CN115905800A - Space target track determination precision analysis method and system based on optical observation - Google Patents
Space target track determination precision analysis method and system based on optical observation Download PDFInfo
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Abstract
The invention provides a method and a system for analyzing the determination accuracy of a space target track based on optical observation, which comprises the following steps: step S1: setting parameters of optical observation equipment and parameters of an observation platform; step S2: calculating the position of the platform under the epoch geocentric celestial coordinate system; and step S3: calculating the position of the target under the epoch geocentric celestial coordinate system; and step S4: calculating an observed time period; step S5: calculating the angle measurement direction of the target relative to the platform in the observable time under the epoch geocentric celestial coordinate system; step S6: generating a plurality of groups of simulation data under different random noises; step S7: acquiring a target position estimation value, and comparing the target position estimation value with a target actual position to generate an average position deviation; step S8: and changing two lines of data of the target track, repeating the step S3 to the step S7, and carrying out statistical analysis on results of different targets and different random noises. The method can avoid inaccurate precision analysis caused by randomness, and intuitively reflect the efficiency which can be achieved by the track determination algorithm or scheme.
Description
Technical Field
The invention relates to the technical field of precision analysis, in particular to a method and a system for determining precision analysis of a space target track based on optical observation.
Background
The determination of the space target track based on the optical observation refers to observing the space target by using optical observation equipment, and acquiring the angle measurement information of the target relative to the observation equipment, thereby resolving the track parameters of the target. The optical observation device generally has an observation capability inversely proportional to the square of the distance, and the observation capability of an active device (such as a microwave radar and a laser radar) is inversely proportional to the fourth power of the distance, so that the optical observation device has wide application in the field of determining a space target track.
Because the optical observation equipment can only obtain the relative angle measurement information of the target, when the track parameter settlement is carried out on the space target and the effectiveness and the robustness of the orbit determination algorithm or scheme are evaluated, the accuracy analysis of the orbit determination cannot be carried out, particularly when the space target, the space debris and the like are cataloged and orbited.
The existing method for determining the spatial target orbit only simulates one or more groups of noises aiming at a specific single target for precision analysis, and in document 1 (Huangpu, a calculation method for only measuring angles and initial orbits of a low orbit satellite on a high orbit satellite, flight mechanics, 38 (1), 2020), simulation is performed on 1 specific target under different angle measurement precisions, and a group of data is simulated under each angle measurement precision. Document 2 (li xinran, extremely short arc orbit based on particle swarm optimization, aircraft observational control, 34 (6), 2015) performed 10 sets of simulations on a single target. Document 3 (wu xianhua, "determination of spatial target trajectory based on space-based optical measurements and its accuracy analysis", master academic thesis at the university of harlbine industry, 2011) performs 100 sets of monte carlo simulations on a single target.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method and a system for analyzing the determination accuracy of a space target track based on optical observation.
According to the method and the system for analyzing the space target track determination accuracy based on the optical observation, the scheme is as follows:
in a first aspect, an analysis method for determining accuracy of a spatial target track based on optical observation is provided, the method comprising:
step S1: setting parameters of optical observation equipment and parameters of an observation platform;
step S2: calculating the position of the platform under the epoch geocentric celestial coordinate system;
and step S3: inputting two lines of data of a target track, and calculating the position of the target under an epoch geocentric celestial coordinate system;
and step S4: observing the target through an optical observation device, and calculating an observed time period;
step S5: calculating the angle measurement direction of the target relative to the platform in the observable time under the epoch geocentric celestial coordinate system;
step S6: generating a plurality of groups of simulation data under different random noises by controlling the pseudo-random number seed value;
step S7: calculating through target orbit parameters to obtain a target position estimation value, and comparing the target position estimation value with a target actual position to generate an average position deviation;
step S8: and changing two lines of data of the target track, repeating the step S3 to the step S7, and carrying out statistical analysis on results of different targets and different random noises.
