Abstract
This paper presents an innovative approach aimed at enhancing satellite position determination accuracy within a geostationary equatorial orbit (GEO) by integrating a regional navigation satellite system (RNSS) with a global navigation satellite system (GNSS). In a GEO, incoming GNSS signals are typically constrained to a specific direction on the other side of the Earth, resulting in a significant dilution of precision (DOP) and, consequently, a significant radial error. By incorporating an RNSS, signals from more diverse directions are available, improving observability and enhancing navigation precision. Taking the quasi-zenith satellite system (QZSS) as a representative RNSS, this paper demonstrates the feasibility of receiving signals from GEO satellites across a substantial range. Link budget analyses were conducted using the precise side-lobe patterns of the QZSS, revealing that QZSS signals can be consistently observed across most arcs in a GEO. Two comprehensive simulations were conducted: a point solution and an extended Kalman filter-based orbit determination. The results affirm the anticipated improvement in navigation precision indicated by the DOP analysis. It is essential to note that whereas RNSS signals can be received from any longitude in a GEO, enhanced navigation precision relies on the distance from the satellite to the RNSS. Considering the availability of multiple RNSS options, the concept presented in this research can be adapted to any longitude within a GEO, thereby promoting stable, high-precision navigation.
1 INTRODUCTION
Global navigation satellite systems (GNSSs), such as the Global Positioning System (GPS), are widely used. GNSSs were originally designed to determine the position and velocity of terrestrial and low-altitude users. Subsequently, GNSSs have evolved to encompass orbit determination of low Earth orbit (LEO) satellites. The accurate real-time position determination offered by GPS has resulted in a proliferation of GPS receivers on LEO satellites.
Geostationary equatorial orbit (GEO) satellite users strongly desire real-time navigation. The conventional range-and-range-rate method with batch processing has long been employed to determine satellite orbits. This method necessitates an extensive set of range measurements to precisely calculate positions, a process that ranges from several hours up to a few days and requires ground facilities capable of range measurements. The introduction of GPS receivers makes it possible to determine a satellite’s orbit independently of ground facilities, considerably relaxing satellite design constraints. In particular, there is a growing trend of adopting electrical propulsion systems for GEO satellites to extend their operational life. However, the primary drawbacks of electrical propulsion include power limitations, resulting in frequent and prolonged thruster burns. The need for instantaneous navigation with rapid convergence has arisen to satisfy the requirements for small but prolonged accelerations. Furthermore, because of the limitations of GEOs, there is a need for satellite collocation (Hengnian et al., 2014; Park et al., 2003), where multiple satellites share a single control slot. This step requires highly precise navigation and control, a challenge that GNSS receivers can address. Improved navigation accuracy would enable GEO satellites to maintain their positions autonomously, simplifying ground operations and making satellite operations more cost-effective.
However, GPS-based navigation has not been practical until recently. Figure 1 illustrates the geometric relationship between GEO and GPS satellites. GPS satellites broadcast signals toward the Earth, making it impossible for GEO satellites to receive signals from nearby GPS satellites. Although the Earth obstructs most broadcasted signals, a portion of the signal emitted from the edges of the main lobe and side lobes traverses the Earth’s edge and continues beyond the other side, ultimately reaching GEO satellites, as shown in Figure 1. The extended transmission distance diminishes the signal strength by approximately 20 dB compared with the signals received by LEO satellites. Nevertheless, practical GPS navigation in a GEO is feasible if the decayed signal can be detected. The need for navigation independent of ground systems has driven the development of sensitive receivers, with various organizations dedicating over a decade of efforts to research high-altitude GPS-based navigation. Numerous analytic and simulation studies have affirmed the practicality of using GPS receivers at high altitudes, such as GEOs (Moreau, 2001; Winternitz et al., 2009), highly eccentric orbits (Carpenter, 2004), and even cislunar trajectories (Bamford, 2008).
