Solution set on the natural satellite formation orbits under first-order earth's non-spherical perturbation

Using the reference orbital element approach, the precise governing equations for the relative motion of formation flight are formulated. A number of ideal formations with respect to an elliptic orbit can be designed based on the relative motion analysis from the equations. The features of the oscillating reference orbital elements are studied by using the perturbation theory. The changes in the relative orbit under perturbation are divided into three categories, termed scale enlargement, drift and distortion respectively. By properly choosing the initial mean orbital elements for the leader and follower satellites, the deviations from originally regular formation orbit caused by the perturbation can be suppressed. Thereby the natural formation is set up. It behaves either like non-disturbed or need little control to maintain. The presented reference orbital element approach highlights the kinematics properties of the relative motion and is convenient to incorporate the results of perturbation analysis on orbital elements. This method of formation design has advantages over other methods in seeking natural formation and in initializing formation.

A Parallel Discrete Event Simulation Engine for the Low-Earth-Orbit Satellite Constellation Networks

Low-Earth-Orbit satellite constellation networks(LEO-SCN)can provide low-cost,largescale,flexible coverage wireless communication services.High dynamics and large topological sizes characterize LEO-SCN.Protocol development and application testing of LEO-SCN are challenging to carry out in a natural environment.Simulation platforms are a more effective means of technology demonstration.Currently available simulators have a single function and limited simulation scale.There needs to be a simulator for full-featured simulation.In this paper,we apply the parallel discrete-event simulation technique to the simulation of LEO-SCN to support large-scale complex system simulation at the packet level.To solve the problem that single-process programs cannot cope with complex simulations containing numerous entities,we propose a parallel mechanism and algorithms LP-NM and LP-YAWNS for synchronization.In the experiment,we use ns-3 to verify the acceleration ratio and efficiency of the above algorithms.The results show that our proposed mechanism can provide parallel simulation engine support for the LEO-SCN.

Segment routing for traffic engineering and effective recovery in low-earth orbit satellite constellations

Low-Earth Orbit Satellite Constellations(LEO-SCs)provide global,high-speed,and low latency Internet access services,which bridges the digital divide in the remote areas.As inter-satellite links are not supported in initial deployment(i.e.the Starlink),the communication between satellites is based on ground stations with radio frequency signals.Due to the rapid movement of satellites,this hybrid topology of LEO-SCs and ground stations is time-varying,which imposes a major challenge to uninterrupted service provisioning and network management.In this paper,we focus on solving two notable problems in such a ground station-assisted LEO-SC topology,i.e.,traffic engineering and fast reroute,to guarantee that the packets are forwarded in a balanced and uninterrupted manner.Specifically,we employ segment routing to support the arbitrary path routing in LEO-SCs.To solve the traffic engineering problem,we proposed two source routings with traffic splitting algorithms,Delay-Bounded Traffic Splitting(DBTS)and DBTS+,where DBTS equally splits a flow and DBTS+favors shorter paths.Simu-lation results show that DBTS+can achieve about 30%lower maximum satellite load at the cost of about 10%more delay.To guarantee the fast recovery of failures,two fast reroute mechanisms,Loop-Free Alternate(LFA)and LFA+,are studied,where LFA pre-computes an alternate next-hop as a backup while LFA+finds a 2-segment backup path.We show that LFA+can increase the percentage of protection coverage by about 15%.

Delay-optimal multi-satellite collaborative computation offloading supported by OISL in LEO satellite network

By deploying the ubiquitous and reliable coverage of low Earth orbit(LEO)satellite networks using optical inter satel-lite link(OISL),computation offloading services can be provided for any users without proximal servers,while the resource limita-tion of both computation and storage on satellites is the impor-tant factor affecting the maximum task completion time.In this paper,we study a delay-optimal multi-satellite collaborative computation offloading scheme that allows satellites to actively migrate tasks among themselves by employing the high-speed OISLs,such that tasks with long queuing delay will be served as quickly as possible by utilizing idle computation resources in the neighborhood.To satisfy the delay requirement of delay-sensi-tive task,we first propose a deadline-aware task scheduling scheme in which a priority model is constructed to sort the order of tasks being served based on its deadline,and then a delay-optimal collaborative offloading scheme is derived such that the tasks which cannot be completed locally can be migrated to other idle satellites.Simulation results demonstrate the effective-ness of our multi-satellite collaborative computation offloading strategy in reducing task complement time and improving resource utilization of the LEO satellite network.