Preferably, the position calculation method of the target in the epoch geocentric celestial coordinate system in step S3 is as follows:
step S3.1: calculating the position of the target under a t-time orbit coordinate system according to the SGP4, wherein the t-time orbit coordinate system is defined as: the origin is the geocentric, the XY coordinate plane is the instant equatorial plane at the time t, and the X axis points to the vernality point at the time t;
step S3.2: calculating the position of the target under the epoch geocentric celestial coordinate system according to the conversion relation between the t-time orbit coordinate system and the epoch geocentric celestial coordinate system, and if the position of the target under the t-time orbit coordinate system is
Its position in the epoch geocentric coordinate system->
Comprises the following steps:
wherein T is a conversion matrix;
T＝R z (-z A )R y (θ A )R z (-ζ A )R x (-ε A -Δε)R z (-Δψ)R x (ε A )R z (-Δμ)
therein, ζ A 、θ A 、z A Is a three equator time difference parameter epsilon in an IAU 2006 time difference model A The angle is a flat yellow-red crossing angle, delta epsilon is a crossing angle nutation, delta psi is a yellow meridian nutation, and delta mu is a red meridian nutation; r is x 、R y 、R z The transformation matrixes are respectively rotated around corresponding coordinate axes, and the transformation matrix corresponding to the rotation angle theta is as follows:
preferably, if the position of the platform obtained in step S2 in the epoch geocentric celestial coordinate system is set as
(j =0,1,2, \8230;, N-1), where N is the number of sampling points, and the position of the target obtained in step S3 in the epoch geocentric celestial coordinate system is
Then the angle-measuring direction of the target relative to the platform within the observable time in step S5 under the epoch geocentric coordinate system is pointed->
The calculation method comprises the following steps:
where it is indicated that the vector is modulo.
Preferably, if the position of the platform obtained in step S2 in the epoch geocentric celestial coordinate system is the position
(j =0,1,2, \8230;, N-1), where N is the number of sampling points; the method for constructing the platform position simulated in step S6 includes the following steps:
step S6.1: setting a pseudo random number seed value to i =0;
step S6.2: generating a normal distribution random number with 3 XN dimensional mean value of 0 and standard deviation of sigma, corresponding to
Is recorded as &>
Step S6.3: simulated platform position with measurement noise
Satisfies the following conditions: />
Wherein the content of the first and second substances,
represents the jth sample point of the platform position; />
Corresponding noise (three-dimensional vector);
step S6.4: changing the value of the pseudo random number seed i, repeating the step S6.2 to the step S6.3, and acquiring platform position simulation data under different measurement noises, wherein the number of the simulation data sets is not less than 100.
Preferably, if the position of the target obtained in step S3 in the epoch geocentric celestial coordinate system is the same
(j =0,1,2, \8230;, N-1), the method for constructing the goniometric data simulated in step S6 includes the steps of:
step S6.5: setting a pseudo-random number seed value to i + M, wherein M is an integer and M is greater than 1000;
step S6.6: the mean value of 3 XN dimension is 0 and the standard deviation is sigma a Is normally distributed random number of
Is recorded as
Standard deviation sigma a Calculating according to the achievable angle measurement deviation mean value a and the target distance platform distance mean value L to obtain:
step S6.7: simulated angle measurement data containing measurement noise
Wherein the content of the first and second substances,
representing the jth sampling point of the target position; />
Corresponding noise (three-dimensional vector);
step S6.8: and updating the value of the pseudo-random number seed i + M along with the change of the numerical value i in the step S6.4, and repeating the step S6.7 to the step S6.8 to obtain angle measurement simulation data under different measurement noises.
Preferably, in step S7, the target orbit parameter is calculated to obtain an orbit state quantity at a certain time, and the target position estimation value at each sampling point is calculated according to the state quantity obtained by calculation
And is associated with the actual position->
Comparing and generating an average position deviation d:
preferably, in step S8, when the results of different targets and different random noises are statistically analyzed, the mean value, the maximum value and the standard deviation of the track position deviation are counted, and the variation relationship between the results and the observation duration, the observation arc length and the track relative inclination angle is analyzed.
In a second aspect, there is provided an optical observation based spatial target trajectory determination accuracy analysis system, the system comprising:
a module M1: setting parameters of optical observation equipment and parameters of an observation platform;
a module M2: calculating the position of the platform under the epoch geocentric celestial coordinate system;
a module M3: inputting two lines of data of a target track, and calculating the position of the target under an epoch geocentric celestial coordinate system;
a module M4: observing the target through an optical observation device, and calculating an observed time period;
a module M5: calculating the angle measurement direction of the target relative to the platform in the observable time under the epoch geocentric celestial coordinate system;
a module M6: generating a plurality of groups of simulation data under different random noises by controlling the pseudo-random number seed value;
a module M7: calculating through target orbit parameters to obtain a target position estimation value, and comparing the target position estimation value with a target actual position to generate an average position deviation;
a module M8: and changing two lines of data of the target track, repeating the modules M3 to M7, and performing statistical analysis on results of different targets and different random noises.