Geometrical relationship between GNSS and GEO satellites
The first use of GPS-based navigation at high altitudes was presented by Kronman (2000). A GEO satellite, equipped with transponders, relayed GPS signals to the ground for data collection and processing. Although the navigation was computed on the ground, this was the first report of observing GNSS signals from above a medium Earth orbit (MEO). In 2012, a highly sensitive receiver, the Space GNSS Receiver for Geostationary Earth Orbit (SGR-GEO), was implemented on Galileo In-Orbit Validation Element A (GIOVE-A) and demonstrated onboard navigation just above the GPS constellation at an altitude of 23,300 km (Unwin et al., 2013). This receiver detected numerous GPS signals from the side lobes of the GPS and revealed the possibility of using GNSS signals at an MEO. In 2015, NASA’s Magnetospheric Multiscale (MMS) mission demonstrated the use of GNSS signals above a GEO (Winternitz et al., 2017). The MMS trajectory was highly elliptical, with an apogee of approximately 76,000 km, much higher than a GEO. Although the number of satellites observed at apogee was limited, the receiver demonstrated onboard navigation using the Goddard Enhanced Onboard Navigation System (GEONS) software developed by the National Aeronautics and Space Administration (NASA).
After increasingly complex demonstrations and evaluations, GNSS receivers were deployed in the Geostationary Operational Environmental Satellite R mission under NASA and the National Oceanic and Atmospheric Administration (Winkler, 2017). The Viceroy-4 receiver from General Dynamics provided stable navigation in a GEO. Numerous GEO missions employing GNSS receivers have recently been reported (Winkler et al., 2017; Harada et al., 2021; Zin et al., 2021; Jiang et al., 2018). The flight results of these missions have demonstrated that the navigation accuracy of GNSS receivers for a GEO is not as good as that for an LEO. The cause of the accuracy deterioration is poor dilution of precision (DOP) and ionospheric delays (Jun et al., 2020; Nakajima et al., 2023). The poor DOP is caused by the limited observability in a GEO, where the incoming signal direction is concentrated toward the nadir, as shown in Figure 2(a). This directional bias of incoming signals deteriorates the DOP and causes significant radial errors.
Observable GNSS signals in a GEO for (a) GPS only and (b) GPS and QZSS, where RNSS signals are available and the signal direction is broader
In pursuit of enhanced navigation performance for a GEO, several approaches have been proposed. A straightforward approach is to increase the number of signals by receiving signals from multiple GNSS constellations (Capuano, 2017; Wang, 2021; Li, 2023). Besides GPS, adopting Galileo or the BeiDou Navigation Satellite System (BDS) increases the number of available signals and improves the DOP. Although these approaches significantly reinforce the receiver stability, the improvement in DOP remains modest because of the limited variety of incoming signal directions.
The performance of LEO satellites may be improved by integrating satellite-based augmentation system (SBAS) signals (Allahvridi-Zadeh, 2021). This approach reduces the signal in space user range error (SIS-URE) and orbit determination errors. However, because of the high bit rate, the augmentation signal is challenging to receive and decode in a GEO, where the signal decays over long distances between SBAS and GEO satellites. It is difficult to utilize SBAS signals in a GEO with current receiver technology; thus, no studies focusing on the use of SBAS signals for a GEO have been reported in the literature.
Mitigating ionospheric delay is another strategy for reducing the positioning error in a GEO. While LEO satellites commonly employ an elevation mask to eliminate signals passing through the ionosphere, the same concept cannot be applied to GEO satellites. Several flight results for GEOs have indicated that ionospheric delay persists even in the plasmasphere up to 6,000 km from the Earth (Matsumoto, 2022; Matsumoto, 2023). Although masking all signals up to 6,000 km leaves no valid measurements, masking itself has the potential to improve the navigation accuracy in a GEO. However, it is ideal if delay-free measurements can be added, as most signals will be delayed by the plasmasphere. Matsumoto et al. (2023) proposed using the global core plasma model to mitigate this delay. Although this model can compensate for a significant portion of the delay, modeling errors may persist; moreover, for the worst case in which the model differs markedly from reality, the compensation could deteriorate accuracy. Thus, whereas this approach may be practical for offline orbit determination, where operators can assess and refine the results, it remains impractical for onboard navigation or as input for satellite control systems.
Utilizing regional navigation satellite systems (RNSSs) in conjunction with GNSSs can improve the DOP for GNSS receivers in a GEO, subsequently enhancing navigation precision. Signals transmitted from the main lobe of an RNSS cannot be received, as they are designed for terrestrial and low-altitude users. However, signals emitted from the side lobes of an RNSS, although weaker than the main lobe signals by more than 20 dB, might be detected by GEO satellites, if receiver antennas are designed for this purpose. Additional signals from an RNSS enhance multidirectional observability, as graphically depicted in Figure 2(b). The reception of nearby RNSS signals contributes to improved observability, mitigating the DOP and enhancing navigation precision.
