthe DGPS east-west on on the the westdirection. west side. side. ConsideringConsideringMoreover, thesatellites the rotation rotation with of oflow thethe elevation Earth,Earth, thethe angles appearanceappearan morece significantlyof of satellites satellites isaffect isin in thepositioning the east-west east-west results.direction. direction. In Moreover,Moreover,Figure 12, satellites itsatellites is assumed with with low that low elevation the elevation west angles direction angles more is more signiﬁcantlypositive, significantly and affect the GPS positioningaffect satellite positioning results.has low results. Inelevation Figure In 12, it isFigureangle. assumed If12, it that, is assumed are the the west measurement that direction the west is positive,errors direction of the and is userpositive, the GPSand andRS, satellite respectively,the GPS has lowsatellite and elevation has islow equal angle. elevation to If theδu, δr areangle.correction the measurement If from, arethe the DGPS errors measurement RS, of thethe userresidual errors and errorof RS, the respectively, of user the and user RS, after and respectively, applyingδr is equal the and to correction the is correction equal from to thethe from thecorrectionDGPS DGPS RS RS, canfrom the be the residualpositive, DGPS error implyingRS, the of theresidual that user the error after position applyingof theing user error the after lies correction applyingin the west from the direction. correction the DGPS Figure from RS can 12athe be positive,DGPSshows RSthe implying can case be wherein positive, that the the implying positioning GPS satellite that error theis on position liesthe ineast theing side westerror of the lies direction. user in the and west FigureRS. Figuredirection. 12a 12b shows Figure shows the 12athe case whereinshowscase wherein the case GPS the wherein satellite GPS satellite the is onGPS is the onsatellite east the sidewest is on ofside the the of eastuser the side user and of and RS.the RS. Figureuser and 12 RS.b shows Figure the 12b case shows wherein the thecase GPS wherein satellite the is GPS on the satellite west sideis on of the the west user side and of RS.the user and RS.

(a) (a)

Figure 12. Cont.

ISPRS Int. J. Geo-Inf. 2017, 6, 222 14 of 21 ISPRS Int. J. Geo-Inf. 2017, 6, 222 14 of 21

(b)

Figure 12. (a) case I - GPS satellite is on the east side of user and RS, and (b) case II – GPS satellite is Figureon the 12. west(a) caseside I—GPSof user and satellite RS. is on the east side of user and RS; and (b) case II—GPS satellite is on the west side of user and RS. Tables 4 and 5 present the detailed numerical results including the results of other stations. TheTables results4 andshow5 presentthat the theFKP–DGPS detailed has numerical more accu resultsrate positioning including accuracy the results than of the other DGPS. stations. With Thethe results increase show in the that baseline the FKP-DGPS length, the has effect more of accuratethe FKP positioningcorrection on accuracy the errors than due the to the DGPS. spatial With thedecorrelation increase in theincreases baseline with length, respect the to effectthe positioning of the FKP accuracy. correction Thus, on in the cases errors of duethe FKP–DGPS, to the spatial decorrelationthe improvements increases of the with 95% respect horizontal to the accuracy positioning of all accuracy.stations are Thus, 3%, 18%, in cases 26%, ofand the 40% FKP-DGPS, for the thecorresponding improvements baseline of the lengths 95% horizontal of the RSs accuracycompared of to allthe stationsaccuracy are of the 3%, DGPS. 18%, In 26%, particular, and 40% the for theerror corresponding components baseline of the east lengths direction of the are RSs visibl comparedy reduced to when the accuracy the FKP-DGPS of the DGPS. is applied, In particular, which thewere error large components when the of corrections the east direction were used are from visibly an RS reduced far apart when from the the FKP-DGPS user in the is east applied, direction which wereof DGPS. large when Based the on correctionsthe statistics were in Tables used 4 from and 5, an Figure RS far 13a apart shows from the the 95% user horizontal in the east and direction vertical of results corresponding to the baseline lengths. In addition, Figure 13b shows the RMS errors in the DGPS. Based on the statistics in Tables4 and5, Figure 13a shows the 95% horizontal and vertical results north, east, and downward directions. In Figure 13, the dashed line indicates the FKP–DGPS and corresponding to the baseline lengths. In addition, Figure 13b shows the RMS errors in the north, east, the solid line indicates the DGPS. The results show that the accuracies of the FKP–DGPS remain and downward directions. In Figure 13, the dashed line indicates the FKP-DGPS and the solid line largely constant even if the baseline lengths increase. The valid baseline length of the FKP indicates the DGPS. The results show that the accuracies of the FKP-DGPS remain largely constant even correction for the pseudorange measurements is clearly above 200km. if the baseline lengths increase. The valid baseline length of the FKP correction for the pseudorange measurements is clearlyTable above 4. 200Horizontal km. errors corresponding to baseline lengths.

