CN111596306B - High-orbit space debris laser ranging satellite constellation design method - Google Patents
High-orbit space debris laser ranging satellite constellation design method Download PDFInfo
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- CN111596306B CN111596306B CN202010466828.1A CN202010466828A CN111596306B CN 111596306 B CN111596306 B CN 111596306B CN 202010466828 A CN202010466828 A CN 202010466828A CN 111596306 B CN111596306 B CN 111596306B
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- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S17/00—Systems using the reflection or reradiation of electromagnetic waves other than radio waves, e.g. lidar systems
- G01S17/02—Systems using the reflection of electromagnetic waves other than radio waves
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- G01S17/08—Systems determining position data of a target for measuring distance only
- G01S17/32—Systems determining position data of a target for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated
Abstract
The invention discloses a high-orbit space fragment laser ranging satellite constellation design method, which is characterized in that a satellite constellation is designed to be distributed and arranged on a spherical surface where a geosynchronous orbit is located, the number of satellites is 3 or 4, and the distances between every two satellites are the same; a laser ranging system carried by each satellite in the constellation selects a laser with a kHz repetition frequency; and designing a constellation detection signal-to-noise ratio related to the laser pulse repetition frequency f as an objective function of laser parameter selection to obtain a single-pulse energy minimum value required by the laser carried by the satellite to successfully identify the diffuse reflection echo of the high-orbit space debris, and configuring the laser according to the single-pulse energy minimum value.
Description
Technical Field
The invention relates to the technical field of space debris measurement, in particular to a high-orbit space debris laser ranging satellite constellation design method.
Background
The space debris seriously influences the operation safety of the in-orbit spacecraft, and the accurate measurement of the distance of the in-orbit spacecraft is of great significance to the accurate orbit determination and safe avoidance of the space debris.
In an actual process, a ground-based space debris laser ranging station firstly predicts an orbit according to space debris and then emits laser pulses, and the accurate distance of the space debris is calculated according to the flight time of the laser pulses between the ranging station and the space debris. And analyzing the position error of the space debris by matching with parameters such as system pointing directions, laser divergence angles and the like of a plurality of ranging stations. And further analyzing the precise orbit information of the space debris by combining the forecast orbit and the position error, and predicting the future operation orbit of the space debris. The above processes are repeated to realize effective forecasting of the space debris orbit, guide the in-orbit spacecraft to safely avoid the space debris orbit and the like. The laser ranging position error of the space debris is improved, and the method has direct significance for the precise orbit determination of the space debris and the operation safety of an on-orbit aircraft.
At present, space debris laser ranging is carried out by depending on a ground laser ranging station, and low-orbit space debris laser ranging can be realized. However, when the high-orbit space debris measurement is carried out, the distance between the high-orbit space debris and the ground-based ranging station is 42164km, while the radius of the earth is only 6400km, which means that the debris distance is far greater than the mutual distance between the ground-based ranging stations. At this time, the space debris spacing stations are not widely distributed, each ground laser ranging station is similar to the same laser ranging station which emits laser to the high-orbit space debris, and the position error of the measured space debris echo is very large, as shown in fig. 1. The real space debris is M points, but because of the pointing error of a distance measuring system and the influence of a laser divergence angle, the measured space debris can be distributed in the whole shadow area, the azimuth error of the shadow area reaches several kilometers, and the precision orbit determination precision of the space debris is limited.
In addition, the ground-based laser ranging system is seriously influenced by the atmosphere, the laser energy attenuation is high, the sky light background noise is strong, the laser intensity reaching space debris is very weak, the measurable space debris distance is limited, and the capability of measuring the high-orbit space debris is insufficient. The space-based space debris laser ranging satellite system is developed, and has important significance for improving the space debris measuring distance and the space debris measuring position error.
Disclosure of Invention
In view of this, the invention provides a high-orbit space debris laser ranging satellite constellation design method, which can improve the measurement distance and reliability of space debris and reduce laser energy and measurement errors required by ranging.