2 PROPOSED CONCEPT: NOTABLE ADVANTAGES OF UTILIZING RNSS SIGNALS FOR A GEO
The main contribution of this study is the concept of utilizing RNSS signals in addition to GNSS signals in a GEO to improve navigation performance. RNSSs such as the Quasi-Zenith Satellite System (QZSS), Navigation Indian Constellation (NavIC), and GEO/inclined geosynchronous orbit (IGSO) satellites in the BDS are located close to a GEO and broadcast signals to ground users. Typically, RNSSs broadcast both positioning and augmentation signals. As explained in Section 1, it is difficult for augmentation signals to be decoded by GEO satellites because of their high bit rate, although the positioning signal might be usable in a GEO, thanks to their low bit rate.
Signals from an RNSS cannot be readily received by GEO antennas in the +Z plane of GEO satellites because of their inherent directivity. However, signals leaking from the side lobes of an RNSS can be received with additional antennas oriented toward the RNSS (see Figure 3 for an example of antenna orientation). Actively utilizing signals from nearby RNSSs in a GEO (Figure 2(b)) increases the number of observations, improves the DOP, and enhances navigation precision. Furthermore, whereas GPS signals pass through the ionosphere and suffer from severe delays (Matsumoto et al., 2022), signals from nearby RNSSs avoid such delays because they do not pass through the ionosphere. This delay-free measurement process further contributes to precise navigation.
GEO satellite and antenna orientation
Implementing additional antennas exclusively for signals from nearby RNSSs is impractical, as this approach would invite the complexity and gain resources of the GNSS receiver. Standard GEO satellites are controlled in a local vertical local horizontal (LVLH) frame, with the +Z body axis pointing toward the Earth’s center and the +X body axis pointing in the velocity direction. In the context of orbit determination in a GEO, a single GNSS antenna on the mission plane is sufficient. However, some innovative GNSS receivers can determine their orbit during a geosynchronous transfer orbit (GTO) phase. During the GTO phase, the satellite changes its attitude in order to execute orbit-raising maneuvers and generate power via solar panels. To ensure adequate signal reception during this GTO phase, the receiver typically configures additional broad-beamwidth antennas (Nakajima et al., 2020; Lu et al., 2022; Zentgraf et al., 2010). These GTO antennas are installed solely for the GTO phase and are no longer used after the satellite reaches a GEO. We propose the continued use of these antennas, primarily installed for GTO phase navigation, even after the satellite transitions to a GEO, enabling signals to be received from nearby RNSSs.
RNSS utilization has not been extensively researched, even for LEOs. The validity of employing an RNSS for LEO satellites has been limited, because RNSS coverage is limited to specific regions on the Earth. Several analytical studies have explored the potential benefit of employing RNSSs for LEO satellite navigation. Because of the restricted coverage of RNSSs, precision improvement is limited to certain segments of the orbit. RNSS signals are accessible to LEO satellites for, at most, half an orbit; during the remainder of the orbit, the precision is unchanged because RNSS signals are no longer available. Satellites that maintain consistent and stable navigation performance are preferred in practice, as they simplify satellite system design. Receivers with varying levels of accuracy within each orbit introduce complexities. Despite the long history of GNSS usage, there have been few reports detailing the practical application of RNSSs for onboard GNSS receivers, even in LEOs.
In contrast, there is potential for continuous, stable reception of RNSS signals in GEOs, contingent upon the satellite longitude. This potential is attributed to the slow or synchronized motion of RNSS and GEO satellites, allowing continuous, stable links to be established. Although this benefit can only be realized by GEO satellites located at specific longitudes, because of the limited coverage of RNSSs, those with the capability to observe RNSS signals will experience stable, continuous RNSS links. A reliable communication link provides continuous high-precision navigation, simplifying satellite system design and achieving complex goals such as satellite collocation in GEOs.
