As more spacecraft are launched into the Geostationary Earth Orbit (GEO) belt, the possibility of fatal collisions or unnecessary interference between spacecraft increases. In this paper, a new location-awareness method that uses CubeSats is proposed to assist with radiofrequency (RF) domain verification by means of awareness and identification of the positions of the spot beam emitters of communications satellites in geostationary orbit. By flying a CubeSat (or a constellation of CubeSats) through the coverage area of a spot beam, the spot beam emitter’s position is identified and the spot beam’s pattern knowledge is characterized. The geometry, the equations of motion of the spacecraft, the measurement process, and the filtering equations in a location system are addressed with respect to the location methods investigated in this study. A realistic scenario in which a CubeSat receives signals from GEO communications satellites is simulated using the Systems Tool Kit (STK). The results of the simulation and the analysis presented in this study provide a thorough verification of the performance of the location-awareness method.
As space becomes an increasingly congested, contested, and competitive environment, the need for enhanced space-based capabilities only increases over time [
To verify and monitor the global RF signal usage of satellites in the GEO belt, the traditional approach takes advantage of a wideband spectrum receiver at a fixed ground station terminal [
In another study, Bentley investigated RF signal geolocation techniques applied to geostationary satellites. This technique focused on the use of time difference of arrival (TDOA) and frequency difference of arrival (FDOA) to locate interference [
The shortcomings of the above processes, which are currently used to identify the emitter locations of GEO communications satellites, call for a more active and robust GEO spot beam emitter location-awareness method. In this paper, we propose a new location-awareness method that uses a CubeSat to locate the spot beam emitters of geostationary communications satellites. Section
In this section, first, the geometry used in the spot beam emitter location awareness is described. Then, the spacecraft dynamics and the measurement process associated with the onboard sensor are discussed. Finally, the extended Kalman filter (EKF) estimation algorithm is applied to estimate the position and velocity of a GEO communications satellite’s emitter.
In this paper, a novel approach that involves flying a CubeSat through spot beams of an emitter at the altitude of an LEO is adopted to identify the location of a spot beam emitter. Figure
Awareness method of locating a GEO signal emitter.
The model for the location-awareness system is set up in the standard J2000 Earth centered inertial (ECI) reference frame. The communications satellite and the CubeSat are regarded as two particles that move in response to Earth’s gravity. The details are given in Figure
Geometry of the location-awareness system.
In the J2000 ECI reference frame’s coordinates, the position and velocity vectors for the communications satellite are expressed as
Normally, we assume that Earth and a satellite can be considered a sphere and a particle, respectively, and that they constitute a two-body system. In the two-body system, the satellite is affected by Earth’s gravity. The gravity (
According to Newton’s second law, the satellite’s motion is expressed as follows:
The parameters of the spacecraft’s motion at time
Furthermore, the state vector of the spacecraft’s motion can be derived as follows:
In the two-body problem, substituting (
It should be noted that (
To obtain a measurement for the spot beam emitter of a geostationary communications satellite, it is necessary to have a bearing sensor onboard the CubeSat and to obtain the position information of the CubeSat. The location-aware CubeSat, during a notional orbit, is expected to physically fly through a large number of spot beams with coverage areas of various sizes. Once the emitter signal is detected, the CubeSat with a bearing sensor measures azimuth and elevation angles of the incoming signals and outputs position information at the same time. The position of the CubeSat can be obtained from the GPS receiver mounted on it [
Overall emitter and CubeSat geometry showing azimuth and elevation angles.
It should be noted that (
Furthermore, the measurement matrix defined by (
The state transition vector is given by
The corresponding filter estimate of the state error covariance is given by
The nonlinear measurement equations are rewritten with additive measurement noise as
Computing the partial derivative of nonlinear equations (
The linearized form of the nonlinear measurement matrix becomes
The Kalman gain can be calculated as follows:
The state estimate and error covariance are updated using (
The CubeSat location-awareness process was modeled using the Systems Tool Kit (STK) to simulate a scene in which a CubeSat receives signals from GEO communications satellites, and bearing data and the CubeSat’s position can be obtained from it. The Intelsat Galaxy 28 (G-28) GEO satellite was chosen for modeling in the Ku-band. The G-28 satellite maintains spot beams within the Ku-band and the C-band [
Since most companies do not publish exact antenna and transmission power levels due to their proprietary nature, typical antenna sizes for the simulated K-band beams were assumed in this paper [
Modeled G-28 emitter of beams in the Ku-band.
A special case beam used the same antenna size as that of the Ku-band beams but had a frequency that was increased from the base Ku-band (12 GHz) to the Ka-band (30 GHz). Increasing the transmission frequency reduced the HPBW and thus reduced the beam’s coverage area [
Modeled G-28 emitter of beams in the Ka-band.
