Key Generation Method Based on Multi-Satellite Cooperation and Random Perturbation

In low-earth-orbit (LEO) satellite-to-ground communication, the size of satellite antennae is limited and the satellite motion trajectory is predictable, which makes the channel state information (CSI) of the satellite-to-ground channel easy to leak and impossible to use to generate a physical layer key. To solve these problems, we propose a key generation method based on multi-satellite cooperation and random perturbation. On the one hand, we use multi-satellite cooperation to form a constellation that services users, in order to increase the equivalent aperture of satellite antennae and reduce the correlation between the legal channel and the wiretap channel. On the other hand, according to the endogenous characteristics of satellite motion, a random perturbation factor is proposed, which reflects the randomness of the actual channel and ensures that the CSI of the legal channel is not leaked due to the predictability of satellite motion trajectory. Simulation results show that the proposed method can effectively reduce the leakage of the legal channel’s CSI, which makes the method of physical layer key generation safe and feasible in the LEO satellite-to-ground communication scene.

Minimum altitude variation orbits. Analysis of characteristics and stability

The article discusses the regularities of satellite motion in almost circular orbits under the influence of the second zonal harmonic of the geopotential. The aim of the research is to determine the parameters of orbits with a minimum change in radius and to study the properties of these orbits. It is shown that the problem of determining the parameters of orbits with a minimum change in radius is of theoretical and practical interest. These orbits are the closest to Keplerian circular orbits. The practical interest in such orbits is determined by the possibility of using them for scientific research and Earth observation systems. Based on the analysis of the literature, it was concluded that the solution of the problem under consideration is not complete by now: the algorithm for determining the parameters of the orbits are not well founded and unnecessarily complicated; there is no analytical analysis of the stability of the orbits of the minimum change in radius. The efficiency of application of the previously developed theory of describing the motion of satellites in almost circular orbits for determining the parameters of orbits with a minimum change in radius is shown. For this purpose, the solutions of the first approximation of the motion of satellites in almost circular orbits under the influence of the second zonal harmonic of the geopotential have been improved. These solutions make it easy to determine the parameters of the orbits of the minimum change in radius. The averaged equations of the second approximation of the influence of the second zonal harmonic on the satellite motion are constructed and, on their basis, the stability of the orbits with a minimum change in radius is proved. It is shown that the second approximation in small parameters completely describes the main regularities of the long-period satellite motion under the influence of the second zonal harmonic of the geopotential. With the help of numerical studies, the instability of orbits with a minimum change in radius is shown with allowance for the effect of higher order harmonics of the geopotential. Analysis of the area of possible application of orbits with a minimum change in radius showed that such orbits can be of practical importance for very low and ultra low orbits, where the control action on the satellite movement is carried out at least once every two days.

Transient Attitude Motion of TNS-0#2 Nanosatellite during Atmosphere Re-Entry

Attitude motion reconstruction of the Technological NanoSatellite TNS-0 #2 during the last month of its mission is presented in the paper. The satellite was designed to test the performance of the data transmission via the Globalstar communication system. This system successfully provided telemetry (even during its atmosphere re-entry) up to an altitude of 156 km. Satellite attitude data for this phase is analyzed in the paper. The nominal satellite attitude represents its passive stabilization along a geomagnetic field induction vector. The satellite was equipped with a permanent magnet and hysteresis dampers. The permanent magnet axis tracked the local geomagnetic field direction with an accuracy of about 15 degrees for almost two years of the mission. Rapid altitude decay during the last month of operation resulted in the transition from the magnetic stabilization to the aerodynamic stabilization of the satellite. The details of the initial tumbling motion after the launch, magnetic stabilization, transition phase prior to the aerodynamic stabilization, and subsequent satellite motion in the aerodynamic stabilization mode are presented.