This study evaluated the feasibility of receiving RNSS signals and analyzed the DOP for GEO satellites under the conditions described above. Furthermore, GNSS simulations verified the precision of point solutions and extended Kalman filter (EKF)-based navigation. We employed the QZSS as an example and assessed the improvement in DOP and navigation performance. However, it is important to note that the underlying concept can be extended to other RNSSs, such as the NavIC and GEO/IGSO satellites in the BDS. As stated above, the longitude limitation of the proposed approach can be addressed by selecting a proper RNSS according to the longitude of the GEO satellites.
3 MODELING
This section describes the models and conditions that we assumed for our analysis and simulation. The GPS receiver was modeled from the specifications of a receiver for a GEO satellite. The simulation was conducted via a combination of several software programs, as described below.
3.1 GPS Receiver
A GPS signal received in a GEO is weaker than that of an LEO by approximately 20 dB or more. The Japan Aerospace Exploration Agency and NEC/NEC Space Technologies have jointly developed an advanced GPS receiver tailored for GEO satellites (GEO GPSR). This receiver is based on the design of a GPS receiver originally intended for LEOs (Kondoh et al., 2009), developed in 2013. Minimal modifications were made to its hardware design, but enhancements were made to the onboard software and antennas to increase sensitivity and ensure stable navigation. Figure 4 shows the GEO GPSR.
GEO GPSR (a) Main unit (b) GEO antenna (c) GTO antenna
The GEO GPSR is designed to utilize GPS L1 signals and cannot receive QZSS signals. This study assumed that the receiver would receive QZSS signals, as the positioning signals of the QZSS resemble those of the GPS. The benefits of receiving QZSS signals in a GEO were evaluated.
3.2 GPS Antenna
A patch array antenna in a GEO with high directivity and a narrow beamwidth was adopted to optimize the visibility of GPS satellites. In contrast, patch antennas with a wider beamwidth were developed for a GTO, where incoming signals arrive from unpredictable directions. The two types of antennas are shown in Figures 4(b) and (c), and their respective gain patterns are presented in Figure 5. The red dot and line indicate the gain specification for the GEO antenna. The thin colored lines denote the actual gain experimentally obtained for various azimuth angles, indicating that this antenna has a small azimuth variation. The blue line shows the gain of the GTO antenna.
Antenna beam patterns of GEO GPSR
It Is important to note that, unlike the GEO phase, a satellite’s attitude constantly changes while the orbit is rising during the GTO phase. The GEO antenna was installed in the +Z plane to receive the maximum number of GPS signals in the GEO. Two GTO antennas were mounted in the ±X plane to maximize the observability during the GTO. The antenna arrangement is shown in Figure 3.
3.3 GPS and QZSS Modeling
This section describes the GPS and QZSS models used in this study. The GPS and QZSS orbits and antenna patterns for link analysis were set to evaluate the visibility of the GNSS satellites.
The simulation epoch was begun on January 19, 2022. The GPS constellation was modeled as 24 GPS satellites, the minimum number guaranteed by the interface control document (ICD). The orbits were set based on the ICD (Broy, 2013). The antenna patterns were modeled using data from the GPS Antenna Characterization Experiment (ACE) (Donaldson et al., 2020). This experiment modeled the equivalent isotopically radiated power (EIRP) of each GPS antenna pattern by collecting signal strength data obtained by a GEO satellite and analyzing accumulated long-term data. The EIRP model of each satellite was released independently. Still, for the sake of simplicity, this research chose three satellites as representative of each block: SVN56 for Block IIR, SVN61 for Block IIR-M, and SVN73 for Block IIF. The details of the models are summarized in Table 1.
Modeled GPS and QZSS Parameters
The QZSS was modeled as the final constellation planned for the initiation of operations in 2024 (Sakai & Kogure, 2009). Seven satellites are planned to be launched for full operational capability: four IGSO and three GEO satellites. Two types of antennas are adopted for the QZSS: QZSS-2 and 4 utilized helical array antennas. The five remaining satellites in the constellation have mounted patch antennas (NSPS, 2017). Each antenna pattern is publicly available from the National Space Policy Secretariat (NSPS, 2023). The averaged antenna gain patterns are plotted in Figure 6. The data resolution and range differ between the antennas; thus, QZSS-2 and QZSS-5 were selected as representative helical array antennas and patch antennas, respectively. The SIS-URE of the GPS (Renfro et al., 2020; Heng et al., 2011) and QZSS (Sakai & Kogure, 2018) were modeled based on actual performance.
