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Optimization design of inter-satellite link (ISL) assignment parameters in GNSS based on genetic algorithm
Accepted Manuscript Optimization design of inter-satellite link (ISL) assignment parameters in GNSS based on genetic algorithm Jinhui Huang, Yingxue Su, Wenxiang Liu, Feixue Wang PII: DOI: Reference:
S0273-1177(16)30749-9 http://dx.doi.org/10.1016/j.asr.2016.12.027 JASR 13026
To appear in:
Advances in Space Research
Received Date: Revised Date: Accepted Date:
14 August 2016 12 December 2016 17 December 2016
Please cite this article as: Huang, J., Su, Y., Liu, W., Wang, F., Optimization design of inter-satellite link (ISL) assignment parameters in GNSS based on genetic algorithm, Advances in Space Research (2016), doi: http:// dx.doi.org/10.1016/j.asr.2016.12.027
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Optimization design of inter-satellite link (ISL) assignment parameters in GNSS based on genetic algorithm Jinhui Huang, Yingxue Su, Wenxiang Liu, Feixue Wang* Satellite Navigation R&D Center, National University of Defence Technology, Changsha 410000, China * Corresponding author. E-mail addresses: [email protected] (Jinhui Huang), [email protected] (Yingxue Su), [email protected] (Wenxiang Liu), [email protected] (Feixue Wang) Abstract Global Navigation Satellite System (GNSS) inter-satellite links (ISLs) assignment parameters determine the topology of the satellite network, and directly affect the communication and measurement performance of the system. Key communication performance metric was developed based on the actual needs of the system. This paper studied the effect of time slice length and the number of slices in a polling cycle on the satellite network performance in GNSS. A double-loops algorithm is proposed to solve the optimization problem. Simulation results show that the average delay increases as the time slice length increases. Besides, a large value of the number of slices in a polling cycle is helpful to improve the orbit determination performance. Therefore, in order to improve the communication and measurement performance of the system, we can use both small time slice length and large number of slices in a polling cycle. The finding may give insight into the desige of ISL assignment parameters in GNSS.
Keywords: GNSS; inter-satellite link; satellite network
1
Introduction Inter-satellite links (ISLs) play an important role in the new generation of Global Navigation
Satellite System (GNSS). It is not only used to communicate and measure (D'Angelo et al. , 2012) for guarantee autonomous navigation, but also improves the accuracy of orbit determination for GNSS whose ground stations are limited in regions(Jin et al. , 2011, 2016). Research of ISL technology focuses on aspects of the ISL assignment, routing algorithm, orbit determination, time synchronization and link budget (Han et al. , 2014, Han et al. , 2013, Yi et al. , 2014). Since the ISL assignment decides the topology of satellite network, it directly determines the measurement and communication performance of GNSS. Since the Block IIR satellite came into use, GPS has started using satellites with ISL function.
The time division multiple access (TDMA) scheme is adopted(Jin et al. , 2014). The ISL of Block IIR operates in the UHF band (250-290MHz). A series of problems exist in the UHF ISL: 1) The low communicating rate is difficult to meet the system demand; 2) UHF bands is not allocated for inter-satellite communications by International Telecommunication Union (ITU), so the use of UHF bands in ISL is not protected; 3) The anti-jamming ability of wide-beam is poor; 4) inter-satellite communications are likely to cause interference to terrestrial UHF legitimate users (Lin, 2010). Given all this, the United States plans to use high-frequency (Ka) ISL technology in the Block III (Shi et al. , 2011). Ka-band spot beam antenna is used for communication and ranging. Since high costs limit the number of antennas on the satellite, the number of antennas is typically less than the number of visible satellites (two satellites are defined to be visible to each other if they are within line-of-sight with each other). In order to obtain more inter-satellite pseudo-range observations to improve the accuracy of orbit determination, most recent literatures use phased array antenna on GNSS satellite. The phased array antenna can point to different satellites according to the polling mechanism (Lin et al. , 2011, Yan et al. , 2015). The narrow beam provides more communications throughput. The polling mechanism makes it possible to get better accuracy of orbit determination. From the existing literatures, several points are worth to study as follows. 1) Most previous literatures tend to focus on the design of polling order and overlook the optimization of the length of time slice that a satellite keeps a connection with another one, and the optimization of the number of slices in a polling cycle (Lin et al. , 2011). However, both the time slice length and the number of slices in a polling cycle may have great effect on system performance. It may get better results if both two parameters are optimized as well as the polling order. 2) The average delay between all the satellites in the entire network is usually selected as the metric of communication performance (Yan et al. , 2015). In GNSS, ground stations have to upload navigation message to the satellites. Besides, the satellites have to send some data such as their own health information to the ground stations. In this paper, we focus on the GNSS whose ground stations are limited in regions. In this kind of GNSS, ground stations cannot send data directly to overseas satellites (satellites that are not visible to ground stations). These data have first to be uploaded from ground stations to domestic satellites (satellites that are visible to ground stations), and then be sent through satellite network to overseas satellites. Similarly overseas satellites use domestic satellites as relays to transmit data to ground stations. Therefore, data-transfer between ground stations and overseas satellites makes up most of the network communication. Furthermore, the time delay of GSL (ground station to satellite link) is small (several hundred milliseconds) and can be ignored. Therefore, designers of GNSSs pay more
attention on the communication between domestic satellites and overseas satellites. That’s the reason why we propose using the average time-delay between domestic satellites and overseas satellites as the communication performance metric. 3) The number of satellites in a polling cycle is used as an index of measurement performance in some literature (Yan et al. , 2015). But the accuracy of orbit determination depends not only on the number of satellites in a polling cycle but also on the satellite geometry. Better indicators should be selected to reflect the system measurement performance. The main contribution of this paper includes the following: 1) We proposed using average time-delay between domestic satellites and overseas satellites as the communication performance metric. 2) The mathematical model of ISL assignment optimization problem is developed. 3) The ISL assignment optimization problem is solved based on the genetic algorithm as a multi-objective optimization problem. 4) We analyzed the effect of time slice length and the number of slices in a polling cycle on the system performance.