Table 4. HorizontalYANP errors correspondingWNJU to baseline lengths.YOWL WULJ Horizontal (50 km) (90 km) (140 km) (225 km) HorizontalDGPS YANP (50 0.40 km) m WNJU (90 0.57 km) m YOWL (140 0.71 km) m WULJ 0.93 (225 m km) 50% Accuracy 1 DGPSFKP–DGPS 0.40 0.44 m m 0.57 m 0.42 m 0.71 0.43 m m 0.46 0.93 m 1 50% Accuracy DGPS 1.05 m 1.18 m 1.34 m 1.69 m 95% Accuracy FKP-DGPS 0.44 m 0.42 m 0.43 m 0.46 m DGPSFKP–DGPS 1.05 1.02 m m 1.18 m 0.97 m 1.34 0.99 m m 1.01 1.69 m 95% Accuracy DGPS 0.43 m 0.45 m 0.50 m 0.52 m RMS 2 (North) FKP-DGPS 1.02 m 0.97 m 0.99 m 1.01 m FKP–DGPS 0.45 m 0.42 m 0.45 m 0.45 m DGPS 0.43 m 0.45 m 0.50 m 0.52 m RMS 2 (North) DGPS 0.41 m 0.51 m 0.65 m 0.91 m RMS (East) FKP-DGPS 0.45 m 0.42 m 0.45 m 0.45 m FKP–DGPS 0.33 m 0.32 m 0.32 m 0.35 m DGPS 0.41 m 0.51 m 0.65 m 0.91 m RMS (East) 1 Circular error probability (CEP), 2 Root mean square (RMS). FKP-DGPS 0.33 m 0.32 m 0.32 m 0.35 m 1TableCircular 5. Vertical error probability errors corresponding (CEP), 2 Root meanto baseline square lengths. (RMS).

YANP WNJU YOWL WULJ Vertical Table 5. Vertical errors corresponding to baseline lengths. (50 km) (90 km) (140 km) (225 km) VerticalDGPS YANP (50 0.52 km) m WNJU (90 0.56 km) m YOWL 0.57 (140 m km) WULJ 0.80 (225m km) 50% Accuracy DGPSFKP–DGPS 0.52 0.54 m m 0.56 0.55 m m 0.57 0.47 m m 0.51 0.80 m m 50% Accuracy DGPS 1.51 m 1.60 m 1.66 m 2.15 m 95% Accuracy FKP-DGPS 0.54 m 0.55 m 0.47 m 0.51 m FKP–DGPS 1.68 m 1.60 m 1.41 m 1.50 m DGPS 1.51 m 1.60 m 1.66 m 2.15 m 95% Accuracy DGPS 0.77 m 0.83 m 0.85 m 1.11 m RMS FKP-DGPS 1.68 m 1.60 m 1.41 m 1.50 m FKP–DGPS 0.84 m 0.81 m 0.71 m 0.77 m DGPS 0.77 m 0.83 m 0.85 m 1.11 m RMS FKP-DGPS 0.84 m 0.81 m 0.71 m 0.77 m

