Annotation This article provides an analysis of modern technical solutions for determining the angular orientation of small satellites in orbit. Problematic issues in improving the accuracy of the orientation and stabilization are considered. Using an additional radio navigation landmark, a new method has been devised to increase angular orientation determination reliability of the repeater satellites of the “distributed satellite” network that utilizes a Kalman filter. At the same time, it became possible to determine the orientation of the repeater satellites of the “distributed satellite” network with the usage of a measured signal value of an additional radio navigational landmark, the signal of which can be steadily received on board the root satellite.
the rapid development of this type of satellite are the relatively low cost and the insignificant time required for designing and manufacturing of small spacecraft (SSC), and the low cost of its launch.
microsatellites are used to capture images of the Earth in detail at a resolution of 6–10 m [
In addition, there are reasons for the increasing popularity of the SSC. SSCs provide miniaturization of onboard systems and the new circuit solutions related to multi-satellite groups. The use of SSCs has significantly reduced the mass of the devices and solved the problems that were traditionally carried out by “large” devices, particularly in the field of remote sensing and communications. SSCs are relatively inexpensive, easily modified to accommodate a particular task, create less radio interference, and provide a significant effectiveness increase of obtaining consumer surveillance data by creating a required number of small device groups. Their use helps to reduce the risks associated with orbital launch and space work by decreasing financial losses in the event of such a satellite’s failure or loss.
business organizations, and non-space companies, in general, have an opportunity to enter the space market. Overall, the development of the SSC technology could be considered as one of the fundamental drivers of the creation and development of a new generation of commercial space projects and companies.
technical and operational requirements: Low weight, size, energy consumption, and cost High reliability (operational life of SSC must be at least 5 years). Low complexity. Minimum time required for ground testing and launching preparation.
design contribute to a steep reduction in cost and ease of the development of new SSC models, but on the other hand it limits the level of their functionality compared to traditional spacecraft. Recently, targeted efforts have been made to expand SSC capabilities. However, despite the dynamic process of improving the characteristics of the pico and nano spacecraft, these devices cannot yet provide serious competition for well-developed traditional spacecraft.
problematic issue. The orientation accuracy of most of the currently launched single SSCs “CubeSat”
is limited and is about 10 [
include the organization of spacecraft flight in low Earth orbit in a “formation” or “swarm” [
development of a low-orbit satellite communications system, which is a group of low-orbit spacecraft
(LEO-system) with a “distributed satellite” architecture [
Fig. 1 reflects 1, 2 are root satellites; 3–8 are satellite repeaters of micro-group A; 9, 10 are distributed satellites of micro-group A; 11, 12 are feeder lines of micro-group A; 13 - a service area of the satellite communication system; 14, 15 are feeder lines of micro-group B; 16, 17 are distributed satellites of the micro-group B; 18–23 are satellite repeaters of micro-group B; 24 is inter-satellite terahertz line between distributed satellites.
architecture is new, so to ensure their further practical use, special attention should be paid to the synthesis of algorithms and methods in order to increase the structural and functional reliability of determining the angular orientation of the repeater satellites of the “distributed satellite” network.
The aim of this article is to develop a method for determining the angular orientation of small satellites in orbit. This will increase the structural and functional reliability of determining the angular orientation of repeater satellites of the “distributed satellite” network that utilizes a Kalman filter.
There is a method for determining the angular orientation of the object by using the navigational
radio signals of the navigation spacecraft (NSC) of global navigation satellite systems (GNSS). This
method is based on the reception of signals from one or more NSCs by two or more antenna receivers
that are parallel to one or two axes of the object, signal selection with Doppler frequency, determining
the phase difference for the time interval measurement and determining the angular orientation of the
object. During the time interval measurement, several estimations of the phase difference between the
pairs of antennas are performed, and the angular orientation of the object is determined by solving a
system of equations [
method consists in measuring the linear parameters of at least one GNSS NSC moving along a known
orbital trajectory, forming correction parameters vector accordingly to the obtained data, repeating
these operations at successive time intervals, and correcting the inertial navigation system (INS) using
the generated correction parameters [
the propulsion system of the spacecraft, which, firstly, leads to the consumption of energy resources and reduction of the lifetime of the spacecraft. Secondly, it limits the use of the spacecraft for its intended purpose during the activation period of the propulsion system, as well as the periods of preparatory and final operations that are necessary to create the apparent acceleration.
parameters of two stars using optical sighting telescopes [
The drawbacks of the NSI correction method of measuring the relative two-star angle parameters are: 1. The possibility of illumination of optical devices.