2
System model
2.1. Time-division multiplex ISL The dynamic of satellite networks is deterministic. In fact, the satellite motion is affected by orbit drift. Since the ISL antenna beam is usually wide enough, the inter-satellite communication will not be affected by orbit drift. So in this paper, we don’t emphasize the orbit drift. The satellite motion and the inter-satellite visibility are deemed to have an obvious periodicity. The topology evolution of satellite network is also cyclical and can be described by a sequence of topology slices of satellite network. The satellite network visibility can be considered unchanged within a time slice. The number of satellite antenna is limited due to cost. On the other hand, in order to improve the accuracy of orbit determination, it is helpful for every satellite to establish ISL with more satellites. Thus it’s proposed in recent years to adopt the directional antenna which can point to different satellites in a polling order. It’s called the time-division multiplex ISL scheme, as shown in Fig.1 (Yan et al. , 2015). The system period of the satellite network is divided into many satellite network topology slices. Two satellites are considered to be visible in a topology slice if and only if they are visible to each other throughout the topology slice. Each topology slice is divided into N equal-length polling periods. The polling period is called a polling cycle, which is composed of a plurality of ISL time slices. In each ISL time slice, satellite antenna points to a specific satellite. Directional antennas rotate quickly euough to support the polling mechanism where they have more adjustment than those in the traditional satellite networks.
ISL time slice 1
ISL time slice 2
ISL time slice 3
ISL time slice K
Polling cycle 1
Polling cycle 2
Polling cycle 3
Polling cycle N
Satellite Satellite Satellite network network network topology slice 1 topology slice 2 topology slice 3
Time
Figure 1.Signal structure of time-division multiplex ISL (Yan et al. , 2015) The changes in network topology during a polling cycle can be described by a two-dimensional ISL assignment matrix.
e11 e12 e e E 21 22 eS1 eS 2
e1K e2 K eSK
(1) Matrix E reflects topology evolution of all satellites during a polling cycle. Each line in E
represents a satellite. Each column in E represents a time slice. eij is the element in the i-th row and j-th column of matrix E .
eij represents the satellite with which the i-th satellite establishes ISL in the j-th time slice of the polling cycle. If satellite i does not connects to any satellite in the j-th time slice, then
eij 0 . Since the ISL is bidirectional, when eij 0 , the eij -th satellite establishes ISL with the i-th satellite in the same time slice. eeij j represents the satellite with which the eij -th satellite establishes ISL in the j-th time slice. It's easy to see
eeij j i
(2)
2.2. Performance metrics As has been said before, the ISLs between domestic satellites and overseas satellites take most of the Inter-satellite communication load. The optimal design of ISL should pay more attention to the domestic satellites-overseas satellites communication. This paper regards the average time-delay between domestic satellites and overseas satellites as the communication performance metric. The average time-delay between domestic satellites and overseas satellites
at any given time is as follows: S
S
i 1
j 1 j i V ( i ) V ( j )
WT (i, j, t ) _____
WTt
2 No Nd
(3)
Where, WT (i, j, t ) is the shortest time-delay between satellite i and satellite j while the fastest routing(Wu et al. , 2011) is used. S is the total number of satellites in GNSS constellation.
V (i) is the visibility between a satellite and ground stations. V (i) 1 indicates that the satellite is visible to ground stations, in other words the satellite is domestic. V (i) 0 indicates that the satellite is not visible to ground stations, in other words the satellite is overseas. _____
N o is the number of overseas satellites, N d is the number of domestic satellites. WTt is the average time-delay between domestic satellites and overseas satellites at any given time t . The average time-delay between domestic satellites and overseas satellites in a continuous period of time is as shown below.