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(a) (b) (a) (b) Figure 13. (a) 95% position accuracies corresponding to baseline lengths, and (b) RMS errors in north, FigureFigure 13. 13. (a)( a95%) 95% position position accuracies accuracies corresponding corresponding to tobaseline baseline lengths, lengths; and and (b) ( bRMS) RMS errors errors in innorth, north, east, downward directions corresponding to baseline lengths. east,east, downward downward directions directions corresponding corresponding to to baseline baseline lengths. lengths. An additional test was conducted to compare the performance of the user-oriented FKP-DGPS AnAn additional additional test test was was conducted conducted to to compare compare the the performance performance of of the the user-oriented user-oriented FKP-DGPS FKP-DGPS with those of other alternatives, such as SBAS or VRS-DGPS. The configuration of the additional withwith those those of of other other alternatives, alternatives, such such as as SBAS SBAS or or VRS-DGPS. VRS-DGPS. The The configuration conﬁguration of of the the additional additional test is largely similar to that of the static test; the u-blox LEA-6T evaluation kit is used, and the user testtest is islargely largely similar similar to to that that of of the the static static test; test; the the u-blox u-blox LEA-6T LEA-6T evaluation evaluation kit kit is isused, used, and and the the user user is located at Bldg. 312 in Seoul National University. Figure 14a shows the visible satellites in the sky is islocated located at at Bldg. Bldg. 312 312 in in Seoul Seoul National National University. University. Figure Figure 14a 14 ashows shows the the visible visible satellites satellites in in the the sky sky during the test. Figure 14b shows the PDOP. The test was conducted for approximately 3 hours duringduring the the test. test. Figure Figure 14b 14 bshows shows the the PDOP. PDOP. Th Thee test test was was conducted conducted for for approximately approximately 3 3 hours h from from 1 July 2017 13:30 in local time (UTC+09). For the SBAS test, PRN 137 satellite of MSAS was from1 July 1 July 2017 2017 13:30 13:30 in local in timelocal (UTC+09). time (UTC+09). For the For SBAS the test, SBAS PRN test, 137 PRN satellite 137 of satellite MSAS wasof MSAS used, whichwas used, which is observed at the elevation of 43° and the azimuth of 151° in Korea. For the VRS-DGPS used,is observed which is at observed the elevation at the of elevation 43◦ and theof 43° azimuth and the of 151azimuth◦ in Korea. of 151° For in theKorea. VRS-DGPS For the test,VRS-DGPS we need test, we need an assumption on the dynamic user and its situation to compare the performance with test,an we assumption need an assumption on the dynamic on the user dynamic and its user situation and its to situation compare to the compare performance the performance with VRS-DGPS, with VRS-DGPS, because there is no infrastructure for VRS-DGPS in Korea. VRS-DGPS,because there because is no there infrastructure is no infrastructure for VRS-DGPS for VRS-DGPS in Korea. in Korea.

(a) (b) (a) (b) Figure 14. (a) Skyplot in additional test, and (b) PDOP during additional test. FigureFigure 14. 14. (a)( aSkyplot) Skyplot in inadditional additional test, test; and and (b ()b PDOP) PDOP during during additional additional test. test. The SBAS mode of the U-blox receiver had been set to be enabled via the u-center program. The SBAS mode of the U-blox receiver had been set to be enabled via the u-center program. OnceThe the SBASconfiguration mode of was the U-blox set to the receiver SBAS had mode, been the set rover to be can enabled apply via the the augmentation u-center program. message Once to Once the configuration was set to the SBAS mode, the rover can apply the augmentation message to thegenerate conﬁguration the range was correction set to the appropriate SBAS mode, to the the rover rover’s can applyreal-time the augmentationposition, because message the same to generate SBAS generate the range correction appropriate to the rover’s real-time position, because the same SBAS themessage range is correction broadcast appropriateto all the users to thein the rover’s service real-time area regardless position, their because location. the same SBAS message message is broadcast to all the users in the service area regardless their location. is broadcastOn the toother all thehand, users a generic in the service VRS system area regardless provides their the rover’s location. proper correction only after it On the other hand, a generic VRS system provides the rover’s proper correction only after it got theOn rover’s the other approximate hand, a generic position. VRS Moreover, system provides a VRS theuser rover’s without proper multi-channel correction datalinks only after to it got the rover’s approximate position. Moreover, a VRS user without multi-channel datalinks to gotnearby the VRSs rover’s might approximate experience position. performance Moreover, degradati a VRSon or user discontinuity without multi-channel due to the absence datalinks of the to nearby VRSs might experience performance degradation or discontinuity due to the absence of the nearbycorrection VRSs during might the experience handover performancefrom the previous degradation VRS to ora new discontinuity one. Assu dueming to a the user absence who left of correction during the handover from the previous VRS to a new one. Assuming a user who left thefrom correction WULJ and during arrived the handover at Seoul fromwithout the previousupdating VRS its toreal-time a new one. position Assuming because a user of whoprivacy left from WULJ and arrived at Seoul without updating its real-time position because of privacy problem or RS handover issue, the static DGPS accuracy using WULJ correction is equivalent to the problem or RS handover issue, the static DGPS accuracy using WULJ correction is equivalent to the