Analytic Inversion of Closed form Solutions of the Satellite’s J2 Problem

This report provides some closed form solutions -and their inversion- to a satellite’s bounded motion on the equatorial plane of a spheroidal attractor (planet) considering the J2 spherical zonal harmonic. The equatorial track of satellite motion- assuming the co-latitude φ fixed at π/2- is investigated: the relevant time laws and trajectories are evaluated as combinations of elliptic integrals of first, second, third kind and Jacobi elliptic functions. The new feature of this report is: from the inverse t = t(c) we get the period T of some functions c(t) of mechanical interest and then we construct the relevant c(t) expansion in Fourier series, in such a way performing the inversion. Such approach-which led to new formulations for time laws of a J2 problem- is benchmarked by applying it to the basic case of keplerian motion, finding again the classic results through our different analytic path.

A study of polarimetric error induced by satellite motion: application to the 3MI and similar sensors

This study investigates the magnitude of the error introduced by the co-registration and interpolation in computing Stokes vector elements from observations by the Multi-viewing, Multi-channel, Multi-polarisation Imager (3MI). The Stokes parameter derivation from the 3MI measurements requires the syntheses of three wide-field-of-view images taken by the instrument at 0.25 s interval with polarizers at different angles. Even though the synthesis of spatially or temporally inhomogeneous data is inevitable for a number of polarimetric instruments, it is particularly challenging for 3MI because of the instrument design, which prioritizes the stability during a long life cycle and enables the wide-field-of-view and multiwavelength capabilities. This study therefore focuses on 3MI's motion-induced error brought in by the co-registration and interpolation that are necessary for the synthesis of three images. The 2-D polarimetric measurements from the Second-generation Global Imager (SGLI) are weighted and averaged to produce two proxy datasets of the 3MI measurements, with and without considering the effect of the satellite motion along the orbit. The comparison of these two datasets shows that the motion-induced error is not symmetric about zero and not negligible when the intensity variability of the observed scene is large. The results are analyzed in five categories of pixels: (1) cloud over water, (2) clear sky over water, (3) coastlines, (4) cloud over land, and (5) clear sky over land. The most spread distribution of normalized polarized radiance (Lp) difference is in the cloud-over-water class, and the most spread distribution of degree of linear polarization (DOLP) difference is in the clear-sky-over-water class. The 5th to 95th percentile ranges of Lp difference for each class are (1) [-0.0051,0.012], (2) [-0.0040,0.0088], (3) [-0.0033,0.012], (4) [-0.0033,0.0062], and (5) [-0.0023,0.0032]. The same percentile range of DOLP difference for each class are (1) [-0.023,0.060], (2) [-0.043,0.093], (3) [-0.019,0.082], (4) [-0.0075,0.014], and (5) [-0.011,0.016]. The medians of the Lp difference are (1) 0.00035, (2) 0.000049, (3) 0.00031, (4), 0.000089, and (5) 0.000037, whereas the medians of the DOLP difference are (1) 0.0014, (2) 0.0015, (3) 0.0025, (4) 0.00027, and (5) 0.00014. A model using Monte Carlo simulation confirms that the magnitude of these errors over clouds are closely related to the spatial correlation in the horizontal cloud structure. For the cloud-over-water category, it is shown that the error model developed in this study can statistically simulate the magnitude and trends of the 3MI's motion-induced error estimated from SGLI data. The obtained statistics and the simulation technique can be utilized to provide pixel-level quality information for 3MI Level 1B products. In addition, the simulation method can be applied to the past, current, and future spaceborne instruments with a similar design.

Averaging technique in the problem of satellite attitude stabilization in indirect position in the orbital reference frame with the use of Lorentz torque

A dynamically symmetric satellite in a circular orbit of small inclination is considered. The problem of the Lorentzian stabilization of the satellite in the orbital coordinate system in the indirect equilibrium position is solved under the conditions of the perturbing effect of the gravitational torque. To solve this problem, which is characterized by incomplete control, a method of averaging differential equations is developed. Using the original construction of the unsteady Lyapunov function, we obtain sufficient conditions for the asymptotic stability of the programmed satellite motion mode in the form of constructive inequalities with respect to the control parameters.