WT
WT
t
t
T
(4)
Where, WT is the average time-delay between domestic satellites and overseas satellites in a continuous period of time T . Since in each ISL time slice the satellite ISL antenna points to a specific satellite, the network topology varies every time slice. The evolution of network topology repeats every polling cycle time. In order to reflect the average delay during the network topology evolution roundly, the time slice length is used as the time interval of variable t . The inter-satellite ranging observations are used for orbit determination and autonomous navigation. Thus the performance of inter-satellite ranging is reflected in the accuracies of orbit determination and autonomous navigation. (Liu et al. , 2011) defines the weighted autonomous navigation GDOP: WDOP, which is used to describe the relationship between the performance of orbit determination and the precision of ranging. WDOP is defined as follows:
WDOPi (tk ) tr (( H TW ' H )1 )
(5)
Where, H is inter-satellite observation matrix. H (i, j ) 1 indicates that it is able to gain ranging observations between satellite i and satellite j. H (i, j ) 0 indicates that the ranging observations between satellite i and satellite j is not available. W is the inter-satellite
observation weighting matrix. i is the identification of satellite. The average WDOP at a given time t k is as follows. S
WDOP(tk )
WDOP(t ) i
i 1
k
(6)
S
Where, S is the number of satellites. The average WDOP in a continuous period of time is as follows.
WDOP
WDOP(t
k
)
tk
T
(7)
This paper adopts the average WDOP of satellite network in a continuous period of time as the measurement performance metric.
3
Optimization design of ISL assignment parameters
3.1. Problem description The optimization problem of ISL assignment parameter can be described as follows: Variables:
T _ slice K E
the length of a time slice the number of slices in a polling cycle the ISL assignment matrix
Objective function:
F w1 WT w2 WDOP Constraints:
C1 : H (i, eij ) 1, i, j , eij 0 C 2 : eeij j i C 3 : eij ekj , i k , eij 0 C 4 : eij eik , j k , eij 0 C 5 : 0 eij S The optimization variables include the time slice length, the number of slices in a polling cycle and the ISL assignment matrix. Note that the ISL assignment matrix E is a matrix of size
S , K . The weighted sum of average delay and average WDOP is used as objective function. By setting weights w1 and w2 , different system performance can be reached. In the constraint formulas, C1 is the visibility constraint that a satellite can only establish ISL with satellites visible to itself. C2 ensures that the ISL establishment is bidirectional, namely in the
j-th slice if satellite i establishes ISL with satellite k, then satellite k should also establishes ISL with satellite i. C3 is to ensure that at any time there will not be two satellites which establish ISL with the same satellite. C4 is out of consideration to improve measurement performance. two satellites will not establish ISL repeated to each other in a polling period. C5 defines the range of
eij . 3.2. ISL assignment optimization algorithm A double-loops optimization algorithm is proposed in this paper to solve the ISL assignment problem. First, we set values of T _ slice _ low and T _ slice _ up which determine the searching space of T _ slice . Values of K _ low and K _ up which determine the searching space of K , are set too. T _ slice and K are searched between lower limits and upper limits. Second, for each pair of T _ slice and K , the ISL assignment matrix is optimized based on Genetic algorithm (GA). The variable K determines the size of E . As the increasing of K , the optimization of
E will become computationally intractable. Genetic algorithm (GA) is a random search algorithm widely used for optimization. It can get sub-optimal solutions and has proved to be effective in engineering research. GA maintains a group of ISL assignment matrixes in the population. The population of ISL assignment matrixes generates new ISL assignment matrixes through genetic operations such as crossover and mutation. The objective function value of each ISL assignment matrix is calculated. The objective function value then is used to evaluate the ISL assignment matrix’s performance. Outstanding ISL assignment matrixes have a greater chance to produce offspring. There are generally two genetic operations: crossover and mutation. The crossover is the combination of two ISL assignment matrixes to form a new ISL assignment matrix. The mutation is a change of some ISL assignment matrixes to generate a new ISL assignment matrix. The genetic algorithm has the ability of global searching of the solution space. It established initial population randomly. Every unit in the initial population represents a solution. Then crossover and mutation are carried out to improve the quality of the solution populations. The average time-delay between domestic satellites and overseas satellites and the average WDOP are the objective functions (AF) of GA. The ISL assignment matrixes of the generation group generate new generations until it finds a genetic solution to meet the termination condition. The flowchart of double-loops optimization algorithm is shown in Fig.2.
Initialize the searching space
Search T_slice , K
Initialize the ISL assignment matrix Calculate the objective function Continue iteration of ISL assignment matrix? Yes Selection
Crossover
No
Record the optimization result
Continue iteration of T_slice, K?
Mutation
Yes
No End
Figure 2.The flowchart of double-loops optimization algorithm Since the satellite motion is predictable, we can run the double-loops optimization algorithm off-line. There is no need to optimize in real time.