ISPRS Int. J. Geo-Inf. 2017, 6, 222 16 of 21

fromISPRS WULJInt. J. Geo-Inf. andarrived 2017, 6, 222 at Seoul without updating its real-time position because of privacy problem16 of or21 RS handover issue, the static DGPS accuracy using WULJ correction is equivalent to the VRS-DGPS accuracyVRS-DGPS of theaccuracy rover atof Seoul,the rover because at Seoul, its VRS because was not its changed VRS was from not thechanged initial from VRS, WULJ,the initial through VRS, theWULJ, entire through journey. the entire journey. InIn general,general, thethe SBASSBAS hashas muchmuch widerwider coverage,coverage, butbut itit hashas similarsimilar oror lowerlower positioningpositioning accuracyaccuracy thanthan the local local area area DGPS DGPS whose whose coverage coverage is is within within 150 150 km km [29]. [29 Figure]. Figure 15 shows15 shows the horizontal the horizontal and andvertical vertical position position errors errors of the of theSBAS, SBAS, DGPS DGPS and and FKP–DGPS FKP-DGPS results results in in the the east-north-up (ENU) coordinate.coordinate. In In this test, the DGPS show the positionposition error of the useruser ofof thethe previousprevious VRS-DGPSVRS-DGPS assumptionassumption at Seoul, wherein the correction from the WULJWULJ RS isis used.used. We cancan easilyeasily conﬁrmconfirm thatthat thethe horizontalhorizontal and and vertical vertical results results of of the the FKP-DGPS FKP-DG arePS muchare much better better than than those those of the of SBAS the andSBAS DGPS. and TableDGPS.6 listsTable the 6 detailedlists the detailed numerical numerical results. results.

(a) (b)

FigureFigure 15.15. ((aa)) HorizontalHorizontal ErrorError (SBAS,(SBAS, DGPS, and FKP-DGPS);FKP-DGPS), and ( b) Vertical ErrorError (SBAS,(SBAS, DGPS, andand FKP-DGPS).FKP-DGPS).

Table 6.6. PositionPosition accuraciesaccuracies (SBAS,(SBAS, DGPS,DGPS, andand FKP-DGPS).FKP-DGPS).

