A Study on the Satellite Orbit Design for KPS Requirements

Abstract

This paper analyzes navigation performances of the Korean Positioning System (KPS) constellation with respect to the orbit parameters which fulfills the specification requirements. Specifically, the satellite configuration and navigation requirements of KPS are explained, and the daily mean horizontal dilution of precision (HDOP) and satellite visibility on KPS coverage are analyzed to confirm the adequate orbit parameters. However, due to orbital slot saturation, geostationary-orbit (GEO) satellites may not be allocated in the original orbit as specified in the KPS requirements. Therefore, in a spanned window of 4 degrees from the reference longitude the navigation performance of each GEO satellite orbit is investigated.

1. INTRODUCTION

The satellite navigation system started with the US TRANSIT in 1967, which was designed for military use, and in the 90s, Global Positioning System (GPS) of the United States and Global Navigation Satellite System (GLONASS) of Russia declared full operational capability (FOC) and have maintained the system so far. To date, Galileo of EU and Beidou of China have been developing and operating with the goal of FOC around 2020 as a global satellite navigation system (GNSS). The discontinue of the Selective Availability in 2000 improved satellite navigation signals with a higher accuracy for civilian use than before (Bonnor 2012). However, many advanced countries in the space technology are willing to construct their own satellite navigation systems in order to increase national defense security and maximize their industrial and economic effects. Several regional navigation satellite systems (RNSS), i.e. Navigation with Indian Constellation (NavIC) in India, the Quasi-Zenith Satellite System (QZSS) in Japan are under organization. As a great interest in RNSS, Turkish government recently conducted a preliminary orbit design research for Turkey region (Büyük et al. 2019). South Korean government announced the 3rd Basic Plan for Space Development including the KPS, a Korean navigation satellite system which enables improved stability in positioning and timing performance in Korean Peninsula (Ahn et al. 2019).

The effort for designing the satellite constellation of Korean RNSS is considerably high (Lee et al. 1998, 2005, Kim & Kim 2016). Recently, satellite constellation schemes which provide a stable dilution of precision (DOP) performances was proposed as a RNSS in Korea Peninsula region (Choi et al. 2018). In particular, two formations, the one with 7 satellites of 3 GEO satellites and 4 eccentric-inclinedgeosynchronous-orbit (EIGSO) satellites (referred here as Proposal 1), and the other with 9 satellite constellations with the addition of 2 EIGSO back-ups (referred here as Proposal 2), are evaluated and analyzed in the study.

In this paper, we investigated the orbital parameters based on Proposal 1 which suffices the navigation requirements of KPS. Systems Tool Kit by Analytical Graphics, Inc. was adopted to calculate ground tracks and satellite coordinates of KPS satellites, and we utilized MATLAB code in order to analyze navigation performances, DOP and the visibility. In Chapter 2, the required performance and orbit parameters of KPS is described. In Chapter 3, we show the HDOP value and the visible satellite numbers in KPS coverage for each simulation situation. Finally, we propose the KPS orbit parameters which satisfies the navigation performance of KPS in Chapter 4.

2. KPS REQUIREMENTS AND ORBIT PARAMETERS

Table 1 summarizes the KPS satellite orbit design requirements and performance specification requirements for the open navigation service. All satellites should satisfy 2.5 or less of HDOP in a KPS coverage and should be tracked on the Korean Peninsula. The HDOP value of 2.5 is deduced to satisfy 15 m of the horizontal error value, while assuming the user equivalent range error (UERE) as 7.2 m. The targeted service coverage of KPS open service is determined based on Incheon Fight Information Region (FIR) as shown in Fig. 1. It is a responsible area for providing information for safe operation of foreign private aircraft passing through the airspace of the Korean Peninsula, search and rescue in case of an aircraft accident. This area is established through the approval by the International Civil Aviation Organization (ICAO) Board of Directors based on consultations between neighboring countries (Wikipedia, Incheon FIR 2017). The HDOP presented as a navigation requirement performance index of KPS represents the effect of the horizontal geometrical arrangement of the satellite on position error using Eqs.(1-3) (Langley 1999, Kaplan & Hegarty 2017).

