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15КОНТРОЛЬ И МОНИТОРИНГ ОПАСНОСТЕЙ HARARD MANAGEMENT AND MONITORING
Original article / Оригинальная статья УДК 574:631.4:631.504
DOI: http://dx.d0i.0rg/l0.21285/1814-3520-2018-3-44-68
ALGORITHM OF REAL TIME KINEMATIC USING BEIDOI REGIONAL SYSTEM AND THE REASULTS ANALYSIS
© Zhu Huizhong1, Xu Aigong2, Anatoliy L. Okhotin3, Xu Xinchao4, Gao Meng5
U4,5School of Geomatics, Liaoning Technical University, Fuxin city, Liaoning Province, 123000, People's Republic of China 3Irkutsk National Research Technical University, 83, Lermontov St., Irkutsk, 664074, Russian Federation
The BeiDou-navigation satellite system of China completed the regional navigation constellation in December 2012. So this regional system can provide independent positioning capability for the Asian-Pacific region. And the algorithm of real time kinematic (RTK) using BeiDou regional system can achieve high precision real-time dynamic positioning. The algorithm of RTK using BeiDou regional system is studied in this paper. The indifference error corrections on reference station of BeiDou regional system are calculated, and the centimeter level positioning accuracy of RTK can be realized by using these error corrections to remove the errors of rovers. If there are medium or long baselines between stations of BeiDou system RTK, the wide lane integer ambiguity of the rover will be fixed firstly and then the narrow lane integer ambiguity can be calculated by the ionosphere free combination observation, and the ionosphere free combination observation is used to realize RTK positioning. If there are short baselines between stations of BeiDou system RTK, the carrier phase observations and pseudo range observations of rover are used to fix ambiguity and realize RTK positioning. The test of RTK positioning is carried out by using data of BeiDou regional system. These results indicate that the quality of observation data and the distribution of satellite constellation of BeiDou regional system can meet the need of RTK positioning using the regional system, and the centimeter level accuracy of the rover can be got by real-time dynamic positioning using BeiDou regional system. The horizontal accuracy of the rover positioning result of BeiDou regional system RTK precedes the zenith accuracy, the accuracy of the east direction is better than the north direction. At the same time the GPS RTK positioning results can be got, because of the dual system receiver is used in the test of this paper. So the RTK positioning results of BeiDou regional system are compared with GPS. The bias between the RTK results of these two systems is at centimeter level, the bias between these two systems on east direction is less than the other two directions and the bias on zenith direction is greater than horizontal direction. The research of this paper indicates that BeiDou regional system can provide high-precision RTK positioning services for the users in China, and the results of BeiDou RTK positioning equivalent for the GPS (global positioning system) RTK. Keywords: BeiDou Regional System, RTK, Integer Ambiguity, Ionosphere Free Combination
Information about the article. Received July 20, 2018; accepted for publication August 22, 2018; available online September 28, 2018.
1
Zhu Huizhong, Associate Professor, e-mail: [email protected] Чжу Хэйчжун, доцент, email: [email protected]
2Xu Aigong, Professor, e-mail: [email protected] Сю Айгун, профессор, e-mail: [email protected]
3Anatoliy L. Okhotin, Doctor of Technical Sciences, Professor, Head of Department of Mine Surveying and Geodesy, e-mail: [email protected]
Охотин Анатолий Леонтьевич, доктор технических наук, профессор, заведующий кафедрой маркшейдерского
дела и геодезии, e-mail: [email protected]
4Xu Xinchao, Associate Professor, e-mail: [email protected]
Сю Синьчао, доцент, e-mail: [email protected]
5Gao Meng, Lecturer, e-mail: [email protected]
Гао Менг, преподаватель, e-mail: [email protected]
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For citation. Huizhong Zhu, Aigong Xu, Okhotin A.L., Xinchao Xu, Meng Gao. Algorithm of real time kinematic using BeiDou regional system and the results analysis. XXI vek. Tekhnosfernaya bezopasnost' = XXI century. Technosphere Safety, 2018, vol. 3, no. 3, pp. 44-68. DOI: 10.21285/1814-3520-2018-3-44-68. (In English)
АЛГОРИТМ КИНЕМАТИКИ РЕАЛЬНОГО ВРЕМЕНИ С ИСПОЛЬЗОВАНИЕМ РЕГИОНАЛЬНОЙ НАВИГАЦИОННОЙ СИСТЕМЫ БЭЙДОУ И РЕЗУЛЬТАТЫ АНАЛИЗА
Чу Хэйчжун, Сюй Айгун, А.Л. Охотин, Сюй Синьчао, Гао Менг
Ляонинский инженерно-технический университет, Институт горного дела, 123000, Китайская Народная Республика, провинция Ляонин, г. Фусинь. Иркутский национальный исследовательский технический университет, 664074, Российская Федерация, г. Иркутск, ул. Лермонтова, 83.
