Global Navigation Satellite System Precise Positioning Technology

Nobuaki KUBO

Summary :

In this study, the most recent topics related to the precise global navigation satellite system (GNSS) positioning technology are discussed. Precise positioning here means that the position can be estimated with centimeter-level accuracy. Technologies supporting precise GNSS positioning include an increase in the number of positioning satellites and the availability of correction data. Smartphones are now capable of centimeter-level positioning. For correction data, real-time kinematic positioning (RTK)-GNSS, which has primarily been used in surveying, and the new precise point positioning-real-time kinematic (PPP-RTK) and PPP, are garnering attention. The Japanese Quasi-Zenith Satellite System was among the first to broadcast PPP-RTK and PPP correction data free of charge. RTKLIB has long been popular for both real-time and post-processing precise positioning. Here, I briefly present a method for improving this software. Precise positioning technology remains crucial as the use of GNSS in highly reliable applications, such as advanced driver-assistance systems, autonomous drones, and robots, is increasing. To ensure precise positioning, improving multipath mitigation techniques is essential; therefore, key factors related to these techniques are discussed. I also introduce my efforts to develop software GNSS receivers for young researchers and engineers as a basis for this purpose. This study is aimed at introducing these technologies in light of the most recent trends.

• Publication: IEICE TRANSACTIONS on Communications Vol.E107-B No.11 pp.691-705
• Publication Date: 2024/11/01
• Online ISSN: 1745-1345
• DOI: 10.23919/transcom.2024EBI0001
• Type of Manuscript: INVITED PAPER
• Category: Navigation, Guidance and Control Systems

1.  Introduction

Location-based applications of precise global navigation satellite system (GNSS) positioning are extremely diverse [1]. Examples include surveying, precision agriculture, precision construction machinery, precise monitoring of civil engineering construction, automated navigation using drones, advanced driver assistance systems, monitoring of crustal deformation, marine civil engineering, personal mobility, and smartphone navigation. While GNSS is generally effective outdoors, it cannot provide precise positioning indoors owing to insufficient radio signal reception. Positioning in transitional areas between outdoor and indoor environments is also challenging. Given the importance of location-based services in these difficult areas, I herein discuss methods for reducing GNSS errors. Although indoor positioning is not covered in this study, interested readers can refer to the work by Nishio [2] for more information.

This paper consists of seven sections. Section 1 introduces an outline of the paper. Section 2 discusses the status of global positioning satellites, including the global positioning system (GPS), Globalnaya Navigazionnaya Sputnikovaya Sistem (GLONASS), GALILEO, BeiDou Navigation Satellite (BDS), Quasi-Zenith Satellite System (QZSS), and Navigation with Indian Constellation (NavIC). Section 3 briefly introduces the basics of real-time kinematic positioning (RTK-GNSS), precise point positioning-real-time kinematic (PPP-RTK), and PPP. Section 4 outlines the Japanese QZSS, particularly its correction services to achieve centimeter-level positioning. Section 5 covers multipath mitigation techniques. Section 6 introduces the basics of GNSS receiver software. Section 7 presents RTKLIB, an open-source program package for GNSS positioning, and discusses a few approaches to improve its performance. The final section provides a summary of the paper and suggestions for further research.

2.  Status of GNSS

In this section, the status of the satellite positioning system is discussed [3]. In the 1990s, the US GPS [4] and Russia’s GLONASS [5] technologies were operational. As of 2023, six satellite positioning systems were in operation globally, spanning Europe and five non-European countries [6]-[9]. These multi-satellite positioning systems are collectively referred to as GNSS. Table 1 summarizes the operational status of each system in 2023. At this time, signals from 133 satellites were available. The term “global” in the operational status indicates that the satellite is designed to provide positioning services worldwide. For example, Japan’s QZSS is termed a regional satellite because its service area covers Asia and Oceania. The Indian positioning satellites were not used for positioning calculations in this study; however, the other five systems were consistently in use.

Table 1  GNSS operational status (December 2023).

Originally, positioning satellites were developed by the United States and the former Soviet Union for military purposes; China’s BDS also has military applications. However, Europe, Japan, and India allegedly do not prioritize military use as their primary purpose. Interoperability, a crucial condition for user benefit, refers to the ability to use positioning satellites from different countries simultaneously. Open specifications for non-military signal formats enable general companies to develop GNSS receivers and utilize multiple systems from different countries to calculate the final position. The more satellites visible in the sky, the better the positioning accuracy, especially in urban environments with numerous obstacles. Figure 1 shows a GNSS sky plot obtained from the rooftop of a building on our campus in Tokyo. The GNSS receiver used is a Trimble Alloy.

Fig. 1  Sky plots of GNSS (12/27/2023).

Figure 2 outlines the positioning status. A total of 43 satellites were used for positioning. The type of position is “autonomous,” meaning single-point positioning. The week represents the full GPS week number since the first epoch (January 6, 1980). The GPS seconds indicate epochs from 00:00:00 on Sundays (UTC) for one week. The clock offset represents the difference between GPS and other satellite systems. Because each system has its own master clock, these differences must be estimated when mixing positioning satellites from different constellations. When GPS and GLONASS are mixed, at least five satellites (one from each constellation) are required because the unknown parameters include the three positions (x, y, z), receiver clock offset, and clock offset between GPS and GLONASS. The dilution of precision (DOP) specifies error propagation as a mathematical effect of navigation satellite geometry. If the value is below 1, the positioning accuracy is higher than the accuracy of each satellite measurement.

Fig. 2  Position Information (12/27/2023).

In the BDS, more than 40 satellites operate simultaneously, combining second- and third-generation satellites. This development has been rapid in China over the last 5 to 10 years. Notably, the Russian GLONASS satellite transmits both FDMA-modulated and CDMA-modulated signals. With an increase in the number of such signals, full-scale service of CDMA signals is expected in the future. QZSS is a unique positioning satellite with a signal compatible with GPS, characterized by long stays at high elevation angles in the Asia-Oceania region. It is the first satellite in the world to transmit correction data, enabling centimeter-level accuracy, and its utilization is highly anticipated. The Japanese government’s Strategic Headquarters for Space Policy plans to increase the number of QZSS satellites from 4 to 7 by 2024 and 2025, with a future goal of 11 satellites [10]. These 11 satellites will facilitate 24 h positioning in Japanese territory using only QZSS without GPS. Galileo also provides free-of-charge high-accuracy precise point positioning (PPP) corrections using its signal [11]. This operation is called a high-accuracy service (HAS, which offers improved real-time user positioning performance down to the decimeter level. GPS includes a mixture of satellites from different generations, with the oldest Block IIR satellite (PRN16) launched in 1997. Remarkably, 26 years have passed since then. The names of each generation of GPS satellites were NavStar I and II before Block IIA, followed by IIA, IIR, IIR-M, IIF, and III. Six GPS-III satellites have been launched.