SBASSBAS DGPS DGPS FKP-DGPS FKP-DGPS Horizontal 0.62 m 0.63 m 0.43 m 50% Accuracy Horizontal 0.62 m 0.63 m 0.43 m 50% Accuracy Vertical 1.06 m 1.16 m 0.53 m Vertical 1.06 m 1.16 m 0.53 m Horizontal 1.17 m 1.46 m 0.87 m 95% Accuracy Horizontal 1.17 m 1.46 m 0.87 m 95% Accuracy Vertical 4.23 m 2.35 m 1.51 m VerticalNorth 0.54 4.23 m m 0.50 2.35 m m 0.42 1.51 m m RMS NorthEast 0.49 0.54 m m 0.59 0.50 m m 0.29 0.42 m m RMS VerticalEast 1.98 0.49 m m 1.37 0.59 m m 0.77 0.29 m m Vertical 1.98 m 1.37 m 0.77 m 4.4. Dynamic Test 4.4. DynamicUsing the Test developed real-time FKP–DGPS software, we conducted a dynamic test to verify the feasibilityUsing of the the developed FKP corrections real-time for FKP-DGPS the dynamic software, user. The we configuration conducted a dynamicof the dynamic test to verifytest is thelargely feasibility similar of to the that FKP of the corrections static test. for The the u-blox dynamic LEA-6T user. evaluation The conﬁguration kit is selected of the as dynamic the low-cost test isGPS largely receiver. similar Moreover, to that of thea Trimble static test. zephyr The u-blox model LEA-6T 2 antenna evaluation was used kit is as selected the antenna. as the low-cost In the GPSdynamic receiver. test, Moreover,four RSs (YANP, a Trimble WNJU, zephyr YOWL, model and 2 antenna WULJ) waswere used selected as the located antenna. at distances In the dynamic of 50, test,90, 140, four and RSs 225 (YANP, km south–east WNJU, YOWL, of the user and WULJ)in sequence. were The selected dynamic located test at system distances was ofimplemented 50, 90, 140, andin a 225land km vehicle south–east as shown of the in user Figure in sequence. 16c, which The was dynamic driven testinside system the parking was implemented lot of Seoul in Grand a land vehiclePark, as as shown shown in in Figure 1616a.c, whichThe blue was line driven desc insideribes thethe parking trajectory lot ofof Seoulthe dynamic Grand Park, user. as The shown test inwas Figure conducted 16a. The for blue approximately line describes 25 themin trajectory from 25 ofMay the 2017 dynamic 15:00 user. in local The testtime was (UTC+09). conducted Figure for 16b,d show the visible satellites in the sky and PDOP during the test.

ISPRS Int. J. Geo-Inf. 2017, 6, 222 17 of 21 approximately 25 min from 25 May 2017 15:00 in local time (UTC+09). Figure 16b,d show the visible ISPRSsatellitesISPRS Int. Int.J. inGeo-Inf. J. theGeo-Inf. sky2017 2017, and 6, 222, 6 PDOP, 222 during the test. 17 of17 21 of 21

(a) (a) (b)(b)

FigureFigureFigure 16. 16. 16.(a(a) )Location(a Location) Location of of dynamic of dynamic dynamic test, test; test, (b (b) )(Skyplotb Skyplot) Skyplot in in dynamic in dynamic dynamic test, test; test, (c (c) ) Land(c Land) Land vehicle vehicle vehicle as as dynamic as dynamic dynamic user, user; user, andandand ( (dd)) (PDOPd PDOP) PDOP during during during static static static test. test. test.

Figure 17 shows the horizontal and vertical position errors of the DGPS and FKP–DGPS of the FigureFigure 17 17 shows shows the the horizontal horizontal and and vertical vertical position position errors errors of the of theDGPS DGPS and andFKP–DGPS FKP-DGPS of the of WULJ RS, which is the farthest from the static user, in the ENU coordinate compared to the WULJthe WULJ RS, RS,which which is isthe the farthest farthest fromfrom thethe static static user, user, in the in ENUthe ENU coordinate coordinate compared compared to the reference to the reference positions obtained using the Trimble NetR9 receiver with post-processing Trimble referencepositions obtainedpositions usingobtained the Trimbleusing the NetR9 Trimble receiver NetR9 with post-processingreceiver with post-processing Trimble Business Trimble Center Business Center (TBC) software. The results are similar to the static test results. We can easily Business(TBC) software. Center The(TBC) results software. are similar The to results the static are test simi results.lar to Wethe can static easily test conﬁrm results. that We the can horizontal easily confirm that the horizontal result of the DGPS is slightly biased to the west side, whereas the FKP– confirmresult of that the DGPSthe horizontal is slightly result biased of tothe the DGPS west is side, slightly whereas biased the to FKP-DGPS the west side, obtains whereas a more the accurate FKP– DGPS obtains a more accurate horizontal positioning than the DGPS. Tables 7 and 8 list the detailed DGPShorizontal obtains positioning a more accurate than the horizontal DGPS. Tables positioning7 and8 thanlist the the detailed DGPS. Tables numerical 7 and results 8 list the along detailed with numerical results along with the results of other stations. numericalthe results results of other along stations. with the results of other stations.