Table 1. KPS requirements.

	KPS requirements
Positioning accuracy (open service) Satellite visibility time	HDOP 2.5 or less 24 hours in the national territory

 

Fig. 1. KPS open service coverage: Incheon FIR (Ministry of Land, Infrastructure and Transport, Airspace Management 2012).

\(H=\left[\begin{array}{cccc} a_{x 1} & a_{y 1} & a_{z 1} & 1 \\ a_{x 2} & a_{y 2} & a_{z 2} & 1 \\ \vdots & \vdots & \vdots & \vdots \\ a_{x n} & a_{y n} & a_{z n} & 1 \end{array}\right]\)       (1)

where a_i = (a_xi, a_yi, a_zi) are the unit vectors pointing from the linearization point to the location of the i-th satellite.

\(\left(H^{T} H\right)^{-1}=\left[\begin{array}{llll} D_{11} & D_{12} & D_{13} & D_{14} \\ D_{21} & D_{22} & D_{23} & D_{24} \\ D_{31} & D_{32} & D_{33} & D_{34} \\ D_{41} & D_{42} & D_{43} & D_{44} \end{array}\right]\)       (2)

\(H D O P=\sqrt{D_{11}+D_{22}}\)       (3)

In this paper we suggested the optimal values of 6 orbital elements, i.e., semi-major axis, eccentricity, inclination, argument of perigee (AoP), right ascension of the ascending node (RAAN), and true anomaly (TA) (Montenbruck & Gill 2000), which satisfies the KPS specification requirements. Each parameter has a geometrical meaning between satellite orbit and the Earth as shown in Fig. 2. These parameters should be determined considering the shape of satellite ground tracks. In particular, eccentricity and inclination of KPS EIGSO are closely related to the northern hemisphere passing time and size and shape of the KPS ground coverage, respectively. Therefore, two parameters were decided according to the geopolitical positions of KPS coverage. Then a set of the basic parameters were determined as shown in Table 2. In terms of GEO positions, the longitude arrangement of 80° E, 127° E, and 180° E was proposed (Choi et al. 2018). However, the central longitude of GEO was set at 128° E in this study to avoid the duplicated latitude of EIGSO. Other GEO reference longitudes are set to on 88° E and 168° E, which keep the elevation angles above 30° at Jeju, Korea. In addition, the placement of three GEO satellites is considered at 40° East and West from 128° E central longitude. In chapter 3, the HDOP and the satellite visibility time were analyzed by adjusting the inclination and eccentricity of the KPS EIGSO. Moreover, the HDOP and the GEO elevation angle at Seoul are analyzed within the intervals spanned by 4° from the reference longitudes considering the margin.

Fig. 2. Orbit parameters.

Table 2. KPS orbit parameters.

Orbit parameter	GEO1	GEO2	GEO3	IGSO1	IGSO2	IGSO3	IGSO4
SMA (km) ECC (deg) INC (deg) RAAN (deg) AoP (deg) Central longitude (deg)	42,164 0 0 0 0 88	42,164 0 0 0 0 128	42,164 0 0 0 0 168	42,164 0.075 43~55 218 270 127	42,164 0.075 43~55 128 270 127	42,164 0.075 43~55 38 270 127	42,164 0.075 43~55 308 270 127

 

3. NAVIGATION PERFORMANCE AND VISIBILITY ANALYSIS

3.1 Navigation Performance Analysis Methods

The KPS reference orbit described in Chapter 2 consists of three GEO satellites and four EIGSO satellites, which possess eight-shaped ground tracks over the Korean peninsula as shown in Fig. 3. The ground track and the coverage of the satellite is affected by the inclination change of EIGSO changes as well as the visibility and the DOP of the satellite (Lee et al. 2012).