4
Simulation results
4.1. Simulation conditions We selected standard Walker24/3/1 constellation composed of 24 MEO satellites with other 3 GEO and 3 IGSO satellites as the GNSS constellation. The orbital semi-major axis of MEO is 26559.8 km. The inclination of both the MEO and IGSO is 55 degree. The 3 GEO satellites are deployed in 80 °E , 110.5 °E and 140 °E(Han et al. , 2013). The searching space of K is [6, 20]. The searching space of T _ slice is [2s, 6s]. Since the average delay is one order greater in magnitude than that of average WDOP, we let w1 1 and w2 10 . Furthermore, the proposed optimizetion design method can be readily extended to other weight values.
The visibility between satellites and ground stations in 24 hours is shown in Fig.3. If a satellite is visible to groud stations in an interval, it is regarded as domestic satellite in that interval. Generally speaking, satellites in Asia-Pacific are considered to be domestic satellites.
Figure 3.Domestic satellites and overseas satellites nodes with ground stations tracking
4.2. Results and analysis of simulation Fig.4 illustrates the Influence of T _ slice and K on the average delay. The average delay increases as T _ slice increase. For any given K , the polling cycle time equals to
T _ slice * K . A larger T _ slice means it will take more time to repeat the network topology evolution in a polling cycle. The value of K also has effect on the average delay too. Different
K corresponds to different network topology. But there is no obvious regularity of the K ’s influence on the average delay.
Figure 4.The average delay versus T_slice and K Fig.5 illustrates the Influence of
T _ slice and K on the average WDOP. The
average WDOP decreases as K increase. A larger K means that a satellite can connects to more satellites by ISL in a polling cycle. So a large value of K is helpful to improve the orbit determination performance. The value of T _ slice is not impacting the average WDOP.
Figure 5.The average WDOP versus T_slice and K Fig.6 illustrates the Influence of T _ slice and K on the objective function. The objective function is the weighted sum of the average delay and the average WDOP. In order to decrease the value of the objective function, we can use both small T _ slice and large K . It should be noted that smaller T _ slice is not always better. In satellite network of GNSS, data transmits in frames. Data contents are recognized by the different frame-heads. A very small
T _ slice leads to little data content per frame. Since the length of a frame-head is usually fixed, a short data content means communication inefficiency. On the other hand, as the the GNSS adopts pilot signal in inter-satellite communication. The data signal-pilot signal ratio may decrease as T _ slice decreases. For T _ slice of the order of hundreds of milliseconds, the above two effects should be taken into account. It can be seen from Fig.6. that T _ slice =2, K =18 leads to the minimum value of objective function(19.45).
Figure 6.The objective function versus T_slice and K It should be noted that the construction of the next generation GNSS will be a gradual process. Satellites will be launched one by one. During the construction of GNSS, the satellite constellation will change accordingly. The proposed optimization design method of ISL links does not limit to only one specific constellation, but also applies to different constellations. With more satellites in the constellation, a satellite may be visible to a larger number of satellites. As a result, a larger number of slices in a polling cycle can be used.
5
Conclusions The mathematical model of ISL assignment is established. The double-loops optimization
method of ISL assignment based on genetic algorithm is put forward. The optimization design takes comprehensive factors into account, including the length of time slice and the number of satellites in a polling cycle. The communication and measurement performance indexes are selected according to the system requirements. The effect of time slice length and the number of slices in a polling cycle on the satellite network performance is studied. The finding may give insight into the desige of ISL assignment parameters in GNSS.
Acknowledgments This work is supported by the National Natural Science Foundation of China under Grant No. 41604016. Special our thanks to the colleagues of the Satellite Navigation R&D Center of National
University of Defence Technology for the support, advices and help.