(a) (a) (b)(b)

Figure 17. Cont.

ISPRS Int. J. Geo-Inf. 2017, 6, 222 18 of 21 ISPRS Int. J. Geo-Inf. 2017, 6, 222 18 of 21

(c)

Figure 17. (a) DGPS horizontal error (WULJ), (b) FKP–DGPS horizontal error (WULJ), and (c) FKP– Figure 17. (a) DGPS horizontal error (WULJ); (b) FKP-DGPS horizontal error (WULJ); and DGPS and DGPS vertical errors (WULJ). (c) FKP-DGPS and DGPS vertical errors (WULJ). Table 7. Horizontal errors corresponding to baseline lengths. Table 7. Horizontal errors corresponding to baseline lengths. YANP WNJU YOWL WULJ Horizontal Horizontal YANP (50(50 km) km) WNJU (90(90 km) km) YOWL (140(140 km) km) WULJ(225 (225 km) km) DGPSDGPS 0.28 m 0.28 m 0.40 m 0.40 m 0.59 m0.59 m 0.82 0.82 m m 50%50% Accuracy Accuracy FKP-DGPSFKP-DGPS 0.20 m 0.20 m 0.26 m 0.26 m 0.25 m0.25 m 0.21 0.21 m m DGPS 0.49 m 0.79 m 0.81 m 1.16 m 95% Accuracy DGPS 0.49 m 0.79 m 0.81 m 1.16 m 95% Accuracy FKP-DGPS 0.40 m 0.54 m 0.44 m 0.44 m FKP-DGPS 0.40 m 0.54 m 0.44 m 0.44 m DGPS 0.22 m 0.22 m 0.22 m 0.17 m RMS (North) DGPS 0.22 m 0.22 m 0.22 m 0.17 m RMS (North) FKP-DGPS 0.18 m 0.22 m 0.22 m 0.17 m FKP-DGPS 0.18 m 0.22 m 0.22 m 0.17 m DGPS 0.21 m 0.41 m 0.56 m 0.83 m RMS (East) DGPS 0.21 m 0.41 m 0.56 m 0.83 m RMS (East) FKP-DGPS 0.15 m 0.25 m 0.17 m 0.19 m FKP-DGPS 0.15 m 0.25 m 0.17 m 0.19 m

Table 8. Vertical errors corresponding to baseline lengths. Table 8. Vertical errors corresponding to baseline lengths.