In addition to the space segment described above, the satellite positioning infrastructure is divided into three major segments: the control segment, which manages the positioning satellites, and the user segment, which is used by the users. In terms of operating a positioning satellite, the role of the control segment is more important than that of the actual satellite. The potential of each country’s positioning satellites can be partially expressed by a signal in the space segment.

3.  Basics of Precise Positioning

In this section, the error sources of GNSS and the three types of precise positioning: RTK-GNSS, PPP-RTK, and PPP, are discussed.

3.1  Measurements

GNSS pseudo-range and carrier phase measurements are expressed as follows:

\[\begin{eqnarray*} P_{rov}^{sv1} &=& \rho_{rov}^{sv1} + c\left(dt_{sv1} - dT_{rov}\right)+ \textit{ion}_{rov}^{sv1} + \textit{tropo}_{rov}^{sv1}\nonumber\\ && +MP_{rov}^{sv1} + NOISE_{rov}^{sv1} \tag{1} \\ \varphi_{rov}^{sv1} &=& \rho_{rov}^{sv1} +c \left(dt_{sv1} - dT_{rov}\right)- \textit{ion}_{rov}^{sv1} + \textit{tropo}_{rov}^{sv1}\nonumber\\ && +N_{rov}^{sv1} + mp_{rov}^{sv1} + \textit{noise}_{rov}^{sv1} \tag{2} \end{eqnarray*}\]

The superscript sv1 identifies the terms associated with the GNSS satellite, while the subscript rov denotes a term associated with the rover. Equation (1) indicates the pseudo-range measurements, and Eq. (2) indicates the carrier-phase measurements. In these equations, \(c\) is the speed of light, \(Dt\) is the satellite clock error, \(dt\) is the receiver clock error, \(\textit{ion}\) is the ionospheric error, \(\textit{tropo}\) is the tropospheric error, \(MP\) is the pseudo-range multipath error, and \(mp\) is the carrier-phase multipath error. \(\textit{NOISE}\) is the pseudo-range noise and \(\textit{noise}\) is the carrier-phase noise. \(N\) is the integer ambiguity of the carrier phase measurement [12].

3.2  Error Sources

As shown in the equations, six major sources of error exist in GNSS observations. The first two errors originate from the satellite: the satellite position and clock errors. The satellite broadcasts parameters for estimating its position and clock errors, and the residual error after these calculations is the satellite error. The next two errors are related to the atmosphere: the ionospheric and tropospheric delays. Parameters for estimating the ionospheric delay are broadcasted and can be applied to reduce the error. If dual-frequency observations are available, an artificial observation that generates ionosphere-free coupling can be used to eliminate ionospheric delay. The ionospheric delay is strongly related to solar activity; it is minimal during periods of low solar activity but can cause significant errors when solar activity increases, with large differences between the delays corresponding to periods of strong and weak solar activity.

Ionospheric disturbances caused by solar flares make predictions difficult. The tropospheric delay is divided into dry and wet components. While the dry term can be estimated with high accuracy using model equations, accurately estimating the wet term is challenging, particularly during rainy and humid seasons. The error in the vertical direction is typically between 2.3 to 2.5 meters and does not vary significantly. However, during lightning events, satellite signals arriving from the direction of the lightning can be affected, complicating the achievement of RTK FIX solutions. The other two errors are the multipath error and receiver noise. Multipath error is particularly troublesome, and various methods have been proposed to mitigate it, with the best expected to become standard. The error due to receiver noise depends on the received signal strength, and the error can be estimated accurately using that strength [13]. Both multipath error and receiver noise are strongly related to the internal design of the GNSS receiver. Table 2 presents the six sources of error.

Table 2  Typical errors in GNSS measurements.

Fig. 3  Poor and good geometry.

Additionally, an error is induced by satellite geometry. Ideally, if the distance measurement from the satellite to the receiver is accurate, satellite geometry should not cause errors. In reality, however, measurement errors always occur, and their effect on positioning accuracy depends on the satellite geometry. To address this, a satellite geometry-induced degradation factor called the dilution of precision (DOP) has been defined in GNSS. Figure 3 illustrates that if satellites s1 and s2 are placed in the same direction, the positioning error exceeds the original ranging error. Conversely, if the satellites are placed far apart, the positioning error is closer to the original ranging error. For example, if an antenna is located near a wall, it can only receive signals from satellites on one side of the wall, resulting in increased vertical positioning errors. The DOP can be estimated during the positioning operation using the least-squares method and is uniquely determined by the satellite geometry at any given time. The actual GNSS error is the measurement error multiplied by the DOP. The sources of measurement error are listed in Table 2. For example, the horizontal error is the measurement error multiplied by the horizontal dilution of precision (HDOP). The vertical error is the measurement error multiplied by the vertical dilution of precision (VDOP). The 3D position error is the measurement error multiplied by the position dilution of precision (PDOP).

In urban areas, the HDOP can exceed 10 owing to narrow streets and high-rise buildings. In such cases, a 2-3 meter position error from measurement inaccuracies without multipath interference can potentially become a 20–30 meter error due to the DOP. Additionally, the VDOP can easily exceed 10 in these environments, leading to significant height errors. An error ellipse can estimate the direction in which the error spreads, which is crucial for assessing actual errors. For further details, refer to the study by Fan and Ma [14].

3.3  Stand-Alone Positioning

Standalone positioning primarily uses pseudo-range measurements without correction data from any external source. This method relies on the satellite’s broadcast information for positioning. In standalone positioning, carrier-phase measurements can help reduce noise in pseudo-range measurements. However, without correcting for satellite clock and atmospheric errors, the positioning error can be substantial. The satellite clock error, even with an atomic clock, must be corrected using broadcast information; otherwise, the position error can exceed 1 km. After correcting for satellite clock errors with broadcast parameters, the remaining errors depend on the accuracy of the ionospheric and tropospheric delay estimations. As shown in Table 2, these errors range from 2 m to several meters vertically and are estimated using an obliquity factor based on the elevation angle. When errors are estimated from these models, standalone positioning accuracy can be within a few meters when the multipath error and receiver noise are minimal. However, if atmospheric errors are not considered, the horizontal positional error may still be a few meters, but the vertical error can exceed 10 m. This discrepancy occurs because positioning satellites are always above the user’s position; while horizontal errors may cancel out owing to signals from various azimuths, vertical errors do not cancel out. Both ionospheric and tropospheric delays contribute to the original true ranges.