QZSS L1 average antenna gain patterns (Japanese Cabinet Office, 2023)
3.4 Link Analysis Conditions
The following describes the analysis conditions. AGI’s Systems Tool Kit (STK) was used in the communication link and DOP analyses. The QZSS visibility changes according to the orbital position of the GEO satellites. Therefore, our study evaluated sensitivity to the GEO satellite longitude. Table 2 summarizes the GEO satellite model and parameters of the link analysis. As explained in the previous section, the receiver parameters were chosen to model the GEO GPSR. The ranging error was assumed to be 4 m (1σ), which is a specification of the receiver for 20-dB-Hz signal ranging ability. If a stronger signal can be received, the random error is reduced; however, in this simulation, this effect is not modeled, and a constant σ is assumed for generating the random ranging error. A normal distribution error was generated and added to the real distance generated by the simulator. For the thermal condition, general GEO conditions are selected to model the decay of the carrier-to-noise ratio (C/N0), which will result in a smaller number of observations and a deterioration in navigation accuracy.
Link Analysis Parameters and GEO Satellite Modeling
The longitude of the GEO satellite started at 135° east (E), the approximate average longitude of the QZSS constellation. The visibility of a QZSS satellite depends on the location of the GEO satellite in orbit. Thus, the link analysis was conducted in 45° increments to confirm the sensitivity to longitude. In addition, to evaluate the benefits of receiving the QZSS signal in terms of the DOP, we analyzed two cases: the GPS-only case and a case with both the GPS and the QZSS consisting of four IGSO and three GEO satellites.
3.5 Simulation Setup
A comprehensive simulator was developed for simulating the GPS/QZSS-based navigation. Figure 7 shows the simulator configuration. The SimGEN Positioning Application, a software used to drive the GNSS signal generator from Spirent, was employed to generate the pseudo-GPS observation data. Using the “no hardware dummy run” mode, the software can operate independently and generate GPS observation data in receiver-independent exchange (RINEX) format. The SimGEN software also generated RINEX navigation files and recorded the reference trajectory of the GEO satellite. Simulation results were compared with this reference trajectory, and errors were examined. The observed data in RINEX format were used to obtain the orbit, including the point solution and the solution filtered by the EKF. The EKF estimates the position, clock bias, velocity, clock drift, and empirical acceleration, as given in Table 3. The general error sources are modeled precisely to validate the expected performance in orbit. Different software programs were used for the orbit determination simulation based on their functionalities, but the scenarios and parameters were set to be identical.
Simulator overview
Model and Parameters for EKF-Based Orbit Determination
4 ANALYSIS RESULTS
Analysis results emphasizing the benefits of utilizing an RNSS in a GEO are presented in this section. The QZSS is used as a representative RNSS and was modeled in the analysis. However, as mentioned previously, this concept can be extended to other RNSSs, such as the BDS or NavIC system. For the link analysis and DOP analysis, AGI STK was utilized instead of SimGEN, taking advantage of the rich functions.
4.1 Link Analysis Results
The link analysis was conducted using STK, considering the antenna gain patterns explained in Section 3.3, and the number of satellites that provide a signal stronger than the C/N0 threshold is shown in Figure 8. The statistics of the results are listed in Table 4. The GEO satellite at each longitude was analyzed for 24 h. Because the result was axisymmetric from the starting point of the QZSS, only one side of the data set, from 135° E to 45° west (W), is given. Therefore, the five plots indicate the link analysis results for 135° E, 90° E, 45° E, 0°, and 45° W. The red line is the number of received GPS signals, which remained similar regardless of the longitude. The green line shows the number of QZSS GEO satellites received, and the cyan line shows the number of received IGSO QZSS satellites. The dashed magenta line shows the total number of received QZSS satellites. The blue line indicates the total number of received GPS and QZSS signals. Because the GPS is designed to be used globally, its visibility showed no longitude dependence, and 4–12 satellites could be received at any longitude during the 24-h simulation. On average, 7.3 satellites were received.