References D'Angelo, P., Fernandez, A., Guardabrazo, T., Amarillo, F. Enhancement of GNSS navigation function by the use of Inter-Satellite Links. NAVITEC 2012 and European Workshop on GNSS Signals and Signal Processing. pp. 1-6, 2012. Han, S.H., Gui, Q.M., Li, G.Z., Du, Y.L. Minimum of PDOP and its applications in inter-satellite links (ISL) establishment of Walker-delta constellation. ADVANCES IN SPACE RESEARCH 54, 726-733, 2014. Han, S.H., Gui, Q.M., Li, J.W. Establishment criteria, routing algorithms and probability of use of inter-satellite links in mixed navigation constellations. ADVANCES IN SPACE RESEARCH 51, 2084-2092, 2013. Jin, S., Cardillach, E., Feiqin, X. GNSS remote sensing : theory, methods and applications. Springer, Netherlands, 2014. Jin, S., Feng, G.P., Gleason, S. Remote sensing using GNSS signals: Current status and future directions. Advances in Space Research 47, 1645-1653, 2011. Jin, S., Jin, R., Li, D. Assessment of BeiDou differential code bias variations from multi-GNSS network observations. Annales Geophysicae 34, 259-269, 2016. Lin, J., Yang, J., Yueke., W., Yongbin., Z., Jianyun., C. Optimizing algorithm for the scheduling of GNSS crosslink: a matrix transform approach. 2nd China Satellite Navigation Conference. Shanghai, China, pp. 467-471, 2011. Lin, Y., He Shanbao, Zheng Jinjun. Development Recommendation of Inter-satellites Links in GNSS. Spacecraft Engineering, 1-7, 2010. Liu, W., Yong, S., Wang, F. Effect of Navigation Constellation Incompleteness on Dilution of Precision of Autonomous Orbit Determination Using Inter-satellite Link. Chinese Journal of Space Science 31, 366-371, 2011. Shi, L.-y., Xiang, W., Tang, X.-m. A link assignment algorithm for GNSS with crosslink ranging. IEEE International Conference on Localization and GNSS. pp. 13-18, 2011. Wu, Y., Yang, J., Chen, J., Lin, J. Route Analysis of Satellite Constellation Based on Directional Crosslink with Narrow-Beam Antenna. Practical Applications of Intelligent Systems. Springer Berlin Heidelberg, 639-650, 2011. Yan, H., Zhang, Q., Sun, Y., Guo, J. Contact plan design for navigation satellite network based on simulated annealing. IEEE International Conference on Communication Software and Networks (ICCSN). Chengdu, China, pp. 12-16, 2015. Yi, X., Hou, Z., Zhong, T., Zhang, Y., Sun, Z. Route strategy of satellite network in GNSS based on topology evolution law. Journal of Systems Engineering & Electronics 25, 596-608, 2014.
S0273-1177(16)30749-9 http://dx.doi.org/10.1016/j.asr.2016.12.027 JASR 13026
To appear in:
Advances in Space Research
Received Date: Revised Date: Accepted Date:
14 August 2016 12 December 2016 17 December 2016
Please cite this article as: Huang, J., Su, Y., Liu, W., Wang, F., Optimization design of inter-satellite link (ISL) assignment parameters in GNSS based on genetic algorithm, Advances in Space Research (2016), doi: http:// dx.doi.org/10.1016/j.asr.2016.12.027
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Optimization design of inter-satellite link (ISL) assignment parameters in GNSS based on genetic algorithm Jinhui Huang, Yingxue Su, Wenxiang Liu, Feixue Wang* Satellite Navigation R&D Center, National University of Defence Technology, Changsha 410000, China * Corresponding author. E-mail addresses: [email protected] (Jinhui Huang), [email protected] (Yingxue Su), [email protected] (Wenxiang Liu), [email protected] (Feixue Wang) Abstract Global Navigation Satellite System (GNSS) inter-satellite links (ISLs) assignment parameters determine the topology of the satellite network, and directly affect the communication and measurement performance of the system. Key communication performance metric was developed based on the actual needs of the system. This paper studied the effect of time slice length and the number of slices in a polling cycle on the satellite network performance in GNSS. A double-loops algorithm is proposed to solve the optimization problem. Simulation results show that the average delay increases as the time slice length increases. Besides, a large value of the number of slices in a polling cycle is helpful to improve the orbit determination performance. Therefore, in order to improve the communication and measurement performance of the system, we can use both small time slice length and large number of slices in a polling cycle. The finding may give insight into the desige of ISL assignment parameters in GNSS.
Keywords: GNSS; inter-satellite link; satellite network
1
Introduction Inter-satellite links (ISLs) play an important role in the new generation of Global Navigation
Satellite System (GNSS). It is not only used to communicate and measure (D'Angelo et al. , 2012) for guarantee autonomous navigation, but also improves the accuracy of orbit determination for GNSS whose ground stations are limited in regions(Jin et al. , 2011, 2016). Research of ISL technology focuses on aspects of the ISL assignment, routing algorithm, orbit determination, time synchronization and link budget (Han et al. , 2014, Han et al. , 2013, Yi et al. , 2014). Since the ISL assignment decides the topology of satellite network, it directly determines the measurement and communication performance of GNSS. Since the Block IIR satellite came into use, GPS has started using satellites with ISL function.