GPS has been popular since its development, but estimating the receiver clock error has been problematic. The initial GNSS inventors proposed estimating the receiver clock error during positioning, meaning that 3D positions and receiver clock errors would be estimated simultaneously. The least-squares method is used to estimate the unknown position in three dimensions and the receiver clock errors. A typical standalone result after 24 h is presented in Fig. 4. Data were obtained from the rooftop of our laboratory using a Trimble Alloy receiver in February 2024. The analysis software used was RTKLIB with default parameters. The GPS, QZSS, GLONASS, and GALILEO systems were used.

Fig. 4  Typical result of stand-alone positioning.

In multi-GNSS, positioning is performed simultaneously with satellites that have time standards different from those of GPS. For example, when using GPS and GLONASS in standalone positioning, the difference between the GPS and GLONASS time standards must be estimated simultaneously. Therefore, in the case of GPS + GLONASS positioning, an additional unknown (the time difference between GPS and GLONASS) is added to the four unknowns (three position coordinates and the receiver clock error), necessitating observation values from at least five satellites. Five GPS satellites alone are insufficient; at least one satellite from each system is required. Thus, for GPS + GLONASS + QZSS + GALILEO + BDS positioning, at least seven satellites are needed, with at least one from each system. Although the discussion above focuses on GPS, positioning can also be performed using QZSS or GLONASS alone. However, because GPS is widely used worldwide, many receivers use the GPS time as the basis for positioning.

3.4  DGNSS

The differential global navigation satellite system (DGNSS) uses pseudo-range as the main observation and correction data from a nearby base station to determine the position of the user station. Of the six errors mentioned earlier, the satellite position error can be almost eliminated because both the base and user stations use the same satellite, and the satellite clock error can be completely eliminated using correction data from the same time. In practice, a slight time delay occurs when the user station uses the correction data from the base station, so the satellite clock error must be corrected for that time. The satellite clock error’s time variation can be approximated by a linear function over a short period of approximately 10 s, which helps to nearly eliminate the time difference. Ionospheric and tropospheric delays can be almost completely eliminated if the correction data from the base station can be obtained within approximately 1 min, provided the baseline is not too long. This is because the errors due to these factors change slowly both spatially and temporally.

However, the tropospheric delay varies significantly with elevation angle, necessitating compensation for the error using the obliquity factor based on the elevation angle. For example, if the base and user stations are approximately 100 km apart, the elevation angle differs by approximately 1\(^\circ\), even if the same satellite is observed. The error in the tropospheric delay due to this 1\(^\circ\) difference in elevation angle cannot be ignored. The same applies to the ionospheric delay, but its impact is smaller. Determining the baseline length limitations is complicated by the nature of atmospheric errors. When solar activity is low, a 100 km baseline length for DGNSS is feasible as long as an error of approximately 1 meter is acceptable. A typical DGNSS result obtained after 24 h is shown in Fig. 5. Data were collected from the rooftop of our laboratory using a Trimble Alloy receiver in February 2024. RTKLIB software, with default parameters, was used for analysis. The GPS, QZSS, GLONASS, and GALILEO systems were utilized, with the Ichikawa Station of GEONET serving as the base station. The baseline length was approximately 10 km.

Fig. 5  Typical result of DGNSS (10 km).

There was a significant difference in accuracy between DGNSS with a baseline length of 10 km and that with a baseline length of 100 km. This difference is particularly noticeable in areas with a large spatial gradient of the ionosphere. At distances of 100 km or more, the offset effect of the spatial correlation of atmospheric errors may diminish, and the horizontal bias may exceed 0.1 m. These variations are due to natural atmospheric phenomena, making it difficult to estimate the magnitude of the error over a 100 km distance. The magnitude of the ionospheric delay is especially dependent on solar activity, which follows an 11-year cycle. When solar activity is high, the gradient concerning the horizontal distance can also be large, necessitating caution when using DGNSS. During localized ionospheric disturbances, using satellite signals that pass through the disturbance location can reduce the effectiveness of DGNSS. Table 3 summarizes the extent to which the DGNSS method can reduce various error factors.

Table 3  Typical error mitigations in DGNSS (10 km).

3.5  RTK-GNSS

RTK-GNSS is a precise positioning method that uses carrier-phase measurements as the main observation value and obtains correction data from a nearby base station to estimate the user’s position with centimeter-level accuracy. RTK-GNSS employs a double-difference observation technique. Figure 6 illustrates double-difference observations. Equation (3) provides the formula for generating the double-difference observation, which eliminates the clock error from both the satellite and receiver clocks. The notation follows the same conventions as in Eqs. (1) and (2).

\[\begin{eqnarray*} &&\!\!\!\!\! \varphi_{rov\_ref}^{sv1\_sv2} = \left(\varphi_{rov}^{sv1} - \varphi_{ref}^{sv1}\right) -\left(\varphi_{rov}^{sv2} - \varphi_{ref}^{sv2}\right)\nonumber\\ &&\!\!\!\!\! \mbox{$ =\rho_{rov}^{sv1} + c\left(dt_{sv1}-dT_{rov}\right)+\textit{ion}_{rov}^{sv1} + \textit{tropo}_{rov}^{sv1}+N_{rov}^{sv1}+mp_{rov}^{sv1}+\textit{noise}_{rov}^{sv1} $} \nonumber\\ &&\!\!\!\!\! \mbox{$ -\left[\rho_{ref}^{sv1}+c\left(dt_{sv1}-dT_{ref}\right)+\textit{ion}_{ref}^{sv1} + \textit{tropo}_{ref}^{sv1}+N_{ref}^{sv1}+mp_{ref}^{sv1}+\textit{noise}_{ref}^{sv1} \right] $} \nonumber\\ &&\!\!\!\!\! \mbox{$ -\left[\rho_{ref}^{sv2}+c\left(dt_{sv2}-dT_{rov}\right)+\textit{ion}_{rov}^{sv1} + \textit{tropo}_{rov}^{sv2}+N_{rov}^{sv2}+mp_{rov}^{sv2}+\textit{noise}_{rov}^{sv2}\right] $} \nonumber\\ &&\!\!\!\!\! \mbox{$ +\left[\rho_{ref}^{sv2}+c\left(dt_{sv2}-dT_{ref}\right)+\textit{ion}_{ref}^{sv2}+ \textit{tropo}_{ref}^{sv2}+N_{ref}^{sv2}+mp_{ref}^{sv2}+\textit{noise}_{ref}^{sv2}\right] $} \nonumber\\ &&\!\!\!\!\! =\rho_{rov}^{sv1}-\rho_{ref}^{sv1}+\rho_{rov}^{sv2}-\rho_{ref}^{sv2}+N_{rov}^{sv1} -N_{ref}^{sv1}+N_{rov}^{sv2}-N_{ref}^{sv2}\nonumber\\ &&\!\!\!\!\! +\left(\textit{ion}_{rov}^{sv1}+\textit{tropo}_{rov}^{sv1}\right) -\left(\textit{ion}_{ref}^{sv1}+\textit{tropo}_{ref}^{sv1}\right)\nonumber\\ &&\!\!\!\!\! -\left(\textit{ion}_{rov}^{sv2}+\textit{tropo}_{rov}^{sv2}\right) +\left(\textit{ion}_{ref}^{sv2}+\textit{tropo}_{ref}^{sv2}\right)\nonumber\\ &&\!\!\!\!\! +\left(mp_{rov}^{sv1}+\textit{noise}_{rov}^{sv1}\right) -\left(mp_{ref}^{sv1}+\textit{noise}_{ref}^{sv1}\right)\nonumber\\ &&\!\!\!\!\! -\left(mp_{rov}^{sv2}+\textit{noise}_{rov}^{sv2}\right) +\left(mp_{ref}^{sv2}+\textit{noise}_{ref}^{sv2}\right) \tag{3} \end{eqnarray*}\]