In order to solve the technical problem, the invention is realized as follows:
a high orbit space debris laser ranging satellite constellation design method, the satellites in the satellite constellation are distributed in a distributed manner and are deployed on the sphere where the geosynchronous orbit is located, the number of the satellites is 3 or 4, and the distances between every two satellites are the same;
a laser ranging system carried by each satellite in the constellation selects a laser with a kHz repetition frequency; designing a constellation detection signal-to-noise ratio related to a laser pulse repetition frequency f as an objective function of laser parameter selection to obtain a single pulse energy minimum value E required by a laser carried by a satellite to successfully identify a high-orbit space debris diffuse reflection echotAccording to the minimum value of energy E of a single pulsetConfiguring a laser;
the laser ranging system carried by each satellite in the constellation mainly comprises a laser, an optical system and a detector; n is the dark count rate of the detector, τ is the single pulse width of the laser, h is the Planck constant, c is the speed of light, θtThe divergence angle of the optical system, R is the distance between the space debris and the satellite, SNR is the required signal-to-noise ratio of constellation detection, lambda is the laser wavelength, and D is the transmitting/receiving aperture of the optical systemρ is the average diffuse reflectance of the space debris, and σ is the equivalent cross-sectional area of the space debris.
When the three-star constellation design is adopted, the constellation is deployed on the earth stationary orbit, three satellites form an equilateral triangle configuration, the distance between every two satellites is 73030km, and the longitude of the points under the satellite is separated by 120 degrees.
When the four-satellite constellation design is adopted, the constellation is deployed on a spherical surface where a geosynchronous orbit is located, four satellites form a regular triangular pyramid configuration, and the distance between every two satellites is about 68854 km.
Has the advantages that:
(1) the invention designs a laser ranging satellite constellation for measuring space debris distance. The constellation works in the space environment, the problem that a ground space debris laser ranging system is interfered by the atmosphere can be avoided, and the detectable target distance is farther.
(2) The constellation adopts the distributed design, and the satellite number is not less than 3, separates 4 ten thousand kilometers each other more, compares in ground laser ranging system, and the range finding point distributes more extensively, helps obtaining space piece distance information from different angles, reduces space piece position distribution error, obtains more accurate space piece position information, and the position error can be improved to the meter level from the kilometer level, promotes 3 orders of magnitude, and volume position error can promote 6 orders of magnitude.
(3) The constellation detection signal-to-noise ratio related to the laser pulse repetition frequency f is used as a target function for selecting laser parameters, and the single pulse energy minimum value of the laser carried by the satellite is designed, so that the required laser energy is greatly reduced on the basis of realizing laser ranging of space fragments on the circular surface of the whole geosynchronous orbit.
Drawings
FIG. 1 is a schematic diagram of a position error caused by high-orbit space debris measured by a ground-based laser ranging station.
Fig. 2 is a schematic diagram of the distribution of the three-star constellation of the high-orbit space fragmentation laser ranging satellite (the left diagram is an xyz three-dimensional space perspective diagram, and the right diagram is an xy plan diagram).
Fig. 3 is a schematic diagram of distributed distribution of subsatellite points of a three-star constellation of a high-orbit space fragmentation laser ranging satellite.
Fig. 4 is a schematic diagram of the increase of the position error caused by the coplanarity of the space debris and the samsung constellation (the left diagram is an xyz three-dimensional space perspective diagram, the middle diagram is an xy plane diagram, and the right diagram is a yz plane diagram).
Fig. 5 is a schematic diagram of a four-star distributed distribution of a high-orbit space debris laser ranging satellite constellation.
Fig. 6 is a schematic diagram of constellation geometry of high-orbit space debris and laser ranging satellites and a position relationship under an xyz coordinate system.
FIG. 7 is a schematic diagram of the maximum distance between the space debris and the range finder star in the laser ranging of the space debris on the high rail.
Fig. 8 shows the distribution of echoes and noise (black dots indicate echoes, and gray dots indicate noise).
FIG. 9 is a schematic view of a spatial debris position error pie intersection.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a high-orbit space debris laser ranging satellite constellation design method which comprises three parts, namely satellite constellation configuration design, satellite carried laser key parameter design and laser ranging efficiency analysis. The first two parts represent design ideas and design results, and laser ranging efficiency analysis represents design effects.
One, satellite constellation configuration design
The space debris laser ranging satellite constellation mainly follows a distributed design principle, namely, satellites among the constellation are distributed in a distributed mode and are deployed on a spherical surface where a geosynchronous orbit is located, the number of the satellites in the constellation is 3-4, the distances between every two satellites are the same, and a geometric configuration can be formed on a space position with space debris needing ranging.