Китайская навигационная система Бэйдоу завершила цикл создания регионального навигационного комплекса в декабре 2012 г. Региональная система может обеспечить реализацию функции независимого определения местоположения для всего Азиатско-Тихоокеанского региона. Алгоритм кинематики реального времени (RTK) с использованием региональной системы Бэйдоу может повысить точность определения месторасположения в реальном времени. В данной статье анализируется алгоритм кинематики реального времени (RTK) с использованием региональной навигационной системы Бэйдоу. Корректировка ошибок осуществляется на основе данных системы Бэйдоу. Точность местоположения достигается за счет использования этих корректировок. Если между станциями системы Бэйдоу находятся системы с большой базой, фиксируется широкая целочисленная неопределенность ровера. Затем рассчитывается узкая целочисленная неопределенность путем произвольного наблюдения за ионосферой. Если между станциями находятся короткобазисные системы, осуществляется фазовое или псевдодиапазонное наблюдение за ровером для установления неопределенности и позиционирования RTK. Проверка позиционирования RTK осуществляется с помощью данных системы Бэйдоу. Результаты показывают, что качество данных и распределение группы спутников системы Бэйдоу отвечает потребностям позиционирования RTK. Точность измерения уровня ровера может быть достигнута в результате использования региональной системы Бэйдоу. Горизонтальная точность результатов позиционирования ровера с использованием региональной системы Бэйдоу хуже точности по зениту. Точность в восточном направлении выше, чем в северном. Результаты позиционирования RTK с использованием региональной системы Бэйдоу сравнимы с результатами, получаемыми с использованием системы GPS. Разница между двумя системами минимальная. В восточном направлении разница меньше, чем в двух других направлениях, а в направлении зенита - больше, чем в горизонтальном направлении. Исследование показывает, что региональная навигационная система Бэйдоу обеспечивает точное определение положения RTK для пользователей из Китая, а ее результаты сопоставимы с результатами использования системы GPS.
Ключевые слова: региональная система Бэйдоу, кинематика реального времени (RTK), двойственность целого числа, ионосферная свободная комбинация.
Информация о статье. Дата поступления 20 июля 2018 г.; дата принятия к печати 22 августа 2018 г.; дата он-лайн-размещения 25 сентября 2018 г.
Формат цитирования. Чу Хэйчжун, Сюй Айгун, А.Л. Охотин, Сюй Синьчао, Гао Менг. Алгоритм кинематики реального времени с использованием региональной системы Бэйдоу и результаты анализа // XXI век. Техносферная безопасность. 2018. Т. 3. № 3. С. 44-68. DOI: 10.21285/1814-3520-2018-3-44-68
Introduction
Global Navigation Satellite Systems is the significant means to get the information of position and time. Since 1985 China has been working on the theoretical research and technical test its own navigation satellite system. According to the development and actual situ-
ation of national economic, this system is planned to be established in three steps or phases: demonstrational system, regional system and global system. The system is named as BeiDou, the BeiDou Navigation Satellite System is abbreviated to BDS (BeiDou). On
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December 27, 2012, the official signal-inspace Interface Control Documents (ICD) for BDS Open Services was released. The regional system is officially announced to provide positioning and navigation and timing services over the Asia-pacific region. The second phase of the construction plan of China BeiDou satellite navigation system is accomplished. The constellation of BeiDou regional system includes five Geostationary Earth Orbit (GEO) satellites, five Inclined Geosynchronous Earth Orbit (IGSO) satellites and four Median Earth Orbit (MEO) satellites.
After BeiDou regional navigation satellite system can provide positioning and navigation services over the Asia-pacific region independently, due to the similar signal structure and analogous frequencies of BDS with respect to that of the American GPS and the European Galileo system, BDS-capable multi-GNSS (Global Navigation Satellite Systems) software and hardware receivers were already developed by US and European scientists and manufacturers even before its ICD was publicly disclosed. This enables a number of investigations which have been carried out since the first experimental satellite M1(C30) launched on April 13, 2007. Shortly after the launch of M1 satellite, its PRN code sequence is decoded with directive antennas (Greilier et al. 2007, Gao et al. 2009) and the signals are investigated with software and hardware receivers (De Wilde et al. 2007). A great deal of research has been conducted by the scholars in China to test the signal, satellite clock, frequency and the capability of positioning and navigation by BDS data.
The BeiDou regional system can pro-
vide standard positioning service with accuracy of 10m and velocity measurement with accuracy of 0.2m/s and timing with accuracy 20ns. Though the capability of BeiDou regional system is inferior to GPS using a new generation of satellites, it is equivalent to early GPS. So, the BeiDou regional system can meet the demand of high precision navigation and positioning. Gao et al (2012) researched the algorithm of high precision positioning using BeiDou regional system and GPS. And the high precision relative positioning and data integration using BeiDou regional system and GPS observation is achieved. Shi et al (2012) studied the algorithm of high precision relative positioning only using GEO and IGSO satellites of BeiDou regional system. The data of a week is processed, and the ambiguity resolution and results of relative positioning using GEO and IGSO satellites are analysed. These researches also indicate that BeiDou regional system can meet the demand of high precision positioning. Because the BeiDou regional system can formally provide positioning service not long ago. The articles and studies of high precision positioning of BeiDou System are few, especially the researches of the methods of real-time dynamic positioning using BeiDou system. The positioning of BeiDou regional system is affected by observational errors, so the accuracy of the real-time kinematic positioning is reduced. The accuracy of the realtime kinematic positioning can be enhanced by using differential positioning mode, this method is one of the most important means to realize high precision real time dynamic positioning using BeiDou system.