Preferably, the position calculation method of the target in the module M3 in the epoch geocentric celestial coordinate system is as follows:
module M3.1: calculating the position of the target under a t-time orbit coordinate system according to the SGP4, wherein the t-time orbit coordinate system is defined as: the origin is the geocentric, the XY coordinate plane is the instant equatorial plane at the time t, and the X axis points to the vernality point at the time t;
module M3.2: calculating the position of the target under the epoch geocentric celestial coordinate system according to the conversion relation between the t-time orbit coordinate system and the epoch geocentric celestial coordinate system, and if the position of the target under the t-time orbit coordinate system is
Its position in the epoch geocentric coordinate system->
Comprises the following steps:
wherein T is a conversion matrix;
T＝R z (-z A )R y (θ A )R z (-ζ A )R x (-ε A -Δε)R z (-Δψ)R x (ε A )R z (-Δμ)
therein, ζ A 、θ A 、z A Is a three equator time difference parameter epsilon in an IAU 2006 time difference model A The angle is a flat yellow-red crossing angle, the delta epsilon is a crossing angle nutation, the delta psi is a yellow meridian nutation, and the delta mu is a red meridian nutation; r x 、R y 、R z The transformation matrixes are respectively rotated around corresponding coordinate axes, and the transformation matrix corresponding to the rotation angle theta is as follows:
preferably, if the position of the platform obtained in step S2 in the epoch geocentric celestial coordinate system is set as
(j =0,1,2, \8230;, N-1), where N is the number of sampling points, and the position of the target obtained in step S3 in the epoch geocentric celestial coordinate system is
Then the angle-measuring direction of the target relative to the platform within the observable time in step S5 under the epoch geocentric coordinate system is pointed->
The calculation method comprises the following steps:
where it is indicated that the vector is modulo.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention provides an orbit determination error acquisition method aiming at different targets and different random noises based on a public satellite orbit two-line data (TLE) data set, and avoids inaccurate precision analysis caused by randomness through multiple samples.
2. The method is reasonable, simple in calculation and easy to implement, can visually reflect the efficiency which can be achieved by the track determination algorithm or scheme, and avoids the problem of inaccurate precision evaluation caused by randomness.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph of the average deviation of the positions determined for 100 sets of target tracks under different noises;
FIG. 3 is a statistical result of determining position deviations for 100 sets of tracks under different noise;
fig. 4 is a statistical result of determining the position deviation for the tracks under different noise and different targets.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will aid those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any manner. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
The embodiment of the invention provides a space target track determination accuracy analysis method based on optical observation, and as shown in figure 1, the method specifically comprises the following steps:
step S1: and setting parameters of the optical observation equipment and parameters of the observation platform.
Step S2: and calculating the position of the platform under the epoch geocentric celestial coordinate system.
And step S3: inputting two lines of data of a target track, and calculating the position of the target under an epoch geocentric celestial coordinate system.
And step S4: the target is observed by an optical observation device and the observed time period is calculated.
Step S5: and calculating the angle measurement direction of the target in the observable time relative to the platform under the epoch geocentric celestial coordinate system.
Step S6: and generating a plurality of groups of simulation data under different random noises by controlling the pseudo-random number seed value.
Step S7: and calculating through target orbit parameters to obtain a target position estimation value, and comparing the target position estimation value with the actual target position to generate an average position deviation.
Step S8: and changing two lines of data of the target track, repeating the step S3 to the step S7, and carrying out statistical analysis on results of different targets and different random noises.
In step S3, the position calculation method of the target in the epoch geocentric celestial coordinate system is as follows:
step S3.1: and calculating the position of the target under an orbit coordinate system at the moment t according to the SGP4 (simplified conventional perturbation model), wherein the orbit coordinate system at the moment t is defined as: the origin is the geocentric, the XY coordinate plane is the instantaneous equatorial plane at the time t, and the X axis points to the vernality point at the time t.