Link analysis results
Link Analysis Statistics
In contrast, the QZSS is an RNSS; hence, the number of visible satellites depends on longitude. There are only seven QZSSs in the constellation. Thus, an outage can occur. At 135° E and 90° E, where the distance to a QZSS satellite was low, the QZSS signals were received at 100% for the analysis periods. These two cases indicated that the QZSS signal could always be acquired, and a continuous improvement in DOP is expected. The GEO QZSS contributed to stable links, whereas the IGSO QZSS established links of a short duration with long outages. At 45° E and the Prime Meridian, the number of received QZSS satellites was the lowest, and some outages occurred. However, QZSS satellites could be observed over 90% of the time over the analysis period. Therefore, a stable performance improvement can still be expected. In contrast, at 45° W, the number of received QZSS satellites tended to increase to as many as 3.1 satellites on average. The number of received QZSS satellites was the largest among the five cases because the GEO satellite was on the opposite side of the QZSS constellation. The signal passed closer to the transmitter’s main lobe, which improved the link, even though the distance from the QZSS increased. However, the QZSS satellites were observed in nearly the same direction as the GPS satellites in this case; thus, only a slight improvement in DOP was expected, even though the largest number of QZSS satellites was received. In addition, for a GEO satellite opposite the QZSS constellation, the number of signals received from IGSO QZSS satellites was higher than the number of GEO QZSS satellites, which is the opposite behavior of a GEO satellite located near the QZSS constellation.
4.2 DOP Analysis Results
DOP analysis was also conducted via STK. DOPs for the different longitudes are illustrated in Figure 9 to confirm the improvement in navigation accuracy achieved by the QZSS. The top figure shows the DOP for the GPS-only case at 135° E. The geometric DOP (GDOP) was fairly large, up to 40, because all GPS satellites observed from a GEO are biased toward the Earth. Moreover, inspection of each DOP confirmed that the horizontal DOP (HDOP) was relatively small, whereas the behavior of the vertical DOP (VDOP) followed that of the GDOP, with the VDOP being was the dominant DOP. The 24-h average was 11.9 for VDOP and 16.6 for GDOP. This finding confirmed that the error in altitude tends to be larger in the GEO than in the other axes. It is natural for a high-altitude GNSS receiver to have a large VDOP and a large error on the radial axis. Theoretically, the lateral error standard deviations scale with distance d whereas the range and clock error standard deviations scale as d2 for large r << d, where r is the inter-GNSS distance and d is the range from the GNSS to the receiver (Winternitz et al., 2019).
DOP analysis results
PDOP: position dilution of precision; TDOP: time dilution of precision
Figure 9 shows the benefit of receiving QZSS satellites. If QZSS satellites can be received in addition to GPS satellites via the GTO antennas, the DOP improves, as shown by the top-right panel in Figure 9. The VDOP and GDOP drastically decreased. The 24-h average GDOP was 2.7, and the VDOP was 1.6. Therefore, the error in altitude was expected to improve. Because the navigation accuracy of simple positioning is proportional to the DOP, the navigation error is expected to decrease by approximately 80%. Including the navigation satellites in the lateral direction in addition to the radial direction improves the VDOP (Ji et al., 2012). Because the high-altitude scenarios tend to have a large VDOP, as the VDOP improved, the total DOP improved accordingly.
DOP plots for the GPS + QZSS case from 90° E to 45° W are also shown in Figure 9. At 90° E, the DOP was slightly worse than at 135° E, even though the number of visible QZSS satellites showed little change. This result arose because QZSSs could be confirmed on the east and west sides by a satellite positioned at 135° E. In contrast, QZSS satellites could be observed only east of the GEO satellite located at 90° E. The diversity of the QZSS location is wider for 135° E, leading to an improved DOP.
The DOP deteriorated significantly from 45° E to 45° W, as indicated by the bottom row in Figure 9. Because fewer QZSS satellites were observed at 45° E and 0°, the difference from the GPS-only case at 135° E was relatively small. Although many QZSS satellites could be received at 45° W, a slight improvement could be expected because the signal path direction overlapped with the GPS. Because of the overlapping signal directions, the vertical sensitivity was expected to show less improvement than that obtained near the QZSS constellation. The statistics of these results are listed in Table 5.
DOP Analysis Statistics
The DOP analysis results indicate that the proposed approach considerably improves satellite navigation at proper longitudes, with small improvements at other longitudes. This approach reduces the DOP by a factor of 2 or more over half of the GEO longitudes. There are several RNSSs throughout the world. Thus, by choosing a suitable RNSS to receive signals, the benefit can be obtained at wider longitudes for a GEO. In general, once a GEO satellite is positioned in its control slot, the longitude does not change until the end of its life. Therefore, those positioned in a proper slot can benefit from the proposed approach and will obtain constant and permanent navigation performance improvement.