Introduction of BeiDou Navigation Satellite System
Since more than one decade ago China has been working on its own navigation satellite system for the urgent requirement of national defense and its rapid developing economics. The system is named as BeiDou, the
BeiDou Navigation Satellite System is abbreviated to BDS. The system is planned to be established in three steps or phases: demon-strational system, regional system and global system. Now the regional system phase is just
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completed. On December 27, 2012, the regional system is officially announced to provide positioning services over the Asia-pacific region with a constellation of five Geostationary Earth Orbit (GEO) satellites, five Inclined Geosynchronous Earth Orbit (IGSO) satellites and four Median Earth Orbit (MEO) satellites. At the same time, the official signal-in-space Interface Control Documents (ICD) for BDS Open Services was released. Upon the full system completion, BDS can provide positioning, navigation and timing services to worldwide users. With its system-embedded wide area differential services with the accuracy of 1 m and short messages services with the capacity of 120 Chinese characters each time, BDS will play a very important role in satellite navigation industry, and contribute to human civilization and social development along with the other GNSS systems.
The demonstration system, also referred as to BeiDou-1 or Two-Satellite system, was designed to provide active positioning service with two GEO satellites for the Chinese territory and its neighborhood. Under the user's request, the distance between the user terminal and the two satellites are measured and then the position is calculated using the two ranges with the help of a digital terrestrial model of reasonable accuracy.
With the success of the BDS demon-strational system and the rapid development of the Chinese economy and the urgent requirements of the precise positioning and navigation from both civilian and military users, the Beidou-2 system was designed around 2004 as a passive and global satellite navigation system with special concern in China and its surroundings. To meet the urgent requirement of the regional users, the development is scheduled into two steps: first a regional passive system to provide service for China and its neighborhood around 2012, and then the system will be developed continuously and to provide global positive service by 2020.
In Phase II, BDS regional system is planned to be completed and to provide op-
erational services by 2012(December 27, 2012). The functions and performance parameters of BDS regional system are as follows:
• Main functions: positioning, velocity measurement, one-way and two-way timing, short message communications
• Service Area: China and part of Asia-Pacific region
• Positioning Accuracy: better than 10 meters
• Velocity Accuracy: better than
0.2 m/s
• Timing Accuracy: 50 ns
• Short message communications: 120 Chinese characters per message
The constellation of the regional system are planned to consist of five GEO and five IGSO and four MEO satellites. And the space constellation of the regional system is showed as Figure 1. Utilization of GEO and IGSO satellites is a special feature of BDS in order to provide regional service at the very beginning and enhance it after the system is fully in operation. As is well known, the ground track of an IGSO satellite looks like figure "8". The tracks of the three IGSO satellites are coincided with a phase difference of 120° and the longitude of the intersection point is at 118°E. For the regional system, there are two more IGSO satellites with an intersection point at about 95°E.
Each satellite carries about four atomic clocks and all satellites transmit triple-frequency navigation signals. The B1 band is close to the GPS L1 frequency of 1575.42 MHz and the B3 band close to the Galileo E6 with 1278.52 MHz. The B2 frequency of 1207.14Mhz is identical with Galileo E5b. The range code and navigation messages are modulated on carriers. In the recently published ICD for open service signal, the B1 frequency signal is introduced in details. The navigation message structure and calculation of satellite position from BDS broadcast ephemeris are well documented.
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Figure 1. The space constellation of the regional system (Yang et. al.)
Ground control segment consists of several Master Control Stations (MCS), Upload Stations and a network of globally distributed Monitor Stations. The Monitor Stations tracking the satellites continuously and the measurements are sent to the MCS for the precise orbit determination and clock estimation. At MCS, data from all Monitor Stations are collected and processed to generate satellite navigation messages, wide area differential corrections and integrity information. Mission planning and scheduling, system operation and control are also conducted here. All the information generated at the MCS and satellite control commands are sent to satellites via the Upload Stations.
User terminals include various BDS user receivers which are compatible with other navigation satellite systems, and meet requirements of different applications.
According to the currently developing of GNSS navigation and positioning technolo-
gy, it is urgent to study the algorithm of high precision real-time positioning using BDS regional system. The method of RTK is a very significant means of high precision real-time dynamic positioning using BDS regional system. The observation errors on rover such as atmospheric delay errors and satellite orbit error can be removed or weakened with the method of BDS RTK using observations on reference station through the same satellite orbit and clock in broadcast ephemeris. Because BDS and GPS have the similar signal structure and analogous frequencies, the observation model and satellite orbit model of GPS can be used to research the algorithm of BDS positioning by changing. The real-time dynamic observations of BDS are processed by referencing the similar observation model and dynamic positioning model of GPS, at the same time considering its own characteristics of BDS, so the RTK positioning of BDS regional system can be achieved.