Survivability model of LEO satellite constellation based on GERT with limited backup resources

Survivability is used to evaluate the ability of the satellite to complete the mission after failure,while the duration of maintaining performance is often ignored.An effective backup strategy can restore the constellation performance timely,and maintain good network communication performance in case of satellite failure.From the perspective of network utility,the low Earth orbit(LEO)satellite constellation survivable graphical eva-luation and review technology(GERT)network with backup satel-lites is constructed.A network utility transfer function algorithm based on moment generating function and Mason formula is proposed,the network survivability evaluation models of on-orbit backup strategy and ground backup strategy are established.The survivable GERT model can deduce the expected mainte-nance time of LEO satellite constellation under different fault states and the network utility generated during the state mainte-nance period.The case analysis shows that the proposed surviv-able GERT model can consider the satellite failure rate,backup satellite replacement rate,maneuver control replacement ability and life requirement,and effectively determine the optimal sur-vivable backup strategy for LEO satellite constellation with limi-ted resources according to the expected network utility.

MULTI-CLASS TRAFFIC QOS ROUTING FOR LEO SATELLITE NETWORKS

Due to the diversified demands of quality of service（QoS） in volume multimedia application, QoS routings for multiservice are becoming a research hotspot in low earth orbit（LEO） satellite networks. A novel QoS satellite routing algorithm for multi-class traffic is proposed. The goal of the routing algorithm is to provide the distinct QoS for different traffic classes and improve the utilization of network resources. Traffic is classified into three classes and allocated priorities based on their QoS requirements, respectively. A priority queuing mechanism guarantees the algorithm to work better for high-priority classes. In order to control the congestion, a blocking probability analysis model is built up based on the Markov process theory. Finally, according to the classification link-cost metrics, routings for different classes are calculated with the distinct QoS requirments and the status of network resource. Simulations verify the performance of the routing algorithm at different time and in different regions, and results demonstrate that the algorithm has great advantages in terms of the average delay and the blocking probability. Meanwhile, the robustness issue is also discussed.

Shift control method for the local time at descendi ngnode based on sun-synchronous orbit satellite

This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the satellite orbit design and the orbit injection deviation are the causes for the initial shift velocity, whereas the atmospheric drag and the sun gravitational perturbation produce the shift acceleration. To deal with these shift factors, a shift control method is put forward, through such methods as orbit variation design, orbit altitude, and inclination keeping control. The simulation experiment and practical application have proved the effectiveness of this control method.

Analysis of detection capabilities of LEO reconnaissance satellite constellation based on coverage performance

In the design problem of low earth orbit(LEO) reconnaissance satellite constellation, optimization of coverage performance is the design goal in most current methods. However,in the using process, the user only concerns with the detection capabilities rather than coverage performance. To establish the relationship between these two aspects, the reconnaissance processes of normal stochastic targets are considered and the mathematic models of detection processes are built. The indicators of coverage performance are used to evaluate the detection probability and expectation of detection time delay, which are important factors in reconnaissance constellation estimation viewed from military intelligence discipline. The conclusions confirmed by the final simulation will be useful in LEO reconnaissance constellation design, optimization and evaluation.

A DISTRIBUTED QOS ROUTING BASED ON ANT ALGORITHM FOR LEO SATELLITE NETWORK

Low Earth Orbit (LEO) satellites provide short round-trip delays and are becoming in- creasingly important. One of the challenges in LEO satellite networks is the development of specialized and efficient routing algorithms. To satisfy the QoS requirements of multimedia applications, satellite routing protocols should consider handovers and minimize their effect on the active connections. A distributed QoS routing scheme based on heuristic ant algorithm is proposed for satisfying delay bound and avoiding link congestion. Simulation results show that the call blocking probabilities of this al- gorithm are less than that of Shortest Path First (SPF) with different delay bound.

Research on Autonomous Orbit Determination of Navigation Satellite Based on Crosslink Range and Orientation Parameters Constraining

Autonomous navigation of navigation satellite is discussed. The method of auto-orbit determination using the erosslink range and orientation parameters constraining is put forward. On the basis of the analysis of its feasibility, some useful conclusions are given.

Demonstration on the indexes design of gravity satellite orbit parameters in the low-low satellite-to-satellite tracking mode

Combining with the exigent demand of the development of satellite gravimetry system in China, aiming at the determination of technical indexes of gravity satellite orbit parameters, on the basis of the numerical experiments and results analysis, the design indexes of gravity satellite orbit height, inter-satellite range and the orbit inclination are analyzed and calculated, and the issues towards twin gravity satellites such as coherence requirement of the orbit semi-major axes, control requirement of the pitch angle and time interval requirement to keep twin satellites formation in mobility are diseussed. Results show that the satellite orbit height is 400 km to 500 km, the inter-satellite range is about 220 km, the satellite orbit inclination is between polar orbit and sun-synchronous orbit, the semi-major axes difference of twin satellites orbit is within ± 70. 146 m, the pitch angle of twin satellites is about 0.9 degree, and the time interval to keep twin satellites formation in mobility is 7 days to 15 days.