4.3 Point Solutions
The DOP observed for a GEO significantly improved with the introduction of an RNSS, as discussed in the previous subsection. This section describes further insight into the navigation performance improvement obtained via point solutions. SimGEN generates pseudo-observation data. We simulated and compared two cases: 135° E with and without the QZSS. Because of the minimal variations for this comparison, we present data for the first 2 h of simulation for both cases.
Figure 10(a) shows point solutions for GPS data without the QZSS. In the legend, R, T, and N denote the radial, tangential, and normal axes. According to the large DOP and measurement noise, the point solution accuracy is less precise than the typical ground-based GPSR results. The three-dimensional root mean square (3dRMS) error was 27.7 m, with occasional peaks of up to 100 m. As expected from the DOP analysis, the radial axis exhibited a more pronounced error than the other axes. The onboard GNSS receiver generally employs filtering techniques to mitigate these errors at the cost of responsiveness. It would be ideal if the point solution errors could be minimized.
Point solution error for 135° E GEO (a) GPS only (b) GPS and QZSS The addition of the QZSS reduces the radial position error.
The navigation performance was significantly improved by incorporating the QZSS and GPS, as illustrated in Figure 10(b). The 3dRMS error was reduced to 5.9 m, and the error distribution became more stable. Even for the worst case within the simulated time frame, the error remained within 15 m. The horizontal point solution accuracy is consistent with Figure 10(a), whereas the radial axis error shows substantial improvement.
4.4 EKF-Based Orbit Determination
Typically, onboard GPS navigation of satellites involves the application of a filter to mitigate noise and expected errors. EKF-based navigation using pseudo-observation data was simulated to assess the expected in-orbit performance. The EKF estimates the position, velocity, clock bias, and empirical acceleration. The GNSS constellations were configured to meet the minimum number of GNSS satellites guaranteed in IS-GPS-200. The ephemeris was generated from SimGEN in RINEX navigation file format and imported into the filter. The SIS-URE was added to the RINEX navigation file according to the normal distribution with the actual in-orbit performance standard deviation. The Earth’s rotation parameters were taken from information published by the International Earth Rotation and Reference Systems Service. We conducted simulations for the same two cases discussed in the previous subsection: 135° E with and without the QZSS. The duration of a simulation scenario was selected as 24 h, which corresponds to the orbital period of a GEO.
Figure 11(a) presents the number of received signals and the GDOP for the GPS-only condition. The GDOP was 7–18, and the number of satellites was 6–12, consistent with the former analytical results. The number of received signals increased from 8 to 12 with the addition of the QZSS, as shown in Figure 11(b). The navigation filter only accepts 12 satellites, assuming the GNSS receiver hardware specification. The GDOP also improved, ranging from 2 to 5, in agreement with expectations.
GDOP and the number of received signals (a) GPS only (b) GPS and QZSS The number of total satellites is increased by the received QZSS satellites. The GDOP decreased from a range of 10–30 to a range of 3–5.
The EKF-based orbit determination results are depicted in Figure 12(a). The filtered solution exhibited a 3dRMS accuracy of 11.1 m, with a maximum error of approximately 40 m for the least favorable condition within the simulated 24 h. The navigation error was smaller than that of the point solution shown in Figure 10(a) because of the filter’s effect. The 3dRMS velocity error was 7.6 cm/s, with a peak velocity error of 25 cm/s within 24 h.
Filtered navigation error for a GEO (a) GPS only (b) GPS and QZSS
Including QZSS signals minimized navigation errors, as demonstrated in Figure 12(b). The 3dRMS position error was reduced to 4.8 m, significantly improving the radial axis error. Although the improvement in velocity was modest compared with the position error, it still represents an enhancement, with a 3dRMS error of 5.3 cm/s.
GPS signals are subject to ionospheric delays in orbit as they traverse the ionosphere and plasmasphere. In contrast, signals from nearby RNSSs avoid such delays, as they do not pass through the ionosphere. This simulation did not model these delays, implying that the performance difference should be more pronounced when the QZSS it utilized in an actual orbit, because only GPS signals are affected by the ionosphere.