As seen from the equation, atmospheric error is negligible if the baseline is short. Estimating the integer ambiguity using only carrier-phase measurements is challenging; however, with this technique, the integer ambiguity can be easily estimated using the integer least squares method, resulting in centimeter-level accuracy. Consider a case where the base and rover stations are in the same position (antenna). The baseline vector is zero, and in Eq. (3), only the integer ambiguity of the double difference of the carrier phase remains. Consequently, the integer ambiguity is known. Additionally, the multipath error is completely eliminated, leaving only the noise of the carrier-phase measurement. Thus, several important points can be learned by observing the zero-baseline double difference. Typical RTK-GNSS results after 24 h are shown in Fig. 7. Data were obtained from the rooftop of our laboratory using a Trimble Alloy receiver in February 2024. RTKLIB software was used for analysis, with parameters set to default. GPS, QZSS, GLONASS, and GALILEO were used. The base station is the same as that used in the DGNSS test. The fixed rate was 91.6%. Table 4 summarizes the degree to which the RTK-GNSS method can reduce various error factors. Under normal conditions, a bias or error of approximately 1 cm can be expected for every 10 km baseline extension, presumably allowing an RTK-FIX solution to be obtained.

Fig. 6  Double-difference operation.

Fig. 7  Typical result of RTK-GNSS (10 km).

Table 4  Typical error mitigations in RTK-GNSS (10 km).

Consequently, the baseline vector from the base station to the user station can be estimated with centimeter-level accuracy. This is the essence of RTK-GNSS. As the baseline length increases, atmospheric errors become significant, with errors exceeding approximately 1 cm at 10 km. This is an estimate. When the baseline length exceeds 30 km, the amount of error due to atmospheric delay becomes a significant obstacle, complicating the determination of the integer ambiguity. If the atmospheric error can always be corrected to 1 cm even with a 100 km baseline, long baseline RTK becomes feasible. However, the increasing atmospheric error with longer baselines complicates long baseline RTK. VRS [15] and PPP-RTK have been developed to improve this situation.

PPP-RTK will be described later in this paper. Generally, short-baseline RTK is used for baseline lengths up to approximately 10 km, medium-baseline RTK for lengths up to 100 km, and long-baseline RTK for lengths exceeding 100 km. To smoothly estimate the integer ambiguity in RTK for medium and long baselines, the concept of wide lanes is employed. A wide lane indicates that the virtual wavelength exceeds that of a single L1 or L2 band. For example, if a virtual signal of L1–L2 is generated, the frequency is approximately 348 MHz and the virtual wavelength is approximately 86 cm, which facilitates the estimation of integer ambiguity. Additionally, for baselines exceeding 100 km, the Melbourne–W\(\ddot{\mathrm{u}}\)bbena linear combination [16] can be used, enabling the accurate estimation of wide-lane integers even over long distances. However, even if wide-lane integers can be estimated accurately, the atmospheric error in the double-difference observation of the carrier phase measurement cannot be eliminated. Therefore, the position estimated using the wide-lane integers contains certain errors, complicating medium-length baseline RTK and making long-baseline RTK relatively difficult to achieve. While atmospheric errors and baseline length have been discussed, multipath errors also remain. Multipath errors are particularly troublesome because they are difficult to predict and mitigate. Multipath errors affect RTK performance regardless of the baseline length. The biggest challenge for short-baseline RTK is multipath error. Typical RTK-GNSS results for 24 h using a wide lane are shown in Fig. 8. Data were obtained from the rooftop of our laboratory using a u-blox F9P receiver in February 2024. Modified RTKLIB software was used for analysis, with the mask angle set to 30\(^\circ\). GPS, QZSS, GLONASS, BDS, and GALILEO were used. The base station was the Tateyama station in Chiba Prefecture, with a baseline length of approximately 70 km. The fixation rate was 93.9%.

Fig. 8  Typical result of wide-lane RTK (70 km).

3.6  PPP-RTK

PPP-RTK provides centimeter-level positioning accuracy with fewer base stations than conventional RTK. The actual accuracy is approximately 1 cm RMS in the horizontal direction, which is slightly less optimized than RTK. PPP-RTK is a correction method for the Japanese centimeter-level augmentation service (CLAS) and the centimeter-level correction method of QZSS. Specifically, GNSS observation data from multiple base stations with a mid-baseline of approximately 50 km are collected, and correction data are generated and broadcast. The expertise of each PPP-RTK service provider is incorporated into generating correction data to minimize loss of accuracy and data volume. The correction data include the satellite’s precise orbit, precise clock, and ionospheric and tropospheric delays. The ionospheric delay is corrected by generating a grid with latitude and longitude and providing a vertical ionospheric delay on the grid. Similar correction data are provided for the tropospheric delay, reducing the volume of data to be transmitted. Although centimeter-level positioning cannot be achieved instantaneously as with RTK, it can be determined within approximately 1 min. It is called PPP-RTK because the correction data are broadcast separately for the satellite’s precise orbit, clock, and atmospheric delays, similar to PPP, while the user-side positioning is determined by integer ambiguity, as in RTK. If user-side positioning uses the generation of a double-difference observation, it is also similar to RTK. Several companies have announced PPP-RTK services. For details of the PPP-RTK method, refer to the article by engineers at Mitsubishi Electric Corporation, the service provider [17], [18]. Typical PPP-RTK results after 24 h are shown in Fig. 9. Data were obtained from the rooftop of our laboratory using a Core AsteRx4 receiver in February 2024. The fixation rate was 99.3%.