The time division multiple access (TDMA) scheme is adopted(Jin et al. , 2014). The ISL of Block IIR operates in the UHF band (250-290MHz). A series of problems exist in the UHF ISL: 1) The low communicating rate is difficult to meet the system demand; 2) UHF bands is not allocated for inter-satellite communications by International Telecommunication Union (ITU), so the use of UHF bands in ISL is not protected; 3) The anti-jamming ability of wide-beam is poor; 4) inter-satellite communications are likely to cause interference to terrestrial UHF legitimate users (Lin, 2010). Given all this, the United States plans to use high-frequency (Ka) ISL technology in the Block III (Shi et al. , 2011). Ka-band spot beam antenna is used for communication and ranging. Since high costs limit the number of antennas on the satellite, the number of antennas is typically less than the number of visible satellites (two satellites are defined to be visible to each other if they are within line-of-sight with each other). In order to obtain more inter-satellite pseudo-range observations to improve the accuracy of orbit determination, most recent literatures use phased array antenna on GNSS satellite. The phased array antenna can point to different satellites according to the polling mechanism (Lin et al. , 2011, Yan et al. , 2015). The narrow beam provides more communications throughput. The polling mechanism makes it possible to get better accuracy of orbit determination. From the existing literatures, several points are worth to study as follows. 1) Most previous literatures tend to focus on the design of polling order and overlook the optimization of the length of time slice that a satellite keeps a connection with another one, and the optimization of the number of slices in a polling cycle (Lin et al. , 2011). However, both the time slice length and the number of slices in a polling cycle may have great effect on system performance. It may get better results if both two parameters are optimized as well as the polling order. 2) The average delay between all the satellites in the entire network is usually selected as the metric of communication performance (Yan et al. , 2015). In GNSS, ground stations have to upload navigation message to the satellites. Besides, the satellites have to send some data such as their own health information to the ground stations. In this paper, we focus on the GNSS whose ground stations are limited in regions. In this kind of GNSS, ground stations cannot send data directly to overseas satellites (satellites that are not visible to ground stations). These data have first to be uploaded from ground stations to domestic satellites (satellites that are visible to ground stations), and then be sent through satellite network to overseas satellites. Similarly overseas satellites use domestic satellites as relays to transmit data to ground stations. Therefore, data-transfer between ground stations and overseas satellites makes up most of the network communication. Furthermore, the time delay of GSL (ground station to satellite link) is small (several hundred milliseconds) and can be ignored. Therefore, designers of GNSSs pay more
attention on the communication between domestic satellites and overseas satellites. That’s the reason why we propose using the average time-delay between domestic satellites and overseas satellites as the communication performance metric. 3) The number of satellites in a polling cycle is used as an index of measurement performance in some literature (Yan et al. , 2015). But the accuracy of orbit determination depends not only on the number of satellites in a polling cycle but also on the satellite geometry. Better indicators should be selected to reflect the system measurement performance. The main contribution of this paper includes the following: 1) We proposed using average time-delay between domestic satellites and overseas satellites as the communication performance metric. 2) The mathematical model of ISL assignment optimization problem is developed. 3) The ISL assignment optimization problem is solved based on the genetic algorithm as a multi-objective optimization problem. 4) We analyzed the effect of time slice length and the number of slices in a polling cycle on the system performance.
2
System model
2.1. Time-division multiplex ISL The dynamic of satellite networks is deterministic. In fact, the satellite motion is affected by orbit drift. Since the ISL antenna beam is usually wide enough, the inter-satellite communication will not be affected by orbit drift. So in this paper, we don’t emphasize the orbit drift. The satellite motion and the inter-satellite visibility are deemed to have an obvious periodicity. The topology evolution of satellite network is also cyclical and can be described by a sequence of topology slices of satellite network. The satellite network visibility can be considered unchanged within a time slice. The number of satellite antenna is limited due to cost. On the other hand, in order to improve the accuracy of orbit determination, it is helpful for every satellite to establish ISL with more satellites. Thus it’s proposed in recent years to adopt the directional antenna which can point to different satellites in a polling order. It’s called the time-division multiplex ISL scheme, as shown in Fig.1 (Yan et al. , 2015). The system period of the satellite network is divided into many satellite network topology slices. Two satellites are considered to be visible in a topology slice if and only if they are visible to each other throughout the topology slice. Each topology slice is divided into N equal-length polling periods. The polling period is called a polling cycle, which is composed of a plurality of ISL time slices. In each ISL time slice, satellite antenna points to a specific satellite. Directional antennas rotate quickly euough to support the polling mechanism where they have more adjustment than those in the traditional satellite networks.
ISL time slice 1
ISL time slice 2
ISL time slice 3
ISL time slice K
Polling cycle 1
Polling cycle 2
Polling cycle 3
Polling cycle N
Satellite Satellite Satellite network network network topology slice 1 topology slice 2 topology slice 3
Time
Figure 1.Signal structure of time-division multiplex ISL (Yan et al. , 2015) The changes in network topology during a polling cycle can be described by a two-dimensional ISL assignment matrix.
e11 e12 e e E 21 22 eS1 eS 2
e1K e2 K eSK
(1) Matrix E reflects topology evolution of all satellites during a polling cycle. Each line in E
represents a satellite. Each column in E represents a time slice. eij is the element in the i-th row and j-th column of matrix E .