According to the number of satellites in the constellation, the invention is divided into a three-star constellation and a four-star constellation.
Constellation of three stars
Fig. 2 is a satellite distribution diagram of a constellation of three stars. Because three points define a plane, the constellation of the three stars, which is distributed and deployed on the sphere on which the geosynchronous orbit lies, must be coplanar. The most dispersed design of the three-star distribution isThree points of an equilateral triangle are formed on the hemispherical section of the spherical surface of the geosynchronous orbit, as shown in fig. 3. Radius of sphere Rgeo42164km, the distance R between the satellites A, B, C is shown in the following formula (1)csIs 73030 km.
Rcs＝2×Rgeo×cos30°＝73030km (1)
Considering the cost of constellation launch, the lowest cost constellation of samsung is that the samsung deployed on the earth's stationary orbit, i.e., the subsatellite points are all near the equator, since the lower the latitude of the satellite launch into the orbit, the less fuel is consumed. At this time, within the range of 360 degrees of east-west longitude, as long as the longitude interval of the subsatellite points of the three stars is 120 degrees, the maximum dispersion distribution of the constellation of the three stars on the spherical surface of the geosynchronous orbit can be met. The invention selects a three-star constellation with the points longitude under the star of 120 degrees of the west longitude, 120 degrees of the east longitude and 0 degree of the east longitude for specific design, as shown in figure 3.
Four-star constellation
In the practical application process of the three-star constellation, there is a small probability that the three-star and the space debris are coplanar, as shown in fig. 4. At this time, the space debris position error regions obtained by the three-star ranging cannot be completely and effectively intersected, the intersected region is similar to a long quadrangular prism, and the height error of the cylinder of the long quadrangular prism in the coplanar vertical direction is several kilometers as the overlapped part of the dotted lines in the right figure.
From the perspective of improving engineering reliability, in order to avoid the problem that the space fragments and the three stars which are positioned in the earth stationary orbit are coplanar, and therefore the position error is too large, a satellite can be added in a proper amount in the design of a ranging satellite constellation, and the ranging satellite constellation is designed into a four-star constellation of the embodiment. The four stars are distributed with maximum dispersion on the spherical surface of the geosynchronous orbit, and will form a regular triangular pyramid configuration, as shown in fig. 5. The distance relationship between the constellations is shown in equation (2) below, with the distance R between satellites A, B, C, D being two by twocs68854 km.
The distance measurement position error intersection region obtained by the four-star constellation is basically consistent with the three-star constellation, but the reliability of the distance measurement constellation can be enhanced, the problem that fragments and three-star are coplanar is avoided, and therefore the measurement accuracy of fragments in more ranges is ensured. Meanwhile, when any satellite fails, the other three satellites still can keep effective ranging capability.
It is worth to be noted that from the perspective of cost and reliability, the three-star constellation and the four-star constellation are selected as more appropriate constellation numbers in the high-orbit space fragmentation laser ranging satellite constellation, the reliability of ranging is damaged when the number of satellites is reduced, and the cost of ranging is increased when the number of the constellations is increased.
Second, key parameters of laser carried by satellite
The laser is the most critical element in the constellation of laser ranging satellites and is an important component of a laser ranging system. The laser parameters are directly related to the efficiency and cost of ranging. Because the number of the satellites of the four-star constellation is one more than that of the three-star constellation, the distance between each satellite in the four-star constellation and the space fragment is shorter than that between the satellite in the three-star constellation and the space fragment, and the required laser energy is smaller. Therefore, the key parameters of the laser that the samsung constellation needs to carry are designed with emphasis below.