The mathematical models of BDS positioning
The double frequency observations of B1 and B2 with BDS are easily obtained. So
the double frequency observations are used to realize RTK positioning of BDS. The double
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frequency observations of B1 and B2 include pseudo range and carrier phase. The signal structure and analogous frequencies of BDS are similar to that of the American GPS sys-
tem, the indifference observation equations of pseudo range and carrier phase of double frequency B1 and B2 can be respectively written as:
P =p + c■ (t, -ts) + o +11 + T + mP1 + s'P1 (1)
P2 =p + c ■(tr - ts ) + o +12 + T + mP2 + s'p2 (2)
^■Ф1 =p + c\tr - ts )-4-N1 + o - Il + T + mфl + £ф! (3)
Л ^ =p + c\tr - ts )-Ä2 ■ N2 + o -12 + T + mф 2 + s^2 (4)
Where P and O are the BDS code and carrier phase observations respectively; p is the geometric distance of satellite to receiver; o denotes the error of satellite orbit; tr and ts are clock errors of satellite and receiver respectively. i and i2 are the ionosphere
delay errors on the carriers of B1 and B2 respectively; T is the troposphere delay; m is the multipath effect of each observations; s is the noise of observations and the errors of modeling; n denotes ambiguity of carrier phase observations; A = c / B and B are wavelength of carrier phase and frequency respectively; c = 2.99792458x 108m / 5 is the beam in vacuum, and the subscripts denote the frequency of the carrier. The double frequency observations of B1 and B2 with BDS are 1561.098 MHz and 1207.140MHz respectively; The clock errors of tr and ts are expressed in seconds, the ambiguity and carrier phase observations in cycles, The remaining items in meters.
Every navigation satellite system has its own time reference and coordinate reference system. Therefore, the mathematical models of BDS positioning use BDS time reference and coordinate reference system. According to the BDS ICD, the time reference for BDS is the BeiDou Navigation Satellite System Time (BDT), which is a continuous time-
keeping system. The length of second of BDT is the international system of units (SI) seconds. The start epoch of BDS week is at 00:00 UTC on Jan. 1st2006. BDT is synchronized with UTC in 100 nanoseconds (modulo one second).
The BDS coordinate reference system is defined as: the origin is located at the mass center of the Earth; its Z-axis is in the direction of the IERS (International Earth Rotation and Reference System Service) Reference Pole; X-axis is directed to the intersection of IERS Reference Meridian and the plane passing the origin and normal to the Z-axis; Y-axis together with Z-axis and X-axis constitutes a right handed orthogonal coordinate system.
The reference system is realized through the China Geodetic Coordinate System 2000 (CGCS2000). Since 1980s, new satellite geodetic techniques such as GPS have been widely used in China for positioning and other applications, the coordinate systems based on traditional technologies cannot meet the necessity of the new techniques. In 2003, the GPS control network 2000(GPS2000) was established after the combination of various GPS networks in China. Afterwards, the combined adjustment between astro-geodetic networks and GPS2000 was carried out. In July 2008, CGCS2000 was officially adopted as the new national geodetic reference system.
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The mathematical models of BDS RTK
The errors in expressions (1)-(4) can influence the positioning using BDS observations. The observation errors of BDS users can be removed by using observations of reference station. The multipath effect on reference station can be ignored normally, because the reference station is usually located at the
OMC^ = pRR =-( c-(tR
location which is open. Taking the carrier phase observation on frequency B1 as an example, because the coordinates of reference station are known, the OMC (Observation Minus Calculation) of carrier phase observation on frequency B1 is shown as:
-ts+ oR -IR + TR + еф) (5)
OMC,/ = Л ■ Ф - pR = с • (tR - ts ) - Л ■ NR + o: - IR + TR + еф
Where the superscript R denotes reference station; The errors of satellite orbit, ionosphere delay and troposphere delay have the characteristic of regional correlation, and are similar to these errors on the rover; The
error of satellite clock t is equivalent to the
rover. So, the observation equation of carrier phase on frequency B1 can be shown as:
Л + OMC,1 =PU + H• SX + с• (tU -ts)-\^NU + oU -IU + TU + еф + OMCU1 (6)
Л - OMCm =PU + H SX + с • (tUr - ts )- Л • NU + oU - IU + TU + e'U - OMC
Where the superscript U denote the rover; p0 is the approximate geometric distance of BDS satellite to the rover; H is the matrix of coefficients; 5X denotes the correction of coordinates. Because the errors of satellite orbit, ionosphere delay and troposphere
delay in the same area have the characteristic of regional correlation. So these errors of reference station are similar to rover, and the error of satellite clock ts is equivalent to rover, there are:
Л-ФЦ7 + OMC,1 =pU + H • SX + с (tU - tR )- Л • (NU - NR ) + eф1 -еф1 + S ; (7)
Л-ФЦ7 - OMC,1 =PU + H • SX + с^ (tU - tR )-Л-( NU - NR ) + еф1 -еф1 + S.
Where the influences of satellite orbit, ionosphere delay and troposphere delay are weakened exceedingly; 5 is residual error, and the observation noise of carrier phase can be ignored. In order to remove the clock error
of receiver (tUr - tR), the observation equations between satellites are subtracted, there are:
(8)
лф^ =лpu / л+Ля • SX / Л -(Щи -ÁNR )+лs / Л - лoмcф, / Л
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лфu =apu i л+ah ■ Sx i л -( ANU -ANR )+as i л+aomq! i л.