Fig. 9  Typical result of PPP-RTK using QZSS correction.

3.7  PPP

In contrast to conventional RTK and PPP-RTK, PPP generally uses only precise information on the satellite’s orbit and clock as correction data, with the receiver’s positioning software estimating the rest to achieve centimeter-level accuracy. The ionospheric-free combination is the most common method, although a method that does not use an ionospheric-free combination and instead uses ionospheric estimation to converge has also been devised. Starting with the model, the tropospheric delay can be estimated more accurately because the error model for tropospheric delay is precise. The dry delay can be estimated at the centimeter level using this error model. Integer ambiguity determination also exists in PPP positioning, known as precise point positioning ambiguity resolution (PPP-AR). If PPP-AR is used, it can achieve the same accuracy as PPP-RTK. In contrast, PPP without PPP-AR generally achieves a horizontal accuracy of less than 10 cm. The convergence time for normal PPP is approximately 15–20 min to achieve a horizontal accuracy of 10 cm. However, Trimble RTX, a commercial PPP service, achieves convergence in 2–3 min, as confirmed using the rooftop antenna at our laboratory and a Trimble NetR9 receiver. This performance, achieved with a correction amount of below 1 kbps, suggests there may be a key factor in shortening convergence time. In commercial services, because the base station and user receiver can be specified, their hardware biases are known, reducing the need to consider them as unknown quantities. Often, the same model is used, allowing full use of multi-GNSS, securing the number of satellites. General open-source PPP faces difficulties in convergence time, requiring approximately 15–20 min to obtain a horizontal positioning solution of less than 10 cm owing to a shortage of precise atmospheric delay information. Therefore, using PPP for mobile applications is challenging. However, as long as satellite signals are not interrupted by obstacles, centimeter-level positioning can be maintained.

Typical PPP results for 24 h are shown in Fig. 10. Data were obtained from the rooftop of our laboratory using an MSJ 3008-GM4-QZS receiver in February 2024, with correction data from QZSS [17], [19]. For example, Fig. 11 shows the PPP results for crustal movement during the Noto earthquake. The open-source software MADOCALIB was used in this study [20]. PPP positioning using Geospatial Information Authority of Japan (GSI) GEONET data during a large earthquake can accurately estimate the crustal deformation at the antenna locations to within centimeters, regardless of the baseline length. The results were compared with the official GSI results, and the differences were within a few centimeters. In RTK, this accuracy is not always possible because the base station moves. If a base station is located over 100 km from the earthquake location, a sophisticated software is required. Table 5 summarizes the characteristics of RTK-GNSS, PPP-RTK, and PPP, all of which provide centimeter-level augmented positioning. For more detailed information about correction messages for RTK/PPP-RTK/PPP, refer to this article [21].

Fig. 10  Typical result of PPP using QZSS correction.

Fig. 11  PPP results at Noto earthquake (2024/1/1).

Table 5  Characteristics of RTK/PPP-RTK/PPP.

4.  Quasi Zenith Satellite System (QZSS)

QZSS, also known as Michibiki, is a Japanese positioning satellite system with a unique orbit. The first satellite, launched in 2010, was recently retired and replaced by a new satellite launched in 2021. The second, third and fourth satellites were launched in 2017. Currently, a four-satellite constellation is operated by the Cabinet Office. QZSS adopted a quasi-zenith orbit ahead of other countries, and at the time of its launch, RTK performance in urban areas was greatly improved using GPS and QZSS in the zenith direction. Although the effect is less visible now owing to the increase in the number of other positioning satellites, the advantage of being at the zenith remains significant. QZSS not only is a complement to GPS but also has a positioning augmentation aspect, broadcasting SLAS and CLAS correction data for free since 2018. SLAS is equivalent to DGNSS with a horizontal accuracy of less than 1 m. CLAS is equivalent to PPP-RTK and was the first to freely broadcast PPP-RTK correction data worldwide. PPP has also been broadcasting free of charge on a trial basis and will be officially operational soon, under the name MADOCA-PPP. Although not widely known, QZSS provides a public regulated service that transmits concealed and encrypted signals, usable only by government-approved users to avoid signal jamming and spoofing. A similar signal exists for Galileo satellites, which do not have a military signal.

4.1  QZSS as a Positioning Complement

As a positioning complement, QZSS maintains compatibility with GPS by broadcasting almost the same signals as GPS, making the composition of GPS + QZSS easy to understand. Even with the current four-satellite system, positioning with QZSS alone is possible for approximately 15 h a day in the vicinity of Tokyo, with an actual horizontal accuracy of less than 30 m. Figure 12 shows the positioning results using only four QZSS satellites, with observation data acquired by a u-blox F9P receiver using an antenna on the laboratory roof. Evidently, the horizontal accuracy depends on the DOP, a degradation factor of satellite geometry. Looking at the improvement of RTK-GNSS in dense urban areas, the fix rate can increase approximately 5–10% by simply adding QZSS to other GNSSs because at least one or two QZSS satellites stay at a high elevation angle. Units 5, 6, and 7 of QZSS will be launched within the next 1–2 yrs. The expected satellite configuration at the time of the constellation for the 11 satellites is shown in Fig. 13 [22].

Fig. 12  QZSS only stand-alone positioning.

Fig. 13  Eleven satellites constellation for future QZSS.

4.2  QZSS as Positioning Augmentation

As mentioned previously, SLAS, CLAS, and PPP are the most common types of positioning augmentation. As the CLAS and PPP test results were already shown in the previous section, Fig. 14 shows the 24 h horizontal results of the SLAS acquired at the rooftop of the laboratory in February 2024. The data were acquired using a u-blox F9P receiver. The base station for SLAS was located in Hitachi-ota, Ibaraki, Japan. Except for the ionospheric effects of solar activity, the results were stable. The horizontal RMS of SLAS was approximately 50–60 cm when the results were stable. Please refer to detailed long-term results of these three methods [23]. For PPP, I collaborated with overseas universities, mainly in Southeast Asia, to conduct long-term evaluations using the same receivers as those in my laboratory. These results are almost as accurate as those obtained in my laboratory, and they are available at the Laboratory Home Page website [24]. All the previous results were verified. Because solar activity is expected to reach a maximum in the near future, GNSS positioning is expected to be more difficult, and the performance of SLAS and CLAS will be especially noteworthy. The solar activity forecast provided by NASA is shown in Fig. 15 [25].