Fig. 3. Ground-track change by inclination and eccentricity (left: by inclination, right: by eccentricity).

Therefore, the inclination and eccentricity of EISGO were examined which coincide KPS navigation performance requirements. A set of coordination data for 24-hours of seven KPS satellites was used for the analysis. The HDOP and the number of visible satellites on the KPS coverage were analyzed with the 2° grid mesh of the longitude and the latitude. We also calculated the satellite visible time by evaluating the elevation angles at the two cities of South Korea, namely Seoul and Jeju.

3.2 EIGSO Simulation

EISGO is designed as a geosynchronous orbit that stays in the northern hemisphere for about 13 hours with a 127° E. The simulations were conducted by changing the inclination which affects the size of the ground track of EIGSO and the eccentricity that affects the shape of the ground track as illustrated in Fig. 3. The EIGSO simulations were performed with four types of parameters as shown in Table 3. We investigated three cases, namely Case (a) to Case (c), by changing the inclination to 43°, 45°, and 55°, respectively. The Case (a) represents the case that all the satellites are able to track simultaneously in Seoul and the Case (b) covers the condition that the satellites are observable in Jeju. The Case (c) illustrates the situation that the HDOP possesses a value of 2.5 or lower within the range of 1000 km of Seoul. For Case (d) we increased the eccentricity to 0.1 at the inclination 55° in order to confirm whether the navigation performance index HDOP is less than 2.5 and satellite visibility on KPS coverage are achieved.

Table 3. EIGSO analysis results.

	a	b	c	d
Maximum HDOP value on KPS coverage Visibility time (Seoul) (hrs) Visibility time (Jeju) (hrs)	2.55 24 24	2.46 22.5 24	2.13 20 20.5	2.13 20 20.5

 

Fig. 4 shows the daily mean HDOP contour over KPS coverage for the cases described above. When the inclination is 43°, the maximum value of the daily mean HDOP over the KPS coverage is about 2.5 or more. However, in the case of 45° and 55°, the maximum value of daily mean HDOP is less than 2.5. Therefore, EIGSO satellites satisfies the KPS navigation performance when the inclination is above 45°.

Fig. 4. Daily mean HDOP contours for EIGSO simulation.

In Fig. 5 the number of visible satellites on KPS coverage for each case is illustrated. The number of visible satellites in KPS is related to one of the specification requirements that the domestic monitoring station should be able to track all satellites simultaneously. When the inclination is 43° and 45°, all KPS satellites are visible below 36° N and 34° N, respectively (Figs. 5a and 5b). However, in case of the inclination 55° (Fig. 5c), it was shown that all KPS satellites are observed below 24° N. Finally, there is no significant change in the visible satellite number by varying the eccentricity to 0.1, as shown in Fig. 5d. The change of elevation angles of EIGSO were calculated during 24 hours at Seoul (37° N 127° E) and Jeju (33° N 127° E) with 30 seconds as a one epoch and depicted in Figs. 6 and 7, respectively. In Figs. 6, and 7, the only case with elevation angles of 0 or higher in Seoul is when an inclination is 43°, however, in Jeju, so is the case when the inclination is 45°. The fact clearly shows that the inclination of EIGSO should always be less than 45° for all satellites to be observed at all times in domestic monitoring stations including Jeju.

Fig. 5. The number of visible satellite contours for EIGSO simulation.

Fig. 6. EIGSO elevation angle and visible time at Seoul.

Fig. 7. EIGSO elevation angle and visible time at Jeju.

Table 3 summarized maximum HDOP and satellite visible time. From the simulation results we can conclude that the inclination parameter of EIGSO is suitable with the value of 45° in order to satisfy the navigation performance of HDOP and the conditions that can be tracked at all times in the domestic monitoring stations.