Where A denotes single difference between satellites; because the residual error AS is very small, it can be ignored; at the
same time the ambiguity (ANf -ANf) is integer. Analogously, the observation equations
of carrier phase on B1 frequency and double frequency observations of pseudo range can be got. And the ambiguity of carrier phase on B1 frequency also is integer, these are shown as expressions (9)~(11):
лфu =apu i л +лн ■ sxi л - (an2u - anr )+ asi л - aomcф21 л
ЛФu = Apu i л+ЛН ■ SX i л-(anU -ANR )+лsi л+aomc2 i л ;
APU2 = ApU -AH■ SX + AS-AOMCn. (1Q)
APU2 = ApU -AH■ SX+ AS+AOMCn ;
APU =ApU-AH ■ SX + AS-AOMCP2 ; (11)
APU = ApU -AH■ SX + AS + AOMCP2.
The observation equations after error correction of carrier phase of wide lane and narrow lane can be formed by the observation equations of carrier phase on frequencies B1 and B2 as expressions (8), (9). And the ambiguities of carrier phase of wide lane and narrow are integer. Then the carrier phase integer ambiguity of rover can be fixed, and the position of rover is calculated.
The errors of satellite orbit, ionosphere delay, troposphere delay and so on are removed by mW combinations. And the observation noise in which the observation noise of pseudo range is the main influences the ambiguity fixing. The wide lane ambiguity can be
The location parameters can be removed in ambiguity fixing by MW combinations which is used to fix ambiguity by single one. So the geometric model of positioning has no influence on ambiguity fixing by MW combinations. The MW combinations are used to calculate wide lane ambiguity as expressions (12), (13):
(12)
(13)
calculated and fixed by observations of a number of epochs. In some cases, the wide lane ambiguity calculating and fixing of GEO satellite is inefficient and unreliable by MW combinations, because the observation noise of pseudo range is lager. Therefore, the geo-
c- (лф2 -лф2 ) (aaf + b2apu )
amw = ■ ' v '
( r - b2 ) ( b + b2 )
(R -B) ■aMW
aN -^-
c
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metric model is also used to fix the BDS ambiguity of rover. The set of observation equa-
tions which is used to fix wide lane ambiguities is written as expression (14):
Л -лф, -p 1+лoмc
-ф,
Л, -au, -ApU +NOMC
-ф,
лн 1
АН'
Sx
Sy
ôz
AN,
w
an:
w ,
Ae1
As'
(14)
Where, OMC is the OMC of wide lane observation which is composed by OMC of carrier phase observations on frequencies B1 and B2; AH denotes the correction of three coordinate directions; As is residual error; the superscripts 1 denote satellite number. The set of observation equations is solved by observations of a number of epochs. And the float solution and covariance matrix of ambiguities can be got, then the ambiguities are searched and fixed by the method of LAMBDA. When the parameters are estimating in kinematic positioning, the loose constraint is a distance limit between the location parameters of the two epochs. The geometrical configuration of BDS satellites which are observed by rovers is changing slowly in realtime kinematic positioning. Because the GEO satellites is relative rest to the earth and the period of motion of IGSO satellite is approximately 24 hours. It is a disadvantage to realtime dynamic fix ambiguity and calculate positional parameters. This is the characteristic of
BDS ambiguity fixing of RTK positioning relative to GPS system. So, the method of BDS ambiguity real-time fixing needs further research in order to enhance the accuracy and efficiency of ambiguity real time dynamic fixing.
After the wide lane integer ambiguity of rover is fixed, if the range of rover between reference station is long (such as more than 10 kilometers), the narrow lane integer ambiguity can be calculated by the ionosphere free combination observation equation. Then the ionosphere free combination observation is used to calculate positional parameters of rover, and the fixed wide lane and narrow lane integer ambiguities are combined into the ionosphere free combination observation equation. If the range of rover between reference station is short, the errors of carrier phase observations can be removed well by using the OMC corrections directly. So the carrier phase observations without combination are used for positioning by rover.
The positioning results of test and solution analysis
The method of BDS RTK is fulfilled in PANDA software, and can be used by BDS users. The receivers which have function of data collecting of BDS and GPS are applied for the tests of BDS RTK. The tests include the RTK processing of BDS static data and dynamic data. The accuracy of BDS RTK positioning and the quality of pseudo range and
carrier phase observations can be reported by the results of RTK processing of BDS static data. And the satellite visibility is analyzed by the BDS static data. The capability of actual dynamic positioning of RTK can be checked by the test of BDS dynamic data.
The results and analysis of short and middle range of BDS RTK positioning.