Fig. 14  Typical result of SLAS using QZSS correction.

Fig. 15  Solar cycle forecast by NASA.

5.  Multipath Error Mitigation

In this section, several methods for mitigating multipath errors in pseudo-range measurements, which represent the weakest aspect of the GNSS, are introduced. Although the multipath error in carrier-phase measurements is also important, its magnitude is only a few centimeters; therefore, it is not presented here [26]. The impact of multipath errors in Doppler frequency measurements is illustrated below [27]. Figure 16 depicts the three patterns of multipath cases. The third case in these patterns, where the level of the reflected signal exceeds that of the direct signal, is a major source of error and is termed a non-line-of-sight (NLOS) signal.

Fig. 16  Three typical patterns of multipath.

Subsequently, I assessed the test results obtained by placing a smartphone (Google Pixel 6) in front of the car navigation system on the dashboard of the vehicle. The smartphone results consist of the NMEA data acquired by the GNSS Logger (an Android application provided by Google), and I did not investigate whether the results were output in real time. Figure 17 illustrates the ground track of the test route, while Fig. 18 presents the actual horizontal errors. These errors were estimated using the Applanix POSLVX system, a compact, fully integrated, turnkey position and orientation system that utilizes integrated inertial technology to generate stable, reliable, and repeatable positioning solutions for land-based vehicle applications. Notably, the maximum error is only approximately 8 m, with a root mean square (RMS) of 2.9 m, even when using only the smartphone.

Fig. 17  Ground track produced using smartphone.

Fig. 18  Horizontal errors by smartphone.

The Nihonbashi and Marunouchi areas boast numerous high-rise buildings, presenting a challenge for achieving accuracy with the commercial receivers I evaluated. Remarkably, the accuracy achieved in these areas surpassed expectations. One reason for this outcome is that in such environments, the signal often includes reflections, complicating location determination with GNSS receivers alone, despite these receivers having antennas installed on the vehicle roof, which typically provides a more optimized environment than smartphones. There are several potential explanations for these results. First, smartphones rely on positioning by mobile base stations, and urban areas are abundant in mobile base station antennas, integrated with their positioning services. Second, smartphones utilize the IMU sensor built into them, integrating it with positioning data. Thirdly, they leverage the map-matching function of Google Maps. Lastly, they incorporate information from 3D maps. I believe there are various methods for mitigating large multipath errors by utilizing additional information, even though doing so with GNSS alone is challenging. Details on the Google Smartphone Decimeter Challenge, a competition focusing on accuracy using smartphone observation data, can be found in the report by Chow et al. [28]. Additionally, Odolinski et al. demonstrated the feasibility of RTK-GNSS using smartphone observation data (Google Pixel 6) [29].

Below, I introduce several multipath error mitigation methods for GNSS receivers. I cannot cover all mitigation methods here; therefore, for more information on reducing multipath errors, please refer to the report by Smolyakov et al. [30]. Recently, factor graph optimization (FGO) has also been employed to enhance accuracy in challenging areas [31].

5.1  Mitigation Using GNSS Antenna

The antenna serves as the initial receiver of signals from the satellite, and mitigating multipath effects here is crucial. One approach is to minimize the impact of multipath signals originating from the lower hemisphere of the antenna. Because positioning satellite signals invariably come from above the user, receiving signals from the upper hemisphere is essential. Conversely, signals arriving from the bottom of the antenna are considered multipath. Hence, my goal was to suppress signals originating from the bottom of the antenna as much as possible. Various methods have been developed to achieve this. One widely used method employs an antenna design known as a choke ring, particularly favored for GNSS base stations requiring high accuracy. Another approach utilizes a ground plane to suppress multipath signals. Figure 19 illustrates two antenna examples: one featuring a ground plane on the left and a choke ring on the right. To assess multipath errors originating from the bottom of the antenna, we evaluated the accuracy of pseudo-range output from the GNSS receiver under two conditions: with the antenna placed on the ground in an open sky and when elevated to a height of approximately 1 m. Accuracy is consistently increased when the antenna is grounded, as receiving signals from the bottom of the antenna becomes nearly impossible. The code-minus-carrier (CMC) metric offers a method for determining multipath errors [32]. By subtracting the carrier phase from the code (pseudo-range) and compensating for ionospheric effects, the multipath error can be observed in the pseudo-range. Another strategy leverages the transmission of satellite signals with right-handed circular polarization, which may shift to left-handed circular polarization depending on reflection from buildings. To counter this issue, some antennas are designed to receive right-handed circularly polarized signals [33]. Recently, compact and lightweight helical antennas have garnered attention for their application in drones and other fields. These antennas were evaluated for their multipath resistance performance and were found to outperform standard patch antennas [34].

Fig. 19  Two types of GNSS antennas.

5.2  Mitigation Using Signal Processing

Several methods have been developed to mitigate multipath effects in the signal processing section of GNSS receivers. Among these are techniques known as strobe and pulse-aperture correlators, as detailed in specific reports [35], [36]. The strobe correlator operates by capturing the peak from the correlation waveform through multiple correlation points within a delay-locked loop (DLL). If the bandwidth of the GNSS receiver allows for signals from the satellite to be received adequately, the top of the correlation waveform can be sharply observed. For instance, with GPS L1-C/A signals, which exhibit a triangular correlation waveform, the apex of the triangle can be observed more precisely. Figure 20 illustrates the correlation waveform obtained from both the direct and one multipath signals, with a delay of approximately 150 m (0.5 chip) and a received signal level approximately half that of the direct signal. The final correlation waveform observed at the receiver closely resembles this waveform. The timing of the direct signal, unaffected by multipath, can be determined by extracting two correlation values at each end of the apex of the triangle. However, this method exhibits imperfections when the multipath delay is too close to the apex of the triangle, typically within 15 m. Moreover, if the level of the reflected signal exceeds that of the direct signal, this method becomes ineffective. A novel approach for capturing the distortion of the code rather than the correlation waveform has been proposed [37].

Fig. 20  Correlation waveform by direct + multipath.

Another signal processing method for accurately estimating the timing of direct signal tracking involves separating the direct signal from the multipath signal using the correlation waveform, known as MEDLL [38]. Additionally, a method utilizing maximum likelihood estimation for separating direct signals from multipath signals has been presented [39]. In contrast to the strobe correlator, this method entails an estimation process and is not widely employed in commercial receivers, although it represents an important concept. If the receiver possesses sufficient computing power, continuously monitoring the correlation waveforms of the satellite signals once they are tracked is preferable. This approach enables seamless tracking even if the received signal level of the multipath surpasses that of the direct signal, as the buried location of the direct signal can be estimated on the basis of continuously observed correlation waveforms over time. Therefore, when the signal level of the direct signal returns to its original level, tracking can proceed smoothly.