3.3 GEO Simulation

In order to guarantee the visibility of GEO in the urban and mountainous areas of Korea, the reference longitude positions of GEO satellite were set by 88°, 128° and 168° E, as discussed in Chapter 2. We note that the elevation angles of all GEO satellites are above 30° in Jeju at these longitudinal points.

The satellites were labeled starting from the reference satellite placed in the center (128° E), to the ones located in 88° E, 168° E as GEO1, GEO2, and GEO3, respectively, as shown Fig. 3. We note that the proper satellite orbits may not be allocated to the GEO satellites due to the orbit slot saturation (Gomez & Cordoba 2013, Space legal issues 2019). To cope with this situation each GEO satellite is moved from side to side by 4° in longitude, and the changes of HDOP and satellite elevation angle are analyzed as well. Finally, the optimal conditions were deduced which satisfies the KPS performance requirements.

Figs. 8-10 shows the HDOP values over the KPS coverage with respect to the longitudes of GEO satellites with the EIGSO inclination value of 45°, as discussed in the Section 3.2. GEO1, located in the center of the GEO satellites layout, exhibit only small changes in the HDOP of KPS with respect to the longitudinal changes. However, we found that the HDOP value decreases as the distance between GEO1 and other satellites increases. Similarly, the value increases when the distance decreases between the reference satellite and the others. This is a straightforward result reminding the definition of DOP, which is a measure that indicates the effect of geometric arrangements of the satellite on position errors. Nevertheless, the result emphasizes that it is difficult to achieve the navigation performance of HDOP value of 2.5 or less, specified by KPS, when the longitude interval between the GEO satellites is less than 40°

Fig. 8. GEO1 simulation (left: 124 deg, right: 132 deg).

Fig. 9. GEO2 simulation (left: 164 deg, right: 172 deg).

Fig. 10. GEO3 simulation (left: 84 deg, right: 92 deg).

Fig. 11 shows the change in the elevation angle according to central longitude of GEO satellites in Seoul area. It indicates that the elevation angle in Seoul increases when the longitude of GEO1 deviates westward from 128° E. This indicates that the central longitude can be moved to 124° E to achieve the better navigation performances. In case of GEO2 and GEO3, the satellite elevation angle in Seoul is reduced by about 1.5° when the satellite is 2° away in longitude from GEO1. Considering the geographical characteristics of the Korean Peninsula with many mountainous areas and the importance of navigation performances in the urbans, we conclude that the visibility of the satellite is considered to be “stable” when the GEO satellite in Seoul possess the elevation angle values of over 30°. We summarized the GEO satellite analysis results as Table 4.

Fig. 11. GEO satellite elevation angle at Seoul

Table 4. GEO satellites analysis results.

	GEO1		GEO2		GEO3
Central latitude (° E) HDOP at Seoul (deg) Elevation angle at Seoul (deg)	124 2.4 46.93	132 2.4 46.55	164 2.55 31.3	172 2.3 25.5	84 2.3 34.4	92 2.55 28.9

 

4. CONCLUSIONS

In this paper it was proposed the satellite orbit parameters that satisfies the KPS navigation specification requirements. Two major requirements which affects satellite orbit design for KPS were explained. In order to find the adequate orbit parameters, the HDOP and the elevation angles over the KPS coverage were analyzed with respect to many cases of EIGSO and GEO parameters.

When EIGSO inclination is at 45° with other reference parameters, HDOP and visible satellite requirements are satisfied. In GEO simulation, it is confirmed that the HDOP enhances as the GEO intervals widens, however, there is a trade-off with the low visibility. We expect that we can suggest the optimal GEO latitudes based on our results even in the case of the failure of the reference longitude allocation when in the fully occupied orbits situations for the KPS satellites.

AUTHOR CONTRIBUTIONS

Conceptualization, M. B. Heo and S. Chun; methodology, D. W. Lim.; software, M. Shin; writing—review and editing, M. Shin and D. W. Lim; visualization, M. Shin.

CONFLICTS OF INTEREST

The authors declare no conflict of interest.