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The CORS of double systems with BDS and GPS at School of Geomatics of Liaoning Technical University is used as reference station, which is shown as figure 2. This station uses the receiver type of UICORE 240CORS. The rover for short range is 4.9 kilometers from the reference station. The static observations are collecting about three and half hours in February 27, 2013. The other rover station is located at Dongliang town of Fuxin city of Liaoning province which is 17 kilometers from
the reference station. The sampling rate of this rover is 1 Hz, the static observation data are collecting two hours in January 22, 2013. The number of visible satellites of BeiDou regional system are shown as figure 3 and figure 4 for these two rovers respectively. The figure 3 shows that the minimum number of visible satellites is nine, and the minimum number of visible satellites in figure 4 is eight, the number of current BDS satellites can meet the need of BDS RTK positioning.
Figure 2. The CORS at School of Geomatics of Liaoning Technical University
285600 288000 290400 292800 295200 297600 Second of week
Figure 3. The number of visible satellites of short range
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20400 21600 22 BOO 24000 2S200 26400 Second of week
Figure 4. The number of visible satellites of middle range
The data of these two rovers are processed by the dynamic positioning method of BDS RTK in this paper. Firstly, the wide lane ambiguities of BDS carrier phase of B1 and B2 are fixed. For the rover of the short range, it consumes the observation time of 45 seconds for the first time of ambiguity fixing. And the ratio of optimal and suboptimal ambiguity combinations is 2.7. Then the ambiguities of carrier phase can be fixed, and the carrier phase observations are used to calculate positional parameters of this rover. For the rover of the middle range, it consumes 51 seconds for the first time of the wide lane ambiguity fixing. The ratio of optimal and suboptimal ambiguity combinations is 2.8. Then the narrow lane ambiguities can be calculated and the ambiguities of ionosphere free combination observation are formed by wide lane and narrow lane ambiguities. The carrier phase observations of ionosphere free combination are used to calculate positional parameters of rover, because the range between reference station and rover is larger than 10 kilometers. The PANDA and static observation data are used to calculate the BDS accurate coordinates of these two rovers. The RTK positioning results of these
two rovers are compared with the accurate coordinates on three coordinate directions on E(east),N(north),U(zenith). The deviations of E,N,U at each epoch are shown as figure 5 for short range and figure 6 for middle range.
The RMS of these deviations are 0.006m, 0.011m, 0.027m respectively on three coordinate directions of E, N, U in figure 5. The RMS of deviations are 0.009m, 0.021m, 0.051m respectively on three coordinate directions of E, N, U in figure 6. These results meet the accuracy demand of centimeter level of BDS RTK positioning. And the horizontal accuracy of rover positioning results precedes the U(zenith) accuracy, the accuracy of E(east) direction is better than N(north) direction.
The results and analysis of long range of BDS RTK positioning. The observation data of two stations in the area of North China are used for BDS RTK test. One of these stations is continually operating BDS station as reference station, the other one which is temporary static observation station of BDS is 50 kilometers far from the reference station. The observation data on November 7, 2013 and November 8, 2013 are processed by
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the BDS RTK in this paper respectively. The number of visible satellites of BeiDou regional system on stations is shown as figure 7 and figure 8. The visible times of each BDS satellite of reference station in the observation period are shown as figure 9 and figure 10.
The receivers on each station can only track the BDS satellites from NO C01 to NO C12 and can't observe the NO C13 and NO C14 on November 7, 2013 and November 8,
2013. The figure 7 and figure 8 show that the minimum number of visible satellites is eight and the maximum number of visible satellites is twelve. The number of BDS satellites can meet the need of realizing high precision positioning only using BDS. The BDS satellites from NO C01 to NO C05 are GEO satellites, so these satellites can be tracked by the user in 24 hours one day.
Figure 5. The deviations of positioning results of BDS RTK
Figure 6. The deviations of positioning results of BDS RTK
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Figure 7. The number of visible satellites (November 7)
Figure 8. The number of visible satellites (November 8)
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Figure 9. The visible times of each BDS satellite (November 7)
Figure 10. The visible times of each BDS satellite (November 8)
The temporary static observation station is conducted as rover station. Firstly, the observations of pseudo range of BDS B1 frequency are used for difference positioning at single epoch. Firstly, the results of pseudo range difference positioning at single epoch
positioning are compared with the known coordinates on three coordinate directions on E(east), N(north), U(zenith). The deviations of E, N, U at each epoch are shown as figure 11 and figure12.
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Figure 11. The deviations of pseudo range difference positioning (November 7)
Figure 12. The deviations of pseudo range difference positioning (November 8)
The figure 11 and figure 12 show that the deviations of results of pseudo range difference positioning at single epoch are compared with the accurate coordinates on three coordinate directions of E(east), N(north), U(zenith). And overwhelming majority of these deviations is less than 10 meters. And the horizontal deviations of positioning results are
less than 5 meters. The deviations of E(east) direction are less than 2 meters. The RMS of the deviations on three coordinate directions are shown as Table 1. This positioning accuracy of BDS pseudo range difference positioning can meet the demand of mapping with small scale and vehicle navigation and so on, and provide initial value for ambiguity resolu-
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tion of BDS RTK. The data of rover on November 7, 2013 and November 8, 2013 are processed by kinematic mode according to BDS RTK positioning in this paper respectively. The ambiguities of carrier phase observations on November 7, 2013 of rover are fixed for the first time by consuming observations with 30 minutes, and the ratio of optimal and suboptimal ambiguity combinations is 2.9. The observations with 11 minutes are consumed for the first time of ambiguities fixing and the ratio is 2.4. Then the positional parameters of rover are calculated at each epoch by the
fixed ambiguities. And the fixed ambiguities are dragged in observation equations of the front epochs, the positional parameters of rover are calculated by using the few minutes of the front observations. So the results of the BDS RTK positioning of each epoch in 24 hours can be got. The RTK positioning results are compared with the known coordinates on three coordinate directions on E(east), N(north), U(zenith). The deviations of E, N, U at each epoch are shown as figure 13 and figure 14.
