National Conference on Information Technology and Computer Science (CITCS 2012) Constellation Design of The Beidou Satellite Navigation System and Performance Simulation Wang Xiaomeng Liu Ruihua Civil Aviation University of China Civil Aviation University of China School of Electronic and Information Engineering School of Electronic and Information Engineering Tianjin, 13752416223 Tianjin, 13034362088 [email protected] [email protected] Abstract—To improve the positioning accuracy and reliability of equator, the orbit is a circular orbit in the geocentric inertial Beidou ,an analysis of the Beidou satellite navigation system has coordinate system. been performed; combination of technical experience of the foreign global satellite navigation system and the current release (2)Medium earth orbit (MEO) of technical information, we have designed Beidou satellite Height parameters of the satellite is generally 10,000 to navigation system constellation, by satellite visibility analysis and 25,000 km, a maximum length of time that the satellite a variety of DOP's numerical comparison of the different design appears in the ground plane is for a few hours. The application options, we can prove the Beidou second-generation constellation of this track to establish a global communications satellite program can meet the needs of the global satellite location, system only needs 2-3 orbital planes to complete the global especially in China and its surrounding areas, the designed coverage. Beidou second-generation satellite navigation system have more precise positioning compared to other global navigaiton system. (3) Inclined geosynchronous orbit (IGSO) The return period is one sidereal day (1436.1 minutes). The Keywords- Beidou satellite navigation system; satellite center located at a set of longitude on the equator , the altitude constellation design; the DOP value; simulation is same as geostationary satellites, IGSO is also an efficient regional constellation between GEO and MEO. I. INTRODUCTION (4) Huge elliptical orbit (HEO) Beidou satellite navigation system is a new all-day-lasting This is a large eccentricity orbit with its apogee over the and regional satellite navigation positioning system, which is high latitudes of the northern hemisphere, their nadir trajectory developed by China own, provides fast positioning to users moves slowly, it can maintain the effective running of 10 and novel short digital message communications and timing hours for 5 days. The altitude of this kind of satellites change services. Now the space segment of Beidou satellite navigation obviously, it is very detrimental for the design of the channel. system which China is building consists of five geostationary satellites and 30 non-geostationary satellites ,it will provide two services: open service and authorization service. China B. Geometric Errors plans to cover the Asia-Pacific region by "Beidou" system in Constellation positioning (Dilution Of Precision, DOP) is about 2012, and to cover global coverage in about 2020. China an important factor to influence the positioning accuracy, it’s is implementing the construction of the Beidou satellite also an important indicator to measure the merits of a navigation system, has successfully launched 13 Beidou navigation satellite constellation. navigation satellites. There is no doubt that the Beidou system Set pseudorange equation (1). will play a major role in the military and civilian region. The 222 (1) article mainly plan constellation of the 35 satellites for the ii()()()xx yy iiu zz Ct Beidou system to ensure optimal positioning. refers user receiver position, refers the xyz,, xyziii,, position of the satellite i, refers the pseudorange II. BEIDOU CONSTELLATION DESIGN i measurements from the user to the satellite, C refers radio A. Satellite Orbital Theory Introduction wave propagation speed, tu refers the clock interval between Considering the period of earth autobiography movement the user receiver clock and Beidou system clock. So is 24 hours, the following four kinds of tracks are commonly used in the navigation satellite: 1111 (2) xyz x (1)The geostationary orbit (GEO) 1 2221 y 2 xyz H ΔX The satellite orbital plane coincides with the equatorial z plane, running a period of 24 hours, stationary above the Ct u i iii1 xyz Funded projects: basic scientific research and operational requirements of the Central Universities Civil Aviation University of China ZXH2010B004 504 © 2012. The authors - Published by Atlantis Press When i 4 higher positioning accuracy; otherwise lower. So it is 1 essentially an error amplification factor. ΔX=H Δρ (3) When i 4 ,we can get the least squares 2) GDOP is only related to the relative geometric layout TT1 between the user location and the positioning satellite, ΔX=(HH) H Δρ (4) regardless of the chosen coordinate system. TT1 ddX=(HH) H ρ (5) There are other DOP parameters for the characterization of We can get (6) based on the definition of covariance the position / time solution components which commonly used, cov(dEddXXX ) [T ] for the