Space debris and satellite constellation configuration
A space right-angle xyz coordinate system is selected in space, wherein the y axis points to the direction of east-west longitude 0 degrees on the earth equator, the z axis points to the direction of north pole of the earth, and the x axis and the xy axis meet the configuration of a right-hand coordinate system. For a space debris (for example, a 60-degree angle) in a geosynchronous orbit and having an angle with an equatorial plane, the configuration of a ranging constellation of three stars and the positional relationship between A, B, C three stars and the space debris M in an xyz coordinate system are shown in fig. 6, and the coordinates of each point are a (42164 xcos 30 degrees, -42164 xcin 30 degrees, 0) (36515, -21082,0) (3)
B＝(0,42164,0) (4)
C＝(-42164×cos30°,-42164×sin30°,0)＝(-36515,-21082,0) (5)
M＝(42164×cos60°×cos45°,42164×cos60°×sin45°,42164×sin60°)＝(14907,14907,36515) (6)
The distances between the space debris M and A, B, C samsung are 55637km, 47943km and 72614km respectively. When measuring space debris of synchronous orbit, the maximum distance R between the space debris and the distance measuring star Bmax＝2RgeoAs shown in fig. 7 by the space debris at position M'. Since the longer the distance, the higher the laser energy required. Therefore, the following is by this longest distance RmaxAs a calculation reference for estimating the capacity of the lasers required to be carried by the constellation of samsung. Any high-track space debris can be measured as long as laser ranging at this longest distance is met.
(II) objective function and laser key parameters
Each satellite in the ranging satellite constellation carries the same laser ranging system, and each laser ranging system mainly comprises a laser, an optical system and a detector. The laser emits pulse laser, the pulse laser is modulated and compressed by the optical system and then is emitted to the space debris, the space debris receives and diffusely reflects the pulse laser, and echo photons are received by the optical system and then reach the detector to be detected.
Echo intensity n from space debris detected by laser ranging satellites0Determined by the equation of the number of photons of the echo
Wherein, λ is laser wavelength, D is transmitting/receiving aperture of optical system (for saving volume and weight, space-based laser ranging system is designed as receiving-transmitting common optical path system), ρ is average diffuse reflectance of space debris, σ is equivalent cross-sectional area of space debris, h is Planck constant, c is light speed, R is distance between space debris and ranging star, θ is distance between space debris and ranging startIs the optical system divergence angle. The system divergence angle is mainly determined by the divergence angle of the laser and the attitude stability of the satellite platform.
For remote laser ranging, R is often greater than 100km, R thetatThe/2 is far greater than the D/2, so the above formula can be simplified to
In the space environment, there is no influence of ground atmospheric light noise, the system receives noise mainly from the detector dark count rate, for the laser with single pulse width tau, the dark count rate is the detector of N, the noise produced in a pulse time is:
nnoi＝Nτ (9)
in laser ranging, the echoes are gaussian distributed with some concentration, while the noise is uniformly distributed throughout the pulse time, as shown in fig. 8. Therefore, the repetition frequency of the laser pulse is increased, and the effect of echo accumulation can be obtained. In the invention, the number of a designed target function f (x) is a constellation detection signal-to-noise ratio, and the constellation detection signal-to-noise ratio is designed as a function positively correlated with the repetition frequency f of a laser pulse:
taking the constellation detection signal-to-noise ratio f (x) related to the laser pulse repetition frequency f as an objective function of laser parameter selection, and obtaining the relation between the laser single pulse energy and other parameters of the system through the formulas (8) to (10)
Equation (11) gives the lowest value of the single-pulse energy of the laser carried by the satellite, and the diffuse reflection echo of the high-orbit space debris can be successfully identified when the laser carried by the satellite has the parameters.
The values of the relevant parameters in the echo photon number equation are shown in table 1; when ranging is performed using a single intense pulse with a repetition rate of 1 and a pulse with a repetition rate of kHz with a desired signal to noise ratio SNR of 10, the required laser single pulse energy is shown in table 2. When the laser repetition frequency is 1, the pulse can be used to identify the pulseWhen the wave signal is generated, the required laser energy is up to 60J. By using kHz laser pulses, i.e. laser repetition frequency of 1kHz, since the echo signal can be identified by pulse superposition, the signal is correlated and the noise is random, within a pulse, as long as n/nnoi0.01, that is, n/n within 1s can be basically ensurednoiAt this time, the required laser energy can be greatly reduced to 10.