Step S3.2: calculating the position of the target under the epoch geocentric celestial coordinate system according to the conversion relation between the t-time orbit coordinate system and the epoch geocentric celestial coordinate system, and if the position of the target under the t-time orbit coordinate system is
Its position under epoch geocentric celestial coordinate system->
Comprises the following steps:
wherein T is a conversion matrix;
T＝R z (-z A )R y (θ A )R z (-ζ A )R x (-ε A -Δε)R z (-Δψ)R x (ε A )R z (-Δμ)
therein, ζ A 、θ A 、z A Is three equatorial age parameters epsilon in the IAU 2006 age model A The angle is a flat yellow-red crossing angle, the delta epsilon is a crossing angle nutation, the delta psi is a yellow meridian nutation, and the delta mu is a red meridian nutation; r is x 、R y 、R z The conversion matrixes are respectively rotation matrixes around corresponding coordinate axes, and the conversion matrixes corresponding to the rotation angles theta (unit: radian) are as follows:
if the position of the platform obtained in the step S2 under the epoch geocentric celestial coordinate system is the same as that of the platform obtained in the step S2
N is the number of sampling points, and the position of the target obtained in the step S3 under the epoch geocentric coordinate system is set as->
(j =0,1,2, \8230;, N-1), then the goniometric orientation @, in the epoch geocentric celestial coordinate system, of the target relative platform during the observable time in step S5 is determined>
Calculation methodComprises the following steps:
where it is indicated that the vector is modulo.
If the position of the platform obtained in the step S2 under the epoch geocentric celestial coordinate system is the same as that of the platform obtained in the step S2
N is the number of sampling points; the platform position constructing method simulated in step S6 includes the following steps:
step S6.1: the pseudo random number seed value is set to i =0.
Step S6.2: generating a normally distributed random number with a 3 XN dimensional mean of 0 and a standard deviation of sigma, corresponding to
Is recorded as->
Step S6.3: simulated platform position with measurement noise
Satisfies the following conditions:
wherein the content of the first and second substances,
represents the jth sample point of the platform position; />
Corresponding noise (three-dimensional vector).
Step S6.4: changing the value of the pseudo random number seed i, repeating the step S6.2 to the step S6.3, and acquiring platform position simulation data under different measurement noises, wherein the number of the simulation data groups is not less than 100.
If the position of the target obtained in the step S3 under the epoch geocentric celestial coordinate system is the same as that of the target obtained in the step S3
The method for constructing the simulated angle measurement data in step S6 includes the following steps:
step S6.5: setting a pseudo random number seed value to i + M, where M is an integer and M is greater than 1000.
Step S6.6: the mean value of 3 XN dimension is 0 and the standard deviation is sigma a Is normally distributed random number of
Is recorded as
Standard deviation sigma a Calculating according to the achievable angle measurement deviation mean value a and the target distance platform distance mean value L to obtain:
step S6.7: simulated angle measurement data containing measurement noise
Wherein the content of the first and second substances,
represents the jth sampling point of the target position; />
Corresponding noise (three-dimensional vector).
Step S6.8: and updating the value of the pseudo-random number seed i + M along with the change of the numerical value i in the step S6.4, and repeating the step S6.7 to the step S6.8 to obtain angle measurement simulation data under different measurement noises.
In step S7, the target orbit parameter is calculated to obtain an orbit state quantity (which may be a position, a speed, or an orbit instantaneous kepler root, or a first-class non-singular-point root, etc.) at a certain time, and the target position estimation value at each sampling point is calculated according to the calculated state quantity
And is associated with the actual position->
Comparing and generating an average position deviation d:
in step S8, when the results of different targets and different random noises are statistically analyzed, the mean value, the maximum value, the standard deviation, etc. of the track position deviation can be counted, and the variation relationship between the results and the observation duration, the observation arc length, the track relative inclination, etc. can be analyzed.