Figure 13. The deviations of RTK positioning (November 7)
Figure 14. The deviations of RTK positioning (November 8)
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Figure 13 and figure 14 show that the deviations of results of BDS RTK positioning are most in the centimeter level on three coordinate directions of E,N,U. And overwhelming majority of the horizontal deviations are less than 5 centimeters. The RMS of the deviations on three coordinate directions are shown as Table 1, the requirements of positioning accuracy RTK in centimeter level can be fulfilled. And the horizontal accuracy of rover position-
ing results precedes the U accuracy, the accuracy of E direction is better than that of N direction. These results are got by RTK positioning using broadcast ephemeris. In order to research the influencing factors in RTK using BeiDou regional system, the precise ephemeris of BDS are used to process in this example. The deviations of RTK positioning on three coordinate directions are shown as figure 15 and figure 16.
Figure 15. The deviations of RTK positioning using precise ephemeris (November 7)
Figure 16. The deviations of RTK positioning using precise ephemeris (November 8)
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The figure 15 and figure 16 show that the overwhelming majority of the horizontal deviations of positioning results are less than 5 centimeters and the zenith deviations are less than 10 centimeters. The RMS of the deviations of results by using precise ephemeris on three coordinate directions are shown as Table. Table shows that the positioning accuracy on zenith of RTK positioning by using precise ephemeris is evidently better than the positioning accuracy by using broadcast ephemeris in this example. Because the range between reference station and rover is 50 kilometers, the error of satellite orbit of broadcast ephemeris is large and the precise
ephemeris are used to reduce the influence of satellite orbit. And taking the satellites of C05 and C09 as an example, the broadcast ephemeris of C05 and C09 comparing with precise ephemeris are show as figure 17 and 18. Most of the errors on X and Y directions of C05 are greater than 10m. The majority of the errors on X direction of C09 are also greater than 10m, and the errors on Y direction is in the meter level. So in order to guarantee the positioning accuracy, especially the positioning accuracy on zenith of RTK positioning by using BeiDou regional system, the range between reference station and rover should not be too long.
Figure 17. The broadcast ephemeris comparing with precise ephemeris of C05
Figure 18. The broadcast ephemeris comparing with precise ephemeris of C09
H
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The RMS of deviations of TK positioning
Observation Time Coordinate Direction The Results of Pseudo Range Difference The Results of RTK The Results of RTK by Using Precise Ephemeris
November 7 X 0.893 m 0.008 m 0.005 m
Y 1.786 m 0.022 m 0.014 m
Z 3.146 m 0.060 m 0.032 m
November 8 X 0.756 m 0.006 m 0.006 m
Y 1.952 m 0.018 m 0.014 m
Z 3.268 m 0.066 m 0.040 m
The tests of BDS RTK positioning by dynamic data. In order to check the capability of actual dynamic positioning of BDS RTK, the test of BDS dynamic data is employed. The CORS of BDS and GPS at School of Geomatics of Liaoning Technical University is used as reference station. The receiver type of South S86+C505 is used as rover at stadium of Liaoning Technical University (shows as figure 19) to test by kinematic positioning. The test 1: The experimenter is taking the receiver of South S86+C505 as rover and walking
along the field lines of the football field ground. This football field ground is from north to south and toward east. Firstly, the rover stops at the south east for static measurement in 105 seconds for initialization and the ratio is 2.8 of ambiguity fixing. The dynamic observations are processed by the method of BDS RTK in this paper, and the results of rover positioning are got. The map of football field ground is drawn by the results of BDS RTK and shown as figure 20.
Figure 19. The experimental site of kinematic positioning
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The figure 21 which is the map of football field ground is drawn by the results of GPS RTK. The two maps show that the shapes of football field ground with the BDS
RTK and GPS RTK match each other well. The figure 22 is the deviations on three coordinate directions of E(east),N(north),U(zenith) of BDS and GPS RTK at each measure point.
Figure 20. The map of the BDS RTK
Figure 21. The map of the GPS RTK
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Figure 22. The deviations of the BDS RTK comparing with GPS RTK
The figure 22 shows that there are system biases between BDS RTK and GPS RTK. The system biases on zenith are larger than the bias on horizontal, and the biases between the results on east of BDS-RTK positioning and the results on east of GPS-RTK are fewer than biases on the other two orientations. All of the biases on three orientations are at the centimeter level, and the RMS of the biases are 0.009m 0.01m and 0.035m on three orientations of E, N and U respectively. For the receiver, the biases on zenith between BDS-RTK and GPS-RTK are larger than zero, and most of the biases on horizontal are less than zero. At the same time some of the BDS-RTK results are compared with the actual length of this part of the field, all of these biases are at the centimeter level too. These experimental results indicate that the BDS-RTK and GPS-RTK have the analogous accuracy and efficiency of kinematic positioning.