2. The need to carry out preliminary operations for the scheduling of measurement sessions, including the complex processing of the star catalog, in order to determine the reference stars for measuring direction vectors for which there are favorable conditions for orbital flight, excluding the illumination of optical telescopes.
necessary accuracy in determining the orientation parameters, during which the use of the spacecraft for the intended purposes is limited.
There is a well-known domestic technical solution [
The geometric size of a “distributed satellite” is the area around a root satellite with a radius of about 1 km. This means that the CubeSat’s carry out a group flight at a distance less than 1 km from the root satellite. The space segment of the LEO system consists of different orbital planes with the same number of distributed satellites, the same method, and differing in the length of the ascending node. In each orbital plane, the distributed satellites are evenly spaced with the same relative true anomaly, with each distributed satellite connected to the two adjacent distributed satellites in its orbital plane and the two nearest distributed satellites in the two adjacent orbital planes - one in each orbital plane.
orbit satellite radio system for the provision of quality services in integrated 5G and IoT networks.
2.2.
The technical result obtained by this method shows the increased reliability in determining the angular orientation of the repeater satellites of the “distributed satellite” that utilizes a Kalman filter due to the additional radio navigation landmark and the ability to determine the orientation of the satellite repeaters according to the measured value of the signal of the additional radio navigation landmark, the signal of which can be steadily received on board of the root satellite. In addition, the application of the proposed method allows controlling the parameters of the orientation of the INS for most of the time of the orbital flight by determining the systematic error of inertial orientation and then, if necessary, adjust the parameters of the spatial inertial orientation of the INS by making corrections.
The essence of the proposed method can be explained as follows: suppose that the onboard equipment of the group of the root (leading) satellites (SC) and repeater satellites (slave) of the satellite network of the “distributed satellite” includes INS. In this way, it is assumed that as appropriate signal sources to determine the orientation of the SC, NSC GNSS or terrestrial stationary radio stations could be used, the signal of which can be reliably received by the onboard equipment of the SC. The spatial orientation of the coordinate axes of the connected coordinate system of the root (leading) satellites is carried out according to the data from INS and at some flight interval t, the angular position control system orients the connected coordinate axes of the root (leading) satellites parallel to the axes of the orbital coordinate system.
The position orientation system in the orbit of the repeater satellites of the low-orbit satellite micro-grouping system “distributed satellite” operates as follows: a scanning radio photon radar is installed on the root satellite, and the miniature optical sensors are installed on the repeater satellites, which are located on the sides of the satellites by groups. On each side panel, the location of such a group should be unique, thus the exact side and precise repeater satellite location in space will be determined. Knowing the size of the observed satellites and the exact location of the miniature optical sensors on each facet, it is possible to determine the coordinates of the vertices of the CubeSat in relation to the root satellite. 2.2.1. The
for Determining the
follows: the OY axis is directed vertically upwards, the OX axis is in the direction of the satellite’s motion, and the OZ axis is on the right for an observer looking along the OX axis. The position of the slave satellite-repeater relative to the master (root) is determined by three Euler angles. Let’s determine the matrices of the guide cosines in the transition from the original coordinate system OXYZ to the coordinate system
, associated with the body of the master satellite. First, consider the rotation of the satellite from its original position relative to the OX axis at an angle ψ counterclockwise, if it is observed from the positive part of the OY axis:
Y’, Z’. observed from the positive side of the intermediate axis OZ’:
The matrix Aψ is an operator that converts the initial coordinates X, Y, Z into the coordinates X’, Similarly, consider the rotation at an angle ϑ relative to the axis OY’ counterclockwise when ]
= [ ] = [
]
= ^
[
] = [ ′ ′ ′] = [ ′′ ′′ ′′] = [ ] where the matrix A is the desired transformation matrix from the initial coordinate system OXYZ to the coordinate system
associated with the root satellite. The result is the following:
In this case, matrix A will have a certain structure. And since the matrix of guide cosines A is orthogonal, the inverse matrix B can also be determined: (1) (2) (3) (4) (5) (6) (7) [ ] = [
]
the near radar, in which the oscillations received in the radar station are sampled in an
analog-todigital converter. Then the envelope of the received signal with a large signal-to-noise ratio is
allocated. Next, the time delay of the received signal up to the sampling period is determined, which
shows the distance to the target [
at high signal-to-noise ratios. In addition, the sampling rate must be selected for specific signal parameters, as the errors of the signal phase measurement depend on the sampling rate. Therefore, it is necessary to determine the sampling frequency intervals at which the phase difference is measured most accurately. The authors do not provide a method for selecting the sampling frequency, so the practical application of this method is difficult.
the radio signal to measure the distance to the micro-grouping of repeater satellites.