Vertical YANP (50YANP km) WNJU (90WNJU km) YOWL (140YOWL km) WULJWULJ (225 km) Vertical DGPS 0.33 m 0.62 m 0.94 m 1.74 m 50% Accuracy (50 km) (90 km) (140 km) (225 km) FKP-DGPSDGPS 0.44 m 0.33 m 0.71 m 0.62 m 0.82 m0.94 m 0.45 1.74 m m 50% Accuracy DGPS 1.19 m 2.20 m 1.93 m 2.88 m 95% Accuracy FKP-DGPS 0.44 m 0.71 m 0.82 m 0.45 m FKP-DGPSDGPS 1.30 m 1.19 m 2.35 m 2.20 m 2.02 m1.93 m 2.23 2.88 m m 95% Accuracy DGPS 0.58 m 1.06 m 1.10 m 1.89 m RMS FKP-DGPS 1.30 m 2.35 m 2.02 m 2.23 m FKP-DGPS 0.67 m 1.14 m 1.08 m 0.92 m DGPS 0.58 m 1.06 m 1.10 m 1.89 m RMS FKP-DGPS 0.67 m 1.14 m 1.08 m 0.92 m Like the static test, the FKP-DGPS has more accurate positioning accuracy than the DGPS for most of theLike results the because static test, of the the compensate FKP–DGPS error has factorsmore a dueccurate to the positioning spatial decorrelation. accuracy than Thus, the in DGPS the cases for ofmost the of FKP-DGPS, the results the because improvements of the compensate of the 95% error horizontal factors accuracy due to the of spatial all stations decorrelation. are 18%, 32%, Thus, 46%, in andthe cases 62% forof the the FKP–DGPS, corresponding the improvements baseline lengths of ofthe the 95% RSs horizontal compared accuracy to the accuracy of all stations of the are DGPS. 18%, Although32%, 46%, it and is not 62% clear for tothe show corresponding the vertical baseline accuracy lengths improvement of the viaRSs thecompared FKP-DGPS to the in aaccuracy short-time of periodthe DGPS. of the Although dynamic it test, is not the clear error to components show the ve ofrtical the east accuracy havedefinitely improvement reduced. via the Figure FKP-DGPS 18a shows in thea short-time 95% horizontal period and of the vertical dynamic error test, tendency the error to the components baseline length. of the Figureeast have 18b definitely describes thereduced. RMS ofFigure the error18a shows for each the direction 95% horizontal based onand the vertical result error of Tables tendency7 and8 to. Inthe Figure baseline 18, length. the dashed Figure lines 18b indicatedescribes the the FKP-DGPS RMS of the and error the for solid each lines direction indicate base thed on DGPS. the result From of these Tables figures, 7 and we 8. In can Figure confirm 18, the dashed lines indicate the FKP–DGPS and the solid lines indicate the DGPS. From these figures, we can confirm that the FKP-DGPS can significantly contribute to the reduction in the spatial decorrelation effect in the position-domain and the improvement in the position accuracy.

ISPRS Int. J. Geo-Inf. 2017, 6, 222 19 of 21 that the FKP-DGPS can signiﬁcantly contribute to the reduction in the spatial decorrelation effect inISPRS the Int. position-domain J. Geo-Inf. 2017, 6, 222 and the improvement in the position accuracy. 19 of 21

(a) (b)

Figure 18. (a) 95% 95% position position accuracies accuracies corresponding corresponding to baseline lengths, lengths; and ( (b)) RMS RMS errors errors in in north, north, east, and downward directions correspondingcorresponding toto baselinebaseline lengths.lengths.