eij represents the satellite with which the i-th satellite establishes ISL in the j-th time slice of the polling cycle. If satellite i does not connects to any satellite in the j-th time slice, then
eij 0 . Since the ISL is bidirectional, when eij 0 , the eij -th satellite establishes ISL with the i-th satellite in the same time slice. eeij j represents the satellite with which the eij -th satellite establishes ISL in the j-th time slice. It's easy to see
eeij j i
(2)
2.2. Performance metrics As has been said before, the ISLs between domestic satellites and overseas satellites take most of the Inter-satellite communication load. The optimal design of ISL should pay more attention to the domestic satellites-overseas satellites communication. This paper regards the average time-delay between domestic satellites and overseas satellites as the communication performance metric. The average time-delay between domestic satellites and overseas satellites
at any given time is as follows: S
S
i 1
j 1 j i V ( i ) V ( j )
WT (i, j, t ) _____
WTt
2 No Nd
(3)
Where, WT (i, j, t ) is the shortest time-delay between satellite i and satellite j while the fastest routing(Wu et al. , 2011) is used. S is the total number of satellites in GNSS constellation.
V (i) is the visibility between a satellite and ground stations. V (i) 1 indicates that the satellite is visible to ground stations, in other words the satellite is domestic. V (i) 0 indicates that the satellite is not visible to ground stations, in other words the satellite is overseas. _____
N o is the number of overseas satellites, N d is the number of domestic satellites. WTt is the average time-delay between domestic satellites and overseas satellites at any given time t . The average time-delay between domestic satellites and overseas satellites in a continuous period of time is as shown below.
WT
WT
t
t
T
(4)
Where, WT is the average time-delay between domestic satellites and overseas satellites in a continuous period of time T . Since in each ISL time slice the satellite ISL antenna points to a specific satellite, the network topology varies every time slice. The evolution of network topology repeats every polling cycle time. In order to reflect the average delay during the network topology evolution roundly, the time slice length is used as the time interval of variable t . The inter-satellite ranging observations are used for orbit determination and autonomous navigation. Thus the performance of inter-satellite ranging is reflected in the accuracies of orbit determination and autonomous navigation. (Liu et al. , 2011) defines the weighted autonomous navigation GDOP: WDOP, which is used to describe the relationship between the performance of orbit determination and the precision of ranging. WDOP is defined as follows:
WDOPi (tk ) tr (( H TW ' H )1 )
(5)
Where, H is inter-satellite observation matrix. H (i, j ) 1 indicates that it is able to gain ranging observations between satellite i and satellite j. H (i, j ) 0 indicates that the ranging observations between satellite i and satellite j is not available. W is the inter-satellite
observation weighting matrix. i is the identification of satellite. The average WDOP at a given time t k is as follows. S
WDOP(tk )
WDOP(t ) i
i 1
k
(6)
S
Where, S is the number of satellites. The average WDOP in a continuous period of time is as follows.
WDOP
WDOP(t
k
)
tk
T
(7)
This paper adopts the average WDOP of satellite network in a continuous period of time as the measurement performance metric.
3
Optimization design of ISL assignment parameters
3.1. Problem description The optimization problem of ISL assignment parameter can be described as follows: Variables:
T _ slice K E
the length of a time slice the number of slices in a polling cycle the ISL assignment matrix
Objective function:
F w1 WT w2 WDOP Constraints:
C1 : H (i, eij ) 1, i, j , eij 0 C 2 : eeij j i C 3 : eij ekj , i k , eij 0 C 4 : eij eik , j k , eij 0 C 5 : 0 eij S The optimization variables include the time slice length, the number of slices in a polling cycle and the ISL assignment matrix. Note that the ISL assignment matrix E is a matrix of size
S , K . The weighted sum of average delay and average WDOP is used as objective function. By setting weights w1 and w2 , different system performance can be reached. In the constraint formulas, C1 is the visibility constraint that a satellite can only establish ISL with satellites visible to itself. C2 ensures that the ISL establishment is bidirectional, namely in the
j-th slice if satellite i establishes ISL with satellite k, then satellite k should also establishes ISL with satellite i. C3 is to ensure that at any time there will not be two satellites which establish ISL with the same satellite. C4 is out of consideration to improve measurement performance. two satellites will not establish ISL repeated to each other in a polling period. C5 defines the range of
eij . 3.2. ISL assignment optimization algorithm A double-loops optimization algorithm is proposed in this paper to solve the ISL assignment problem. First, we set values of T _ slice _ low and T _ slice _ up which determine the searching space of T _ slice . Values of K _ low and K _ up which determine the searching space of K , are set too. T _ slice and K are searched between lower limits and upper limits. Second, for each pair of T _ slice and K , the ISL assignment matrix is optimized based on Genetic algorithm (GA). The variable K determines the size of E . As the increasing of K , the optimization of
E will become computationally intractable. Genetic algorithm (GA) is a random search algorithm widely used for optimization. It can get sub-optimal solutions and has proved to be effective in engineering research. GA maintains a group of ISL assignment matrixes in the population. The population of ISL assignment matrixes generates new ISL assignment matrixes through genetic operations such as crossover and mutation. The objective function value of each ISL assignment matrix is calculated. The objective function value then is used to evaluate the ISL assignment matrix’s performance. Outstanding ISL assignment matrixes have a greater chance to produce offspring. There are generally two genetic operations: crossover and mutation. The crossover is the combination of two ISL assignment matrixes to form a new ISL assignment matrix. The mutation is a change of some ISL assignment matrixes to generate a new ISL assignment matrix. The genetic algorithm has the ability of global searching of the solution space. It established initial population randomly. Every unit in the initial population represents a solution. Then crossover and mutation are carried out to improve the quality of the solution populations. The average time-delay between domestic satellites and overseas satellites and the average WDOP are the objective functions (AF) of GA. The ISL assignment matrixes of the generation group generate new generations until it finds a genetic solution to meet the termination condition. The flowchart of double-loops optimization algorithm is shown in Fig.2.