Suppose that at some interval of analysis there is an addictive mixture of useful signal and noise: where ( ) is white Gaussian noise with spectral density 0, ( ) = ( , 0, , 0
) + ( ), ( , , , ) = ( − ) cos( 0 − ), where s(t, τ, A, μ) is a useful signal of duration ; , is a priori unknown amplitude and phase of the signal, approximately constant in the interval of signal duration; 0 is carrier circular frequency; ( ) is an a priori unknown function, which is determined in the general case by the digital sequence used, as well as the band-limiting signal filter; is the unknown time position of the signal from the a priori interval [0,
in (9) is estimated, and the unknown parameters of the signal , - are
accompanying. In the presence of accompanying parameters, it is necessary to
maximize the
functionality of the likelihood ratio for these parameters. The decision is made in favor of the value of
the time position at which the maximized likelihood ratio takes the greatest value [
The logarithm of the maximized likelihood ratio functional in estimating the time position will look like the following: + + ( ) =
2 0
( 12( ) + 22 ( )), 1 ( ) =
∫ ( ) ( − ) cos( 0 ) 2 ( ) =
∫ ( ) ( − ) sin 0 )
Estimation of the maximum plausibility of the parameter is based on the position of the maximum of the output signal (11) (8) (9) (10) (11) = arg sup ( ) ∈ [0,
].
Usually, the receiver produces (11) not for all, but only for discrete values , = 1, from the a priori interval [0,
] shifted relative to each other by some value . The decision on the value of the time position is made by the channel number with the largest output signal (11), so the value is used for an estimation where:
( ) ≥ ( ), ≠ , = 1, . estimate the time position.
parameters of the useful signal and noise but also on the value of the discrete ∆. It can be shown that the following approximate expression is valid for the time position estimation dispersion from which it follows that the accuracy of the estimation, in this case, is significantly limited by the discrete ∆. In this regard, the authors propose to improve the accuracy of the temporal position estimation of the signal by using several values of the decisive function (11).
with the maximum value of the decisive function ( ) is selected. In addition, the values of the crucial function of adjacent time positions ( −1), ( +1) are taken. We use quadratic interpolation to the interpolation algorithm on the signal-to-noise ratio z. The results of calculations are obtained by computer simulations for different values of the number of discrete output signals of the receiver for chip duration . (12) (13) the interpolation algorithm on the signal-to-noise ratio z for different values of the number of discrete output signals of the receiver on the chip duration .
2.3.
shown in Fig. 3.
the micro-grouping of satellite repeaters (additional radio navigation landmark), 7 is an infrared device.
satellite and its speed calculated by a set of inertial sensors 4, GPS - receiver 2, and an additional unit
extended period of time regardless of the state of the GPS receiver 2.
The equation of observations for such an architecture can be written as: where = 1 − 2 − 3 is an observation vector; 1 = [ 1 1 ] is a vector of body position and velocity, which is estimated by the GPS receiver at time k; 2 = [ 2 2 ] is a vector of body position and velocity, which is estimated in INS at time k; 3 = [ 3 3 ] is a vector of body position and velocity, which is estimated by an additional radio navigation landmark at time k; is the observation matrix for the proposed architecture will have the following form: = +
= [ 3 0 3
(14)
(15)
orientation requires the device’s motion determination relative to the center of mass in real-time.
Recursive algorithms for estimating motion parameters such as the Kalman filter [
determination reliability of repeater satellites of the satellite network “distributed satellite” that utilizes a Kalman filter. The effect is achieved by using additional radio navigational landmarks and the ability to determine the orientation of repeater satellites according to the measured value of the signal of the additional radio navigation landmark, the signal of which can be steadily received on board the root satellite.
network and increase the efficiency of tasks according to the mission, it is proposed to transfer the channel for measuring orbital motion parameters and flight control of repeater satellites to the root satellite network, which is a new method and has never been used in world practice.
Thus, using the proposed method it is possible to achieve, above all, the following advantages: along with the high accuracy of the three-dimensional positioning solution, it is possible to simultaneously achieve high availability, continuity, and integrity of the solution of the positioning problem within a limited spatial area. The possibility of achieving a high speed of updating solutions for positioning problems is provided. 4. References