5. Conclusions 5. Conclusions In this study, we suggested a real-time user-oriented FKP–DGPS algorithm as a new In this study, we suggested a real-time user-oriented FKP-DGPS algorithm as a new augmentation augmentation method to improve the positioning accuracy of the DGPS. While the DGPS is the method to improve the positioning accuracy of the DGPS. While the DGPS is the most popular most popular augmentation system for a low-cost L1 single-frequency GPS receiver, the FKP is augmentation system for a low-cost L1 single-frequency GPS receiver, the FKP is originally used originally used for carrier-phase-based positioning to reduce the spatial decorrelation. To use the for carrier-phase-based positioning to reduce the spatial decorrelation. To use the FKP method to FKP method to improve the current DGPS accuracy without implementing a unique infrastructure improve the current DGPS accuracy without implementing a unique infrastructure for the service, for the service, we modified the FKP correction for the low-cost GPS receiver. To implement the we modified the FKP correction for the low-cost GPS receiver. To implement the user-oriented method user-oriented method to real-world applications, we combined the DGPS correction from the to real-world applications, we combined the DGPS correction from the current DGPS server and current DGPS server and the FKP correction from the current network RTK server operated by the the FKP correction from the current network RTK server operated by the NGII, and then provided NGII, and then provided the modified correction in the format of the message type 1 in the RTCM the modified correction in the format of the message type 1 in the RTCM version 2.3. To verify its version 2.3. To verify its effect, mathematical and preliminary test-based analyses have been effect, mathematical and preliminary test-based analyses have been conducted before developing conducted before developing the real-time FKP–DGPS software. The preliminary-test results show the real-time FKP-DGPS software. The preliminary-test results show that the DD residual errors with that the DD residual errors with the FKP correction are less compared to those without the FKP the FKP correction are less compared to those without the FKP correction. After identifying its positive correction. After identifying its positive effect through the analyses, the FKP–DGPS software was effect through the analyses, the FKP-DGPS software was developed in visual C++ and several static and developed in visual C++ and several static and dynamic tests were conducted to improve the dynamic tests were conducted to improve the accuracy of the DGPS using the modified FKP correction. accuracy of the DGPS using the modified FKP correction. From the test results, we can confirm the From the test results, we can confirm the improvement in the positioning accuracy of the DGPS and improvement in the positioning accuracy of the DGPS and the positive effect of the modified FKP the positive effect of the modified FKP corrections. In the static test, compared to the accuracy of corrections. In the static test, compared to the accuracy of the DGPS, the improvements of the 95% the DGPS, the improvements of the 95% horizontal accuracy of all the stations are found to be 3%, 18%, horizontal accuracy of all the stations are found to be 3%, 18%, 26%, and 40% for baseline lengths of 26%, and 40% for baseline lengths of 50, 90, 140, and 225 km, respectively, which are located along 50, 90, 140, and 225 km, respectively, which are located along the south-east direction with respect the south-east direction with respect to the static user. Furthermore, the improvements in the vertical to the static user. Furthermore, the improvements in the vertical accuracy have been identified. accuracy have been identified. From the dynamic test, it is difficult to identify the improvements From the dynamic test, it is difficult to identify the improvements in the vertical accuracy because in the vertical accuracy because the test was conducted for a short period. Nevertheless, compared to the test was conducted for a short period. Nevertheless, compared to the accuracy of the DGPS, the the accuracy of the DGPS, the improvements of the 95% horizontal accuracy of all the stations are 18%, improvements of the 95% horizontal accuracy of all the stations are 18%, 32%, 46%, and 62% for the 32%, 46%, and 62% for the corresponding baseline lengths. The results of the additional test show corresponding baseline lengths. The results of the additional test show the FKP-DGPS has better the FKP-DGPS has better performance rather than the SBAS. Hence, the new real-time FKP-DGPS performance rather than the SBAS. Hence, the new real-time FKP–DGPS algorithm is expected to algorithm is expected to exploit many applications used in our daily lives such as smartphone, car exploit many applications used in our daily lives such as smartphone, car navigation, and Internet navigation, and Internet of things (IoT) devices. of things (IoT) devices.

Acknowledgments: ThisThis research research was was supported supported by a grant by (17CTAP-C129724-01)a grant (17CTAP-C129724-01) from Technology from Advancement Technology Research Program funded by the Ministry of Land, Infrastructure, and Transport of Korean government, contracted throughAdvancement SNU-IAMD Research at the Program Seoul National funded University.by the Ministry of Land, Infrastructure, and Transport of Korean government, contracted through SNU-IAMD at the Seoul National University.

Author Contributions: All the authors have contributed to the presented work. Jungbeom Kim suggested the original algorithm of the FKP–DGPS and validated it through data processing and analysis. Changdon Kee and Byungwoon Park provided valuable comments and critical feedback regarding the algorithm. Byungwoon Park supervised its development and the direction of the research. Junesol Song and Heekwon No provided

ISPRS Int. J. Geo-Inf. 2017, 6, 222 20 of 21

Author Contributions: All the authors have contributed to the presented work. Jungbeom Kim suggested the original algorithm of the FKP-DGPS and validated it through data processing and analysis. Changdon Kee and Byungwoon Park provided valuable comments and critical feedback regarding the algorithm. Byungwoon Park supervised its development and the direction of the research. Junesol Song and Heekwon No provided intuitive insights regarding the basic principle of the algorithm. Deokhwa Han and Donguk Kim helped in conducting the test program. All authors participated in formulating the idea and in discussing the proposed approach and results. All authors read and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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