5 CONCLUSION
This paper has proposed a novel approach for improving the DOP and navigation accuracy by utilizing nearby RNSSs located in GEO and IGSO. The main lobes of an RNSS cannot be received from a GEO; however, the signals emitted from the side lobes can be detected by GEO satellites if the antennas are designed accordingly. While the effectiveness of RNSSs for onboard navigation has been historically questioned for LEO satellites, their continuous links to GEO satellites resulting from slow or synchronized motion enable stable, high-precision navigation. In contrast to a typical GNSS located in an MEO, GEO satellites, particularly those at specific longitudes, can significantly benefit from the integration of nearby RNSSs, resulting in improved DOP and navigation accuracy. The feasibility of this approach hinges on the relative positions of GEO satellites and RNSSs. When GEO satellites are situated on the opposite side of the Earth from the RNSS constellation, the benefits are limited. However, simulations indicated that the integration of QZSS satellites can reduce the DOP by a factor of 2 over at least half of the GEO. Moreover, there are several RNSSs beyond the QZSS; thus, by integrating other RNSSs, the same benefit can be obtained regardless of the GEO satellite longitude. For satellites near an RNSS, continuous and permanent signal reception is attainable, offering advantages throughout the satellites’ operational life.
Unlike GPS signals, which are susceptible to delays when passing through the ionosphere, signals from nearby QZSSs are delay-free, as they bypass the ionosphere entirely. This feature further enhances navigation precision. Adopting additional antennas is imperative to successfully implement this approach. Typical GPS receivers for GEO satellites employ a single high-directivity antenna oriented toward the Earth. Conversely, GTO satellites require broad-beamwidth antennas. Thus, the active utilization of these antennas in a GEO can enhance navigation precision without the need for supplementary resources.
This study evaluated the validity of using RNSSs in addition to GNSSs in a GEO, with the QZSS and GPS as examples. The results indicate that the QZSS signal can be received at most longitudes in a GEO. Signals from GEO satellites in the QZSS constellation exhibit superior link characteristics over IGSO QZSS satellites in terms of stability. DOP analysis confirms a significant reduction in the predominant radial error when GEO satellites are near the QZSS constellation. However, the improvement in DOP was small even if QZSS signals could be received when the GEO satellites were far from the QZSS constellation; thus, a substantial improvement in navigation precision cannot be expected in this case. The analysis demonstrated the benefits of using the QZSS, but the basic concept of this study can be extended to other RNSSs, such as NavIC and BDS satellites.
To validate the proposed approach, two comprehensive simulations were executed. A point solution simulation revealed that the proposed approach reduced the average navigation error from 27.7 m to 5.9 m, with a marked improvement in radial error, as anticipated by DOP analysis. A position estimation simulation employed the EKF to evaluate practical in-orbit performance and yielded accurate results for the proposed approach. A 24-h simulation assessing navigation precision affirmed that including the QZSS alongside the GPS achieved a 3dRMS navigation precision of 4.8 m. This result represents a substantial 60% reduction in error from the case without the QZSS. Notably, the approach achieved high-precision navigation while being cost-effective, leveraging commercially available hardware and software with minimal additional resources by taking advantage of GTO antennas.
The proposed approach has advantages over the conventional approach, considering the in-orbit ionospheric delay. However, a quantitative evaluation is left for future work because a large amount of data is needed to quantitatively evaluate the effect of ionospheric delay in a GEO. Such investigations would effectively underscore the benefits of including an RNSS, particularly considering that only signals from GNSSs are subject to delay due to the ionosphere.
In summary, the proposed approach substantially enhances the DOP and navigation precision by integrating an RNSS. The magnitude of improvement depends on the satellite longitude, with pronounced improvements for certain longitudes. For over half of the longitudes within a GEO, this approach reduces the DOP by at least a factor of 2. Considering that several RNSSs are globally available, selecting an appropriate RNSS for signal reception can yield similar advantages for any GEO longitude. Consequently, satellites located near an RNSS constellation can obtain a consistent and permanent performance improvement in navigation accuracy that extends over their operational life.
HOW TO CITE THIS ARTICLE
Nakajima, Y., & Yamamoto, T. (2024). Enhancing navigation accuracy in a geostationary orbit by utilizing a regional navigation satellite system. NAVIGATION, 71(2). https://doi.org/10.33012/navi.641
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Jump to section
Related Articles
Cited By...
- No citing articles found.