The invention also provides a system for determining and analyzing the precision of the space target track based on optical observation, which is characterized by comprising the following components:
a module M1: setting parameters of optical observation equipment and parameters of an observation platform;
a module M2: calculating the position of the platform under the epoch geocentric celestial coordinate system;
a module M3: inputting two lines of data of a target track, and calculating the position of the target under an epoch geocentric celestial coordinate system;
a module M4: observing the target through an optical observation device, and calculating an observed time period;
a module M5: calculating the angle measurement direction of the target relative to the platform in the observable time under the epoch geocentric celestial coordinate system;
a module M6: generating a plurality of groups of simulation data under different random noises by controlling the pseudo-random number seed value;
a module M7: calculating through target orbit parameters to obtain a target position estimation value, and comparing the target position estimation value with a target actual position to generate an average position deviation;
a module M8: and changing two lines of data of the target track, repeating the modules M3 to M7, and performing statistical analysis on results of different targets and different random noises.
The position calculation method of the target in the module M3 under the epoch geocentric celestial coordinate system is as follows:
module M3.1: calculating the position of the target under a t-time orbit coordinate system according to the SGP4, wherein the t-time orbit coordinate system is defined as: the origin is the geocentric, the XY coordinate plane is the instant equatorial plane at the time t, and the X axis points to the vernality point at the time t;
module M3.2: calculating the position of the target under the epoch geocentric celestial coordinate system according to the conversion relation between the t-time orbit coordinate system and the epoch geocentric celestial coordinate system, and if the position of the target under the t-time orbit coordinate system is
Its position in the epoch geocentric coordinate system->
Comprises the following steps:
wherein T is a conversion matrix;
T＝R z (-z A )R y (θ A )R z (-ζ A )R x (-ε A -Δε)R z (-Δψ)R x (ε A )R z (-Δμ)
therein, ζ A 、θ A 、z A Is three equatorial age parameters epsilon in the IAU 2006 age model A Is flat yellow-red crossing angle, delta epsilon is crossing angle nutation, delta phi is yellow meridian nutation, and Delta mu isThe right ascension nutates; r is x 、R y 、R z The transformation matrixes which rotate around the corresponding coordinate axes are respectively as follows:
if the position of the platform obtained in the step S2 under the epoch geocentric celestial coordinate system is the same as that of the platform obtained in the step S2
N is the number of sampling points, and the position of the target obtained in the step S3 under the epoch geocentric coordinate system is set as->
(j =0,1,2, \8230;, N-1), then the goniometric orientation @, in the epoch geocentric celestial coordinate system, of the target relative platform during the observable time in step S5 is determined>
The calculation method comprises the following steps: />
Where it is indicated that the vector is modulo.
Next, the present invention will be described more specifically.
When the spatial target orbit determination accuracy is analyzed, due to the fact that factors influencing final orbit determination are numerous, a single simulation result has certain randomness and cannot reflect the real accuracy level, and therefore the orbit determination accuracy needs to be evaluated by covering more samples and more working conditions. The satellite orbit two-line data (TLE) data set is issued by North America aerospace national defense commander according to artificial celestial body tracking observation data, covers meteorological satellites, marine satellites, earth resource satellites, educational satellites, rocket fragments and the like, and can be used as simulation target input for determining precision analysis of a space target orbit.
Referring to fig. 1, first, parameters of an optical observation apparatus and parameters of an observation platform are set. And calculating the position of the observation platform under the epoch geocentric celestial coordinate system.
Inputting two lines of data of a target track, and calculating the position of the target under an epoch geocentric celestial coordinate system.
Since the number of TLE tracks defines the track coordinate system at time t, the track coordinate system at time t is defined as: the origin is the geocentric, the XY coordinate plane is the instantaneous equatorial plane at the time t, and the X axis points to the vernality point at the time t. Therefore, the position calculation of the target under the epoch geocentric celestial coordinate system needs to be converted. The position of the target in the orbital coordinate system at time t is first calculated from the SGP4 (simplified conventional perturbation model).