Using G-28 as the basic GEO communications satellite for the CubeSat location-awareness scenario, a CubeSat was then added to the scenario as the monitoring satellite. Note that the CubeSat location-awareness model was built based on the fact that GEO satellite beams can be detected and mapped under the best monitoring conditions. This is because the best beam pattern knowledge can be gained. Therefore, it is necessary to satisfy the basic constraints on CubeSat constellations and orbits mentioned in another paper [
Constraints for the CubeSat constellations and orbits.
Constellation altitude: | 350 km–500 km |
Constellation inclination: | 68 degrees |
Payload sampling rate: | 1 s per data point |
CubeSat planes: | 2 planes |
Number of CubeSats: | 3 satellites |
Duration: | 3 days |
After modeling the CubeSat location awareness, the positions of the CubeSat and the GEO satellite were collected whenever the CubeSat received a signal from the GEO emitter. Finally, this position information was converted into bearing measurement data and then exported to MATLAB for verification of the location algorithm.
The CubeSat location-awareness model was run for three days using the STK. The simulation results indicated that the CubeSat received a signal from the GEO satellite many times and that the duration of each signal reception was less than 1200 s. A set of data for the CubeSat and the GEO satellite geometry was chosen for the analysis of the final positioning results, shown in Figure
CubeSat and GEO satellite geometry.
As discussed in the previous section, the satellite’s motion is complex and nonlinear. As an approximation method, we considered the two-body problem with constant acceleration between two samplings. However, this approximation method could produce position errors in the location-awareness process. The errors were calculated by comparing the state model established by (
State model error.
To check the performance of the EKF, the algorithm was tested in three different cases for the Ku-band beam model. The simulation time was set to 1200 s, and the filtering cycle was 1 s long. The initial position error was fixed at 106 m in the first case. To simulate the data measurement errors, the raw bearings were corrupted by additive zero-mean Gaussian noise prior to processing. Three different noise levels were used to analyze the position and velocity errors. Figure
RMSEs of the position and velocity for a measurement noise level of 0.01°.
RMSEs of the position and velocity for a measurement noise level of 0.05°.
RMSEs of the position and velocity for a measurement noise level of 0.1°.
Figures
Simulation results for the different noise levels.
Noise level, |
RMSE convergence value, m | Convergence time, s |
---|---|---|
0.01 | 962 | 672 |
0.05 | 2126 | 923 |
0.1 | 8294 | 926 |
In the second case, the initial position error was simulated with the maximum value (107 m), and the measurement noise level was set to 0.01°. Figure
RMSEs of the position and velocity in the second case.
In the third case, an initial error of 100 m/s in the velocity was added to the simulation. The initial position error was set to 106 m, and the simulated measurement noise level was 0.01°. The RMSEs of the position and velocity are depicted in Figure
RMSEs of the position and velocity in the third case.
As in the previous results, the RMSEs of the position and velocity converge to steady-state values as the time of measurement increases. However, a longer time is required for convergence, and a greater error magnitude is found when the initial error in the velocity is added to the simulation. Furthermore, the results presented here demonstrate that the performance of the location-awareness method is affected by the initial state error. As a result, further improvements to the algorithms will be made to reduce the influence of the initial state error and enhance the convergence speed.
The time required for the CubeSat to receive a Ka-band beam emitter signal is less than 180 s, according to the location-awareness model result obtained using the STK. The simulation data for the Ka-band beam emitter were output and then simulated using MATLAB. In this simulation, the initial position error was 106 m. In Figure
RMSEs of the position and velocity for the Ka-band beam emitter.
In this paper, a location-awareness method that uses a CubeSat was proposed as a new approach to monitor and identify the emitters of GEO communications satellites on a global scale. The proposed work represented a preliminary analysis of the problem. A realistic scenario in which a CubeSat receives signals from GEO communications satellites was simulated using the STK, through which bearing and position data were collected. The geometry, the spacecraft equations of motion, the measurement process, and the EKF equations in a location system were addressed with respect to the location methods investigated in this study. The results of the simulation and the analysis presented in this study provide a thorough verification of the location-awareness method’s performance.
The bearing measurement accuracy and the initial state error are two critical parameters that impact the capability of the location-awareness method significantly. Therefore, to satisfy the performance requirement of the location-awareness method, the bearing measurement is required to be accurate to within 0.01°, and the initial position error is required to be less than 106 m. As a difficult case, the positon of a Ka-band beam emitter was estimated successfully to show that the method is suitable for emitters with various frequencies. Most importantly, no evidence of instability was observed in all tests. Therefore, it is concluded that the location-awareness method offers an active solution for monitoring and identifying the emitters of GEO communications satellites.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work is sponsored by the Natural Science Foundation of China (Grant no. 61471021) and the China Academy of Launch Vehicle Technology Foundation. The authors would like to thank Lina Bao of Tianjin University of China for her invaluable advice.