TABLE 1
| Physical quantity | Of significance | Value taking |
| h | Planck constant | 6.6×10-34Js |
| c | Speed of light | 3×108m/s |
| λ | Laser wavelength | 1064nm |
| θt | Divergence angle of the system | More than 20 ″) |
| τ | Laser single pulse width | 10ns |
| R | Space debris distance | 84328km |
| SNR | Signal to noise ratio for echo detection | 10 |
| D | Receiving/transmitting aperture of distance measuring optical system | 0.5m |
| ρ | Average diffuse reflectance of space debris | 0.2 |
| σ | Equivalent cross-sectional area of space debris | 1m2 |
| f | Laser repetition frequency | 1000 |
TABLE 1
As can be seen from table 2, the laser repetition frequency is increased, and the requirement of the constellation for transmitting laser single pulse energy can be effectively reduced. Therefore, the laser ranging constellation in the invention selects the kHz laser, when the system posture is stable and the laser divergence angle is compressed to be high, namely the system divergence angle is 20 ", and when the detector dark count is low and about 100cps, the constellation only needs the laser with the single pulse energy of 62.91mJ, and the laser ranging of space debris on the whole geosynchronous orbit circular surface can be realized.
Third, laser ranging efficiency
For the three-star constellation, due to the influence of the system divergence angle, at the space debris distance, the laser forms a light spot in a certain area, the radius of the light spot, the space debris distance and the system divergence angle thetatAre directly related. Table 3 gives A, B, C laser spot radius sizes for samsung at space debris M.
TABLE 2 relationship between laser divergence spot radius and system divergence angle
| System divergence angle θt | Spot radius rA | Spot radius rB | |
| 20 | 5.5637km | 4.7943km | 7.2614km |
| 100 | 27.8185km | 23.9714km | 36.3071km |
Due to the pulse has a certain valueAnd the space debris has certain geometrical depth information, so that the position of the space debris can be deviated. That is, the space debris echo signal obtained by the ranging constellation may be derived from a signal having a thickness d and a radius roThe position of (1) is a disk. Wherein for a single pulse width of 10ns laser, and thickness ddebrisIs a space piece of 1m, the thickness d of the location disk is
Considering the geometry of the constellation of three stars and the space fraction, the shape of the pie in the xyz coordinate system is shown in fig. 9. The most direct effect of the satellite constellation can be found to be that through the three-star distributed configuration, the single constellation measures the position disk error caused by the space debris, and through the three-star disk crossing mode, the real position of the space debris is locked in the crossing region, so that the efficiency of reducing the position error of the space debris is achieved.
Position error cross-region volume VcrossIs approximately Vcross＝2.5m×2.5m×2.5m＝15.625m3 (13)
When the single distance measuring star is used for measuring the distance of the space debris, the volume V of the position error round cakesingleIs composed of
Comparing the formula (13) and the formula (14), it can be seen that the distributed three-star laser ranging satellite constellation improves the volume position error of the space debris by 6 orders of magnitude. And the azimuth error is improved from about 5km to 2.5m by 3 orders of magnitude.
The space debris laser ranging satellite constellation designed by the invention has the ranging efficiency far exceeding that of a ground-based space debris laser ranging system or a single space debris laser ranging satellite, and can obviously improve the measurement position error of the high-orbit space debris.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (1)
1. A high orbit space debris laser ranging satellite constellation design method is characterized in that,
the satellites in the satellite constellation are distributed and deployed on the spherical surface where the geosynchronous orbit is located, the number of the satellites is four, the four satellites form a regular triangular pyramid configuration, the distance between every two satellites is the same, and about 68854km is achieved;
a laser ranging system carried by each satellite in the constellation selects a laser with a kHz repetition frequency; designing a constellation detection signal-to-noise ratio positively correlated with a laser pulse repetition frequency f as a target function of laser parameter selection to obtain a single pulse energy minimum value E required by a laser carried by a satellite to successfully identify a high-orbit space debris diffuse reflection echotAccording to the minimum value of energy E of a single pulsetConfiguring a laser;
the laser ranging system carried by each satellite in the constellation mainly comprises a laser, an optical system and a detector; n is the dark count rate of the detector, τ is the single pulse width of the laser, h is the Planck constant, c is the speed of light, θtThe divergence angle of an optical system is shown, R is the distance between a space debris and a satellite, SNR is the required constellation detection signal-to-noise ratio, lambda is the laser wavelength, D is the emission/receiving aperture of the optical system, rho is the average diffuse reflectance of the space debris, and sigma is the equivalent cross-sectional area of the space debris;
the echo signal of the space debris obtained by the constellation comes from a position pie; through a distributed configuration, the real position of the space debris is locked in the crossing area in a four-star position disk crossing mode, so that the position error of the space debris is reduced.
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