5.3  Mitigation Using GNSS Measurements

Finally, let us delve into mitigation methods that utilize measurement data. Many of the techniques discussed thus far have been employed in survey-class receivers and GNSS units with additional computing power. The methods outlined in this section, however, are tailored for inexpensive survey-class receivers, constrained by hardware limitations. Below are several methods for mitigating multipath errors, especially concerning pseudo ranges.

5.3.1  Satellite Selection Based on Signal Level and Signal Tracking Information of Receiver

One established approach involves using signal levels to determine the usability of satellites and assigning weights to each satellite for positioning. A mask angle to establish the minimum elevation angle at which a satellite can be used is also often used. While adjusting the minimum elevation angle can be beneficial in RTK ambiguity resolution, it may be constrained by the mask angle or signal level due to partial ambiguity, which removes ambiguity from satellites with large covariance values [40]. Furthermore, information from the receiver’s internal tracking loop, which can indicate the accuracy of the phase-locked loop (PLL), frequency-locked loop (FLL), or delay-locked loop (DLL) tracking, can be leveraged. For instance, in urban environments, differences in positioning performance are observed while using satellites locked by the PLL or DLL. In most cases, position and velocity accuracy are higher when using satellites with a locked PLL. However, owing to fewer available satellites, the positioning rate may slightly decrease. Therefore, detailed information about the tracking loop should be incorporated into positioning operations. Nevertheless, such information is sometimes unavailable; for example, RINEX, a common format for GNSS observation data, does not provide detailed tracking status information. To effectively utilize tracking status information for positioning, a thorough understanding of the positioning program and the receiver’s tracking loop is essential. Note that PLL locks imply that, for instance, in the GPS L1-C/A signal, the carrier phase is locked to approximately 1/100th of a 19-centimeter wavelength, which generally indicates reasonably high-quality observations. However, in scenarios involving driving through high-rise buildings, proper signals are often obstructed, leading to significant errors in pseudo ranges even if the carrier phase is locked. In cases where only multipath signals are received, the carrier phase is likely to correspond to the reflected signals, even if it is locked.

5.3.2  Relationship between Speed and Multipath

According to our test results, strong multipath signals are more likely to be received when the speed is very low or zero. This aligns with the tracking loop process: when in motion, the relationship between surrounding buildings and satellite signals changes rapidly, meaning if a direct signal is received, the multipath effect will be less pronounced. In a tracking loop, a continuous signal of approximately 20 ms or more is often integrated. However, if the signal pauses for more than a few seconds, a stable multipath signal may emerge, even in the presence of a direct signal. In such scenarios, the impact of multipath signals seems significant. If other sensors can detect a stop, accurately estimating the position becomes easier, with inertial measurement unit sensors serving the same purpose.

5.3.3  Carrier Smoothing

A smoothing method replaces pseudo-range noise with the time-difference value of the carrier phase measurement, which can mitigate multipath errors and pseudo-range noise. Typically, when the carrier phase is locked, the error due to multipath is only a few centimeters [26], considerably more optimized than pseudo-range accuracy. Setting the time constant for carrier smoothing is crucial; a time constant of 100 s, for instance, can significantly reduce the effect of multipath signals, which fluctuate over approximately 10 s. However, this method may not be universally applicable, as a 100 s time constant is suitable for relatively open environments, not urban driving conditions. Nonetheless, a similar effect to carrier smoothing can be implemented within the receiver. The accuracy of the receiving frequency derived from the PLL or FLL is notably superior to that derived from the DLL; therefore, changing the input frequency of the DLL’s loop filter to a PLL- or FLL-derived receiving frequency can substantially reduce noise caused by the DLL, leading to a significant improvement in pseudo-range accuracy. While pseudo-range remains crucial for absolute measurement, this method is effective in reducing noise in distance information. Adjusting the DLL noise bandwidth to 2 Hz, for instance, provides a reciprocal filtering effect of 0.5 s. Some receivers allow manual adjustment of this noise bandwidth, with a default setting often around 0.05 Hz. The design of the PLL or DLL loop filter is critical, requiring significant ingenuity and expertise from receiver developers to produce accurate pseudo-ranges. Additionally, the Kalman filter can be employed in the receiver’s internal tracking loop to precisely and continuously track the signal.

5.3.4  Integration Velocity and Position Information

With the global introduction of high-sensitivity receivers around 2000, their position trajectories have become smoother compared to conventional receivers. They often utilize velocity information derived from the time difference of carrier phase (TDCP) or Doppler frequency. Indeed, we observed a considerable improvement in position solutions by incorporating velocity obtained from TDCP or Doppler frequency and integrating it with position information using a Kalman filter with varying weights [41]. This enhancement is primarily attributed to the fact that carrier phase and Doppler frequency are less susceptible to multipath effects, resulting in smaller errors compared to pseudo-range measurements. While survey receivers typically achieve similar accuracy in velocity estimation from Doppler frequency and TDCP, in low-cost receivers, TDCP-derived velocity appears to be slightly more optimized. Doppler frequency is essentially an integral part of carrier-phase measurement, hence their principles are similar. However, the time interval plays a crucial role. Utilizing TDCP with a 1 s interval yields velocity accuracy of less than 1 cm/s, whereas velocity estimated from Doppler frequency over a few tens of milliseconds interval achieves accuracy in the range of a few cm/s. Although velocity and position are measured in different units, the accuracy of position derived from pseudo-range is often at the meter level or higher, especially in urban areas. The Kalman filter effectively integrates both velocity and position information. However, using TDCP becomes impractical in the presence of cycle slips.

6.  Software GNSS Receivers

Typically, GNSS researchers focus on improving positioning accuracy using observation data output from commercial receivers. However, conducting in-depth research necessitates the development of GNSS receivers. Despite the challenge faced by students and researchers in developing GNSS receivers with performance comparable to commercial ones, the concept of software GNSS receivers has emerged, with textbooks being published and software GNSS receivers widely adopted among university researchers [42]. The source code is often available on GitHub, and manufacturers test them on FPGA and other devices before eventually selling them as chips in ASICs. Implementing current multi-GNSS and multi-frequency receivers on a PC is challenging due to computational speed requirements; however, Ifen, Germany, introduced a PC-compatible front-end software GNSS receiver. Additionally, Fraunhofer launched the Goose project, an FPGA-based GNSS receiver, providing researchers with an easy-to-use platform [43]. Figure 21 provides an overview of the process following the reception of signals from positioning satellites by the antenna.