And calculating the position of the target under the epoch geocentric celestial coordinate system according to the conversion relation between the orbit coordinate system at the time t and the epoch geocentric celestial coordinate system. If the position of the target in the orbit coordinate system at the time t is
Its position under epoch geocentric celestial coordinate system->
Is composed of
Wherein T is a transformation matrix, and T is a transformation matrix,
T＝R z (-z A )R y (θ A )R z (-ζ A )R x (-ε A -Δε)R z (-Δψ)R x (ε A )R z (. DELTA.. Mu.) (equation 2)
Therein, ζ A 、θ A 、z A Is a three equator time difference parameter epsilon in an IAU 2006 time difference model A The angle is equal to the yellow-red crossing angle, the angle delta epsilon is the crossing angle nutation, the angle delta phi is the yellow meridian nutation, and the angle delta mu is the red meridian nutation. R x 、R y 、R z The transformation matrixes are respectively rotated around corresponding coordinate axes, and the transformation matrixes corresponding to the rotation angles theta (unit: radian) are as follows:
according to the positions of the simulation target and the observation platform, the time period for which the target can be observed by the optical observation device can be calculated.
If the position of the observation platform under the epoch geocentric celestial coordinate system is
(N is the number of sampling points), if the position of the target obtained in step S3 under the epoch geocentric celestial coordinate system is->
Then the angle measurement pointing direction of the target in the observable time relative to the platform under the epoch geocentric coordinate system is greater than or equal to>
The calculation method is
Where it is indicated that the vector is modulo.
Because the actually obtained platform position and the target angle measurement information both contain measurement errors, noise needs to be artificially added in the simulation. In order to avoid the influence of noise randomness introduction, a plurality of groups of simulation data under different random noises are generated by controlling the pseudo-random number seed value.
If the position of the platform under the epoch geocentric celestial coordinate system is
(N is the number of sampling points), a pseudo random number seed value is first set to i =0.
Generating a normally distributed random number with a 3 XN dimensional mean of 0 and a standard deviation of sigma, corresponding to
Is recorded as &>
Simulated platform position with measurement noise
Satisfy the requirement of
And changing the value of the pseudo random number seed i to obtain platform position simulation data under different measurement noises. The number of simulation data sets is generally not less than 100.
If the obtained position of the target under the epoch geocentric celestial coordinate system is as follows
The pseudo random number seed value is set to i + M. (M is an integer, and M may be greater than 1000.) As the value i is changed, the value of the pseudo random number seed i + M is updated.
The mean value of 3 XN dimension is 0 and the standard deviation is sigma a Is normally distributed random number of
Is recorded as &>
Standard deviation sigma a Based on the average value a of the angle deviation and the average value L of the distance between the target and the platform, the value is calculated and then is selected>
Simulated angle measurement data containing measurement noise
And calculating through target orbit parameters to obtain a target position estimation value, and comparing the target position estimation value with the actual target position to generate an average position deviation.
The target orbit parameter is generally obtained by resolving an orbit state quantity (which can be a position, a speed, an orbit instantaneous Kepler root, a first-class non-singular-point root and the like) at a certain moment, and a target position estimation value at each sampling point is calculated by the state quantity obtained by resolving
And is associated with the actual position->
The comparison yields the average position deviation d,
and replacing the simulation target in the TLE data set, and repeating the steps, so that the results under different targets and different random noises can be statistically analyzed. The method can be used for counting the mean value, the maximum value, the standard deviation and the like of the position deviation of the track, and analyzing the change relation between the result and the observation duration, the observation arc length, the relative inclination angle of the track and the like.
The effectiveness of the method of the present invention is verified by combining simulation, under the same observation platform, observation target (target kepler number is 42140.46km,0.0005,2.91 °,39.65 °,75.70 °,126.35 °) and observation time length (10 min), under different random noises of 100 groups which accord with the same statistical rule (observation platform position noise standard deviation σ =6.7m, angle measurement deviation mean a =2000 milli-angular seconds, target distance platform mean L =35715 km), the target orbit determines the position deviation distribution situation as shown in fig. 2, and the statistical result is as shown in fig. 3, mean 51.55, standard deviation 36.17km and maximum 179.82km. In the same way, the simulation target can be replaced in the TLE data set to obtain the accuracy statistical results under different targets and different random noises, which are shown in fig. 4 as the statistical results under different targets (all high-orbit rails) and different random noises, wherein the average value is 53.43km, the standard deviation is 42.08km, and the maximum value is 287.79km.
The embodiment of the invention provides a method and a system for analyzing the determination accuracy of a space target orbit based on optical observation, which are used for simulating on the basis of disclosing a double-line data (TLE) data set of a satellite orbit, covering different targets and different random noises, avoiding the inaccuracy of accuracy analysis caused by randomness through multiple samples and visually reflecting the efficiency which can be achieved by an orbit determination algorithm or scheme. The method is reasonable, simple in calculation and easy to implement, can visually reflect the efficiency which can be achieved by the track determination algorithm or scheme, and avoids the problem of inaccurate precision evaluation caused by randomness.
Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, units provided by the present invention as pure computer readable program code, the system and its various devices, modules, units provided by the present invention can be fully implemented by logically programming method steps in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system and various devices, modules and units thereof provided by the present invention can be regarded as a hardware component, and the devices, modules and units included therein for implementing various functions can also be regarded as structures within the hardware component; means, modules, units for performing the various functions may also be regarded as structures within both software modules and hardware components for performing the method.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.
Claims (10)
1. An analysis method for determining the precision of a space target track based on optical observation is characterized by comprising the following steps:
step S1: setting parameters of optical observation equipment and parameters of an observation platform;
step S2: calculating the position of the platform under the epoch geocentric celestial coordinate system;
and step S3: inputting two lines of data of a target track, and calculating the position of the target under an epoch geocentric celestial coordinate system;
and step S4: observing the target through an optical observation device, and calculating an observed time period;
step S5: calculating the angle measurement direction of the target relative to the platform in the observable time under the epoch geocentric celestial coordinate system;
step S6: generating a plurality of groups of simulation data under different random noises by controlling the pseudo-random number seed value;
step S7: calculating through target orbit parameters to obtain a target position estimation value, and comparing the target position estimation value with a target actual position to generate an average position deviation;
step S8: and changing two lines of data of the target track, repeating the step S3 to the step S7, and carrying out statistical analysis on results of different targets and different random noises.
2. The method for analyzing the determination accuracy of the target trajectory in space based on optical observation according to claim 1, wherein the position of the target in the epoch geocentric celestial coordinate system in step S3 is calculated as follows:
step S3.1: and calculating the position of the target under a t-time orbit coordinate system according to the SGP4, wherein the t-time orbit coordinate system is defined as follows: the origin is the geocentric, the XY coordinate plane is the instant equatorial plane at the time t, and the X axis points to the vernal equinox at the time t;
step S3.2: calculating the position of the target under the epoch geocentric celestial coordinate system according to the conversion relation between the t-time orbit coordinate system and the epoch geocentric celestial coordinate system, and if the position of the target under the t-time orbit coordinate system is
Its position under epoch geocentric celestial coordinate system->
Comprises the following steps:
wherein T is a conversion matrix;
T＝R z (-z A )R y (θ A )R z (-ζ A )R x (-ε A -Δε)R z (-Δψ)R x (ε A )R z (-Δμ)
therein, ζ A 、θ A 、z A Is three equatorial age parameters epsilon in the IAU 2006 age model A The angle is a flat yellow-red crossing angle, delta epsilon is a crossing angle nutation, delta psi is a yellow meridian nutation, and delta mu is a red meridian nutation; r x 、R y 、R z The transformation matrixes which rotate around the corresponding coordinate axes are respectively as follows:
3. the method according to claim 1, wherein if the platform obtained in step S2 is located in the epoch geocentric celestial coordinate system, the method is characterized in that
N is the number of sampling points, and the position of the target obtained in the step S3 under the epoch geocentric coordinate system is set as->
Then the angle-measuring direction of the target relative to the platform within the observable time in step S5 under the epoch geocentric coordinate system is pointed->
The calculation method comprises the following steps:
where, | | represents modulo a vector.
4. The optical observation-based spatial target trajectory determination accuracy analysis method of claim 1,it is characterized in that if the position of the platform obtained in the step S2 under the epoch geocentric celestial coordinate system is set as
N is the number of sampling points; the platform position constructing method simulated in step S6 includes the following steps:
step S6.1: setting a pseudo random number seed value to i =0;
step S6.2: generating a normally distributed random number with a 3 XN dimensional mean of 0 and a standard deviation of sigma, corresponding to
Is recorded as &>
Step S6.3: simulated platform position with measurement noise
Satisfies the following conditions:
wherein the content of the first and second substances,
represents the jth sample point of the platform position; />
Corresponding noise (three-dimensional vector);
step S6.4: changing the value of the pseudo random number seed i, repeating the step S6.2 to the step S6.3, and acquiring platform position simulation data under different measurement noises, wherein the number of the simulation data groups is not less than 100.