Evaluation of CHAMP Satellite Orbit with SLR Measurements

The technique of Evaluating CHAMP satellite orbit with SLR measurements is presented. As an independent evaluation of the orbit solution, SLR data observed from January 1 to 16, 2002 are processed to compute the residuals after fixing the GFZ’s post science orbits solutions. The SLR residuals are computed as the differences of the SLR measurements minus the corresponding distances between the SLR station and the GPS-derived orbit positions. On the basis of the SLR residuals analysis, it is found that the accuracy of GFZ’s post science orbits is better than 10 cm and that there is no systematic error in GFZ’s post science orbits.

Comparison of Linearized Kalman Filter and Extended Kalman Filter for Satellite Motion States Estimation

The performance of the conventional Kalman filter depends on process and measurement noise statistics given by the system model and measurements.The conventional Kalman filter is usually used for a linear system,but it should not be used for estimating the state of a nonlinear system such as a satellite motion because it is difficult to obtain the desired estimation results.The linearized Kalman filtering approach and the extended Kalman filtering approach have been proposed for a general nonlinear system.The equations of satellite motion are described.The satellite motion states are estimated,and the relevant estimation errors are calculated through the estimation algorithms of the both above mentioned approaches implemented in Matlab are estimated.The performances of the extended Kalman filter and the linearized Kalman filter are compared.The simulation results show that the extended Kalman filter is much better than the linearized Kalman filter at the aspect of estimation effect.

A Power Reduction Method for Pilot Channel of LEO Satellite Based on Dynamic Compensation

Since the lower power requirement of code division multiple access(CDMA) than that of other multiple access, the CDMA technology is suitable to be used in low earth orbit(LEO) satellite communication system whose space power is limited due to the small size of satellite. The pilot channel of CDMA technology is very important for earth mobile station(EMS) in LEO system to recover carrier and code, but the power requirement of pilot channel is very higher than that of other channels. In this paper, a power reduction method for pilot channel is proposed. By the new method, the power of pilot channel transmitted from LEO satellite is reduced to a lower level. For improving the signal to noise ratio(SNR) of pilot channel with lower power, coherent integration is employed in EMS at the pre-processing stage. Considering the high dynamic situation of LEO satellite, the long period of time for integration will deteriorate the receiving performance of EMS, therefore, a dynamic compensation module is added to carrier tracking loop against the high dynamic. Meanwhile, the transfer function of the new tracking loop and the condition for steadystate zero error are deduced. Numerical examples are provided to demonstrate effectiveness of the proposed approach.

Comparison between several satellite constellation schemes for MEO-TDRSS of China

The satellite constellation classes, which are suitable for the medium earth orbit tracking and data relay satellite system （MEO-TDRSS） of China, are investigated. On the basis of the functionality and the traffic distribution characteristic of MEO-TDRSS, the coverage performance and inter-satellite link properties of four different constellation schemes are compared by simulations. Simulation results indicate that the rosette and common-track constellations, whose satellites are distributed on the celestial sphere more uniformly, are appropriate for the implementation of MEO-TDRSS of China.

Long Range Wireless Sensor Network Employing Cooperative Relaying-UAVs via LEO Satellite

In this study we proposed unique system model for wireless sensor network data telemetry in a wide area and long range. This system is made up with a wide area wireless sensor nodes, UAVs （unmanned aerial vehicles） and LEO （low earth orbit） communication satellite. Wirelessly data signals relaying from sensor nodes on ground to flying UAVs and relaying them to LEO satellite were studied. Three cases of studies were conducted： system without UAV-relay case, one UAV-relay case and two UAV-relay cases. In all the cases, the outage probabilities of data signal channel in Rayleigh fading environment were analyzed and overall system performance was quantified while considering an adaptive decode-and-forward relaying protocol scheme for UAVs. Then, the overall system channel signal-to-noise ratio required in order to achieve a predefined outage probability was analyzed at different channel data rate.