Fig. 21  Overview of the process of GNSS-SDR.

Once the signal passes through a high-frequency section known as the front end and is converted into digital data, development of a GNSS receiver on a PC becomes feasible. Initially, in signal acquisition, the receiver captures the signal coarsely, estimating the approximate code correlation and Doppler frequency. Subsequently, in the signal-tracking stage, a finer resolution is employed to track the code correlation and Doppler frequency, while also performing carrier-phase tracking and decoding of navigation messages. This stage also involves estimating pseudo-range and carrier-phase measurements, which constitute the foundation of GNSS observation data. Finally, the receiver estimates its position using the observed measurements.

Various methods for position estimation have been delineated. External correction data may be necessary in some cases. Since the GNSS receiver generates pseudo-range and carrier-phase measurements crucial for positioning estimation, comprehending the portion responsible for generating these observations is pivotal for improving position accuracy. For instance, understanding the operation of the correlation in the signal-tracking segment is essential if multipath mitigation techniques are to be implemented using the correlation part. It is imperative to elucidate the mechanism for determining the accuracy of pseudo-range and carrier-phase measurements, as well as the generating part within the receiver. Notably, the accuracy, reliability, and availability levels of pseudo-range, Doppler frequency, and carrier-phase measurements may vary among different commercial receivers. Understanding the software GNSS receiver would help elucidate the distinctions among commercial receivers. The potential advantages of a software GNSS receiver include:

• Exploration of particular signal characteristics, new GNSS signals

• Easy to customize source code compared to FPGA

• New signal processing development

• Specific receiver development (scintillation monitor etc.)

• Deep integration with other sensors

• Suitable as an education tool of communication

• Excellent for prototyping

• LEO positioning

• Spoofing and jamming

From 2021 to 2023, Tokyo University of Marine Science and Technology, Chubu University, and Chiba Institute of Technology, commissioned by the Ministry of Education, Culture, Sports, Science, and Technology, spearheaded research and engineering education, predominantly focusing on software GNSS receivers to advance Aerospace Science and Technology. The GNSS domain demands a cadre of young individuals well-versed in positioning algorithms and GNSS receiver signal processing, particularly as GNSS undergoes imminent changes. While GNSS has conventionally served convenience purposes like car and pedestrian navigation, it has also found application in ship and airplane navigation, spanning both civil and military domains. In the foreseeable future, GNSS is poised to be instrumental in highly reliable applications such as autonomous vehicles and civilian drones.

To expedite satellite positioning technology, emphasis on the final phase of the positioning section, as well as the signal processing segment of the receiver, as depicted in Fig. 21, is imperative, as highlighted by Kubo et al. [44]. All teaching materials, actual programs, and content scrutinized in the developmental tasks are accessible. In the competition conducted during the program’s culminating year, the student demonstrating the highest proficiency in capturing, tracking, and decoding positioning satellite signals from the intermediate frequency (IF) data acquired by the front end was honored. The source code utilized by the victors is readily available.

7.  Open Source Program and Some Modifications

RTKLIB, an open-source program for precise positioning developed by Takasu [45], has been an integral tool in our lectures and seminars for over 15 years, serving as a valuable resource for learning GNSS positioning and conducting research and development (R&D). The RTK performance of commercial receivers has notably advanced with the availability of low-cost dual-frequency receivers. Derived programs like rtklibexplorer [46] have also found application. Here, we provide a brief overview of an enhanced RTK algorithm tailored for vehicles in urban settings, along with experimental findings [47].

7.1  Three Modifications

Our modification to RTKLIB involved replacing the entire relative position function, a core feature responsible for resolving both float and fixed solutions in RTK-GNSS. This entailed utilizing the original RTKLIB source code, excluding the relative positioning component, which is denoted as “relpos.”

First, we implemented a satellite selection approach employing subsets of GNSSs. While partial ambiguity resolution can offer enhanced efficacy, precautions must be taken against erroneous fixes. Second, we introduced a smoothed floating solution to mitigate large errors commonly encountered in pseudo-range measurements within urban environments. This involved integrating the pseudo-range-based position with velocity data derived from carrier phase or Doppler frequency using a loosely coupled Kalman filter. Additionally, we incorporated the concept of an Adaptive Kalman filter [48]. Thirdly, we adopted ambiguity resolution techniques leveraging velocity information derived from Doppler frequency or time difference of carrier-phase measurements [49]. These strategies represent combinations of conventional methods, with our future focus aimed at reducing the incidence of incorrect fixes.

7.2  Precise Positioning Challenge

The Institute of Positioning, Navigation, and Timing of Japan sponsored the Precise Positioning Challenge in FY2023, where GNSS observation data from low-cost receivers in downtown Tokyo and Nagoya were made publicly available for analysis, with the accuracy of the positioning algorithm results duly verified. Kubo et al. [47] have reported some of the outcomes of this data analysis. We eagerly anticipate the involvement of young enthusiasts in such endeavors. Please refer to The Institute of Positioning, Navigation, and Timing of Japan website [50] for further details.

8.  Conclusion

In this paper, I have delved into the technology behind achieving precise positioning with GNSS. Initially, I highlighted the current era of multi-GNSS and provided an overview of the fundamentals of precise positioning technology. Subsequently, I elucidated the characteristics and correction data of QZSS, a Japanese positioning satellite. Following this, I explored multipath mitigation technology, recognized as pivotal for achieving precise positioning, underscoring the importance of comprehending GNSS receivers for this purpose. I also outlined the fundamentals of software GNSS receivers. Lastly, I introduced RTKLIB, a globally recognized open-source program for precise positioning, along with some modifications to its functionality. Regrettably, due to space constraints, I was unable to discuss the integration of GNSS with other sensors in this paper. However, I would be delighted if students and young engineers could acquaint themselves with the integration technology of GNSS with IMU and other sensors. Additionally, it is noteworthy that issues concerning interference and spoofing of GNSS signals have surfaced in recent years. I hope that some of you will engage in addressing these challenges both theoretically and practically.

Acknowledgments

I wish to express my sincere appreciation for the students in the lab who prepared a few materials for the present study.

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Authors

Nobuaki KUBO
  Tokyo University of Marine Science and Technology

Keyword

GNSS,  precise positioning,  multipath mitigation,  QZSS,  PPP-RTK,  PPP,  RTK-GNSS,  software GNSS receiver