5. The method according to claim 1, wherein the position of the target obtained in step S3 in the epoch geocentric celestial coordinate system is the position of the target
The method for constructing the simulated angle measurement data in step S6 includes the following steps:
step S6.5: setting a pseudo-random number seed value to i + M, wherein M is an integer and M is greater than 1000;
step S6.6: the mean value of 3 XN dimension is 0 and the standard deviation is sigma a Is normally distributed random number of
Is recorded as->
Standard deviation sigma a Calculating according to the achievable average value a of the measured angle deviation and the average value L of the distance between the target distance platform to obtain:
step S6.7: simulated angle measurement data containing measurement noise
Wherein the content of the first and second substances,
representing the jth sampling point of the target position; />
Corresponding noise (three-dimensional vector);
step S6.8: and updating the value of the pseudo-random number seed i + M along with the change of the numerical value i in the step S6.4, and repeating the step S6.7 to the step S6.8 to obtain angle measurement simulation data under different measurement noises.
6. The method according to claim 1, wherein in step S7, the target orbit parameter is calculated as an orbit state quantity at a certain time, and the estimated value of the target position at each sampling point is calculated from the calculated state quantity
And is associated with the actual position->
Comparing and generating an average position deviation d:
7. the method of claim 1, wherein in step S8, when the statistical analysis is performed on the results of different targets and different random noises, the method counts the mean value, the maximum value and the standard deviation of the orbit position deviation, and analyzes the variation relationship between the results and the observation duration, the observation arc length and the orbit relative inclination angle.
8. An optical observation-based spatial target trajectory determination accuracy analysis system, comprising:
a module M1: setting parameters of optical observation equipment and parameters of an observation platform;
a module M2: calculating the position of the platform under the epoch geocentric celestial coordinate system;
a module M3: inputting two lines of data of a target track, and calculating the position of the target under an epoch geocentric celestial coordinate system;
a module M4: observing the target through an optical observation device, and calculating an observed time period;
a module M5: calculating the angle measurement direction of the target relative to the platform in the observable time under the epoch geocentric celestial coordinate system;
a module M6: generating a plurality of groups of simulation data under different random noises by controlling the pseudo-random number seed value;
a module M7: calculating through target orbit parameters to obtain a target position estimation value, and comparing the target position estimation value with a target actual position to generate an average position deviation;
a module M8: and changing two lines of data of the target track, repeating the modules M3-M7, and performing statistical analysis on results of different targets and different random noises.
9. The system according to claim 8, wherein the position of the target in the module M3 in the epoch geocentric celestial coordinate system is calculated as follows:
module M3.1: calculating the position of the target under a t-time orbit coordinate system according to the SGP4, wherein the t-time orbit coordinate system is defined as: the origin is the geocentric, the XY coordinate plane is the instant equatorial plane at the time t, and the X axis points to the vernality point at the time t;
module M3.2: calculating the position of the target under the epoch geocentric celestial coordinate system according to the conversion relation between the t-time orbit coordinate system and the epoch geocentric celestial coordinate system, and if the position of the target under the t-time orbit coordinate system is
Its position under epoch geocentric celestial coordinate system->
Comprises the following steps:
wherein T is a conversion matrix;
T＝R z (-z A )R y (θ A )R z (-ζ A )R x (-ε A -Δε)R z (-Δψ)R x (ε A )R z (-Δμ)
therein, ζ A 、θ A 、z A Is a three equator time difference parameter epsilon in an IAU 2006 time difference model A The angle is a flat yellow-red crossing angle, delta epsilon is a crossing angle nutation, delta psi is a yellow meridian nutation, and delta mu is a red meridian nutation; r x 、R y 、R z The transformation matrixes which rotate around the corresponding coordinate axes are respectively as follows:
10. the system of claim 8, wherein if the platform obtained in step S2 is located in the epoch geocentric celestial coordinate system, the system is characterized in that
N is the number of sampling points, and the position of the target obtained in the step S3 under the epoch geocentric celestial coordinate system is set as->
The target in the observable time in step S5 points in angle measurement direction ≥ based on epoch geocentric coordinate system with respect to the platform>
The calculation method comprises the following steps:
where | represents modulo a vector.
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