Periodic orbits around areostationary points in the Martian gravity field

This study investigates the problem of areostationary orbits around Mars in three-dimensional space. Areostationary orbits are expected to be used to establish a future telecommunication network for the exploration of Mars. However, no artificial satellites have been placed in these orbits thus far. The characteristics of the Martian gravity field are presented, and areostationary points and their linear stability are cal- culated. By taking linearized solutions in the planar case as the initial guesses and utilizing the Levenberg-Marquardt method, families of periodic orbits around areo- stationary points are shown to exist. Short-period orbits and long-period orbits are found around linearly stable areostationary points, but only short-period orbits are found around unstable areostationary points. Vertical periodic orbits around both lin- early stable and unstable areostationary points are also examined. Satellites in these periodic orbits could depart from areostationary points by a few degrees in longitude, which would facilitate observation of the Martian topography. Based on the eigenval- ues of the monodromy matrix, the evolution of the stability index of periodic orbits is determined. Finally, heteroclinic orbits connecting the two unstable areostationary points are found, providing the possibility for orbital transfer with minimal energy consumption.

A Novel Probability-Based Handoff Strategy for Multimedia LEO Satellite Communications

A novel bandwidth allocation strategy and a connection admission control technique arc proposed to improve the utilization of network resource and provide the network with better quality of service （QoS） guarantees in multimedia low earth orbit （LEO） satellite networks. Our connection admission control scheme, we call the probability based dynamic channel reservation strategy （PDR）, dynamically reserves bandwidth for real-time services based on their handoff probability. And the reserved bandwidth for real-time handoff connection can also be used by new connections under a certain probability determined by the mobility characteristics and bandwidth usage of the system. Simulation results show that our scheme not only lowers the call dropping probability （CDP） for Class I real-time service but also maintains the call blocking probability （CBP） to certain degree. Consequently, the scheme can offer very low CDP for rcal-time connections while keeping resource utilization high.

Principal component analysis and cluster analysis based orbit optimization for earth observation satellites

This paper proposes a design optimization method for the multi-objective orbit design of earth observation satellites, for which the optimality of orbit performance indices with different units, such as: total coverage time, the frequency of coverage, average time per coverage and maximum coverage gap, etc. is required simultaneously. By introducing index normalization method to convert performance indices into dimensionless variables within the range of [0, 1], a design optimization method based on the principal component analysis and cluster analysis is proposed, which consists of index normalization method, principal component analysis, multiple-level cluster analysis and weighted evaluation method. The results of orbit optimization for earth observation satellites show that the optimal orbit can be obtained by using the proposed method. The principal component analysis can reduce the total number of indices with a non-independent relationship to save computing time. Similarly, the multiple-level cluster analysis with parallel computing could save computing time.

Simulation for MSS-2 low-perigee elliptical orbit satellites:an example of lithospheric magnetic field modelling

A future constellation of at least four geomagnetic satellites(designated Macao Scientific Satellite-1(MSS-1)and Macao Scientific Satellite-2(MSS-2))was recently proposed,to continue high-quality geomagnetic observations in the post-Swarm period,focusing especially on collecting data that will provide a global,three-dimensional survey of the geomagnetic field.In this paper,we present a simulation of two years of orbits(2020.01.01-2022.01.01)of two satellites(tentatively denoted as MSS-2)that are constellated in elliptical(200×5,300 km)low-perigee orbits.By comparing error variances of Gauss coefficients,we investigate the sensitivity of lithospheric magnetic field modelling to data collected from various satellite orbits,including a near circular reference orbit of 300×350km,and elliptical orbit of 180×5,300 km,220×5,300 km,200×3,000 km and 200×1,500 km.We find that in two years the two MSS-2 satellites can collect 35,000 observations at altitude below 250 km,data that will be useful in advancing the quality of lithospheric magnetic field modelling;this number of observations reflects the fact that only 4.5%of the flight time of these satellites will be below250 km(just 6.4%of their flight time below 300 km).By combining observations from the MSS-2 satellites’elliptical orbits of 200×5,300km with observations from a circular reference orbit,the variance of the geomagnetic model can be reduced by a factor of 285 at spherical harmonic degree n=200 and by a factor of 1,300 at n=250.The planned lower perigee of their orbits allows the new satellites to collect data at unprecedentedly lower altitudes,thus dramatically improving the spatial resolution of satellite-derived lithospheric field models,(up to 80%at n=150).In addition,lowering the apogee increases the time interval during which the satellites fly at near-Earth altitudes,thus improving the model predictions at all spherical harmonic degrees(around 52%-62%at n=150).The upper limit of the expected improvement to the field model at the orbital apogee is not as good as at the perigee.However,data from the MSS-1 orbit can help fill the gap between data from the MSS-2 orbits and from the circular reference orbit for the low-degree part of the model.The feasibility of even lower-altitude flight requires further discussion with satellite engineers.