Initialize the searching space
Search T_slice , K
Initialize the ISL assignment matrix Calculate the objective function Continue iteration of ISL assignment matrix? Yes Selection
Crossover
No
Record the optimization result
Continue iteration of T_slice, K?
Mutation
Yes
No End
Figure 2.The flowchart of double-loops optimization algorithm Since the satellite motion is predictable, we can run the double-loops optimization algorithm off-line. There is no need to optimize in real time.
4
Simulation results
4.1. Simulation conditions We selected standard Walker24/3/1 constellation composed of 24 MEO satellites with other 3 GEO and 3 IGSO satellites as the GNSS constellation. The orbital semi-major axis of MEO is 26559.8 km. The inclination of both the MEO and IGSO is 55 degree. The 3 GEO satellites are deployed in 80 °E , 110.5 °E and 140 °E(Han et al. , 2013). The searching space of K is [6, 20]. The searching space of T _ slice is [2s, 6s]. Since the average delay is one order greater in magnitude than that of average WDOP, we let w1 1 and w2 10 . Furthermore, the proposed optimizetion design method can be readily extended to other weight values.
The visibility between satellites and ground stations in 24 hours is shown in Fig.3. If a satellite is visible to groud stations in an interval, it is regarded as domestic satellite in that interval. Generally speaking, satellites in Asia-Pacific are considered to be domestic satellites.
Figure 3.Domestic satellites and overseas satellites nodes with ground stations tracking
4.2. Results and analysis of simulation Fig.4 illustrates the Influence of T _ slice and K on the average delay. The average delay increases as T _ slice increase. For any given K , the polling cycle time equals to
T _ slice * K . A larger T _ slice means it will take more time to repeat the network topology evolution in a polling cycle. The value of K also has effect on the average delay too. Different
K corresponds to different network topology. But there is no obvious regularity of the K ’s influence on the average delay.
Figure 4.The average delay versus T_slice and K Fig.5 illustrates the Influence of
T _ slice and K on the average WDOP. The
average WDOP decreases as K increase. A larger K means that a satellite can connects to more satellites by ISL in a polling cycle. So a large value of K is helpful to improve the orbit determination performance. The value of T _ slice is not impacting the average WDOP.
Figure 5.The average WDOP versus T_slice and K Fig.6 illustrates the Influence of T _ slice and K on the objective function. The objective function is the weighted sum of the average delay and the average WDOP. In order to decrease the value of the objective function, we can use both small T _ slice and large K . It should be noted that smaller T _ slice is not always better. In satellite network of GNSS, data transmits in frames. Data contents are recognized by the different frame-heads. A very small
T _ slice leads to little data content per frame. Since the length of a frame-head is usually fixed, a short data content means communication inefficiency. On the other hand, as the the GNSS adopts pilot signal in inter-satellite communication. The data signal-pilot signal ratio may decrease as T _ slice decreases. For T _ slice of the order of hundreds of milliseconds, the above two effects should be taken into account. It can be seen from Fig.6. that T _ slice =2, K =18 leads to the minimum value of objective function(19.45).
Figure 6.The objective function versus T_slice and K It should be noted that the construction of the next generation GNSS will be a gradual process. Satellites will be launched one by one. During the construction of GNSS, the satellite constellation will change accordingly. The proposed optimization design method of ISL links does not limit to only one specific constellation, but also applies to different constellations. With more satellites in the constellation, a satellite may be visible to a larger number of satellites. As a result, a larger number of slices in a polling cycle can be used.
5
Conclusions The mathematical model of ISL assignment is established. The double-loops optimization
method of ISL assignment based on genetic algorithm is put forward. The optimization design takes comprehensive factors into account, including the length of time slice and the number of satellites in a polling cycle. The communication and measurement performance indexes are selected according to the system requirements. The effect of time slice length and the number of slices in a polling cycle on the satellite network performance is studied. The finding may give insight into the desige of ISL assignment parameters in GNSS.
Acknowledgments This work is supported by the National Natural Science Foundation of China under Grant No. 41604016. Special our thanks to the colleagues of the Satellite Navigation R&D Center of National
University of Defence Technology for the support, advices and help.
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