position dilution of precision (PDOP), the horizontal dilution of precision (HDOP), the vertical dilution of precision TTTT11 Edd[](H H) H ρρH(H H) (VDOP) and the time dilution of precision (TDOP), each TT11 T component of (HT H)1 is used to represent as (H H) H cov(dρ )H(H H) (6) Generally speaking, the distribution of dρ ’s each PDOP D11 D 22 D 33 component assumed identical and mutually independent, its HDOP D D (12) variance is equal to the satellite pseudoranges squared error 11 22 VDOP D33 factor UERE . Then TDOP D44 cov(dρ ) I 2 nn UERE (7) C. Beidou Constellation Design Put (7) into equation (6), available At present, the world's major satellite navigation systems T 12 cov(dX(HH) ) UERE (8) use the Walker Constellation layout. Walker Constellation Under these assumptions, the error covariance between the consists of a group of circular orbit satellites, which run on the calculated position and the actual deviation is exactly the same orbital period and inclination, denoted by the Walker scalar product of the matrix (HT H)1 . The component of T/P/F. The satellites of each track are distributed evenly. The longitude of ascending node spacing between the raceway matrix T 1 quantitative refered that how to transform (H H) surfaces is also equally distribution,so T (number of satellites) pseudorange error into every component of dX ’s covariance . = s (the satellite number of he same orbital plane) × P (the Based on definition, the accuracy factor DOP parameters is number of orbital plane). The relative phase of satellite obtained the division between sum of components of between two adjacent tracks is determined by the phase parameter F, F is the number of "gap" (360 ° / T) between the cov(dX ) and . The most general parameter called the UERE most eastern satellite orbit and the most Western satellite orbit, GDOP (Geometrical Dilution Of Precision) it means that F is an integer from 0 to P-1. 2222 Satellite navigation need multiple coverage, more GDOP xuuuyzCt b (9) simultaneous visual satellites are needed in navigation UERE application, for the selection of RNSS System constellation, The GDOP relationship is given with a component in the form we need to refer to foreign satellite navigation systems, the of (HT H)1 ,this component form most widely used three foreign satellite navigation systems, are the U.S. Global Positioning System, GPS, and the former D11DDD 12 13 14 Soviet Union / Russian global navigation satellite system DDDD21 22 23 24 (10) GLONASS and the EU's Galileo satellite navigation system (HT H)1 GALILEO which is in building, according to data published DDDD31 32 33 34 by the three satellite navigation system, as well as long-term DDDD 41 42 43 44 practice, available[2~4], GDOP can be calculated out as the square root of the matrix T 1 1) satellite constellation whose height less than 2000km is trace (H H) inappropriate. The analysis showed that the number of GDOP D11 D 22 D 33 D 44 (11) satellites in 2000km highly Walker Constellation is four times GDOP is the geometric factor, which represents the than 20000km highly walker constellation, which will make amount of amplification from the standard deviation of the the system costs and maintenance costs soared. measurement error to the solution. By the formula (11) we can 2) In order to achieve the higher-level performance get that GDOP is merely a function of the geometric layout of indicators, we need at least 24 satellites. The satellite altitude the satellite / user. performance indicators is weakened with the increasing It can be concluded the following characteristics of GDOP: number of satellites. When the global constellation satellite number is greater than or equal to 27, we don’t need to 1) GDOP is the geometric magnification factor from consider the the satellite height’s contribution for the accuracy. measurement errors to position solver error. In the same observation precision , the smaller of GDOP value, the 3) In order to further improve the availability, we should UERE increase the number of in-orbit backup satellite instead of constellation modification. 505 According to information currently published [2~4] ,the The above two simulation pictures are from the sky plan IGSO satellite can make full use of the advantages of GEO, as view, the outermost circle is horizon 0°, and then inside one well as overcoming the weakness that its high latitude regions circle, increasing 15°. Numbers in Figure 1 refer to the are always low elevation. IGSO has the same orbital altitude satellite sequence number, the red line indicates the trajectory with GEO, its orbital inclination is greater than 0°.therefore it of the satellite, it can be clearly seen that the number of stars, has the same orbital period as the Earth's rotation cycle, but its and its trajectory become weak with increasing height of the nadir trajectory on the ground in the equatorial symmetry axis coverage angle, that is satellite visibility becomes worse with "8"-shaped, the larger orbit inclination, the greater "8"-shaped the height coverage angle increasing.