Test 2: The other dynamic experiment is carried out by the receiver type of South S86+C502 which is used by the rover. Firstly, the rover stops at the south east of the stadium track for static measurement in the 32 seconds for initialization and the ratio is 2.5 of
ambiguity fixing. The dynamic observations are processed by the method of BDS RTK in this paper. The map of rover trajectory is drawn by the results of BDS RTK and shown as figure 23. The figure 24 which is the map of rover trajectory is drawn by the results of GPS RTK. The two maps of the shapes of rover trajectory drawn by the BDS RTK and GPS RTK match each other well. The figure 25 is the deviations on three coordinate directions of E(east),N(north),U(zenith) of BDS and GPS RTK at each measure point.
The RMS (Root Mean Square) of the biases between BDS RTK and GPS RTK are 0.010m 0.020m and 0.027m on three orientations of E N and U respectively. The figure 25 shows that there are also system biases between BDS RTK and GPS RTK. The same with the test 1, the system biases on zenith are also larger than the bias on horizontal, and the biases between the results on east of BDS RTK positioning and the results on east of GPS RTK is fewer than biases on the other two orientations. All of the biases on three orientations are at the centimeter level. For this receiver, the biases on three orientations have no strictly regularity especially on zenith be-
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tween BDS RTK and GPS RTK. Most of the biases between BDS RTK and GPS RTK on the E orientation are larger than zero, most on the N orientation are less than zero, and most on the U orientation are changing around zero without strict regularity.
The results of dynamic positioning tests indicate that the BDS RTK and GPS RTK
have the analogous positioning accuracy and working efficiency. And the algorithm of RTK using BeiDou regional system has very good stability and the ability of practical working. So the shapes of the trajectories by the results of BDS RTK and GPS RTK on rover are similar to each other, and the biases between the two systems are at the centimeter level.
Figure 23. The user trajectory of BDS RTK
Figure 24. The user trajectory of GPS RTK
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Figure 25. The biases of the BDS RTK comparing with GPS RTK Conclusions
The BeiDou navigation satellite system which belongs to China has completed the regional navigation constellation independently by China. The pseudo ranges and carrier phase observations of BDS users can meet the demand of the ambiguity resolution and realize high-precision real-time dynamic positioning. This paper studies the algorithm of RTK using BeiDou regional system. The errors of rovers of BeiDou regional system can be removed and weakened by indifference error corrections on reference station, and the centimeter level positioning accuracy of RTK can be realized. The observations of different lengths between rovers and reference station are used to test the algorithm of BDS RTK by processing according to dynamic positioning model. The results indicate that positioning accuracy is at the centimeter level, and the horizontal accuracy of rover positioning results precedes the U accuracy, the accuracy of E direction is better than N direction. This is re-
lated to the satellite constellation distribution of BeiDou regional system. Because the GEO satellites of BeiDou regional system are distributed along the equator from east to west, The period of motion of IGSO satellite is approximately 24 hours, and there are not enough MEO satellites. So the satellite distribution of users observing along east to west is better than that along south to north especially in the north of China. And this is difference to GPS RTK. The results of dynamic positioning tests indicate that the BDS RTK and GPS RTK have the analogous working efficiency, the RTK positioning accuracy at the centimeter level is achieved. For the receivers of BDS and GPS, there are biases between BDS RTK and GPS RTK. The researches of these biases between BDS RTK and GPS RTK can advance the studies of combining dynamic positioning between BDS and GPS. At the same time the findings in this paper indicate that the BeiDou regional system can provide high-
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precision dynamic positioning to the users of regional system. And the BDS has the capability of high-precision positioning equivalent to the GPS. The research works in this paper can be used as the preliminary researches of the method of network RTK by BeiDou region-
al system.
This study was supported by the China National Key R&D Program (2016YFC0803102) and the Liaoning Province University Innovation Team Project (LT2015013).
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Критерий авторства
Чу Хэйчжун, Сюй Айгун, А.Л. Охотин, Сюй Синьчао, Гао Менг имеют равные авторские права и несут ответственность за плагиат.
Конфликт интересов
Авторы заявляют об отсутствии интересов в этой работе.
27. Gao X.W., Guo J.J., Cheng P.F., Lu M.Q., etc. Fusion positioning of BeiDou/GPS based on spatiotemporal system unification. Acta Geodetica et Carto-graphica Sinica, 2012, 41 (5): 743-748.
Contribution
Huizhong Zhu, Aigong Xu, Okhotin A.L., Xinchao Xu, Meng Gao have equal author's rights and bear the responsibility for plagiarism.
Conflict of interests
The authors declare no conflict of interests regarding the publication of this article.
Том 3, № 3 2018 XXI ВЕК. ТЕХНОСФЕРНАЯ БЕЗОПАСНОСТЬ Vol. 3, no. 3 2018 XXI CENTURY. TECHNOSPHERE SAFETY
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