CN113204917A - Space-based optical angle measurement arc section initial orbit determination method for GEO target and correlation method - Google Patents

Space-based optical angle measurement arc section initial orbit determination method for GEO target and correlation method Download PDF

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CN113204917A
CN113204917A CN202110449524.9A CN202110449524A CN113204917A CN 113204917 A CN113204917 A CN 113204917A CN 202110449524 A CN202110449524 A CN 202110449524A CN 113204917 A CN113204917 A CN 113204917A
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闫瑞东
龚建村
罗冰显
刘四清
王荣兰
师立勤
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National Space Science Center of CAS
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Abstract

The invention discloses a space-based optical angle measurement arc section initial orbit determination method aiming at a GEO target, which comprises the following steps: screening the measuring arc sections of the space-based platform, and performing coordinate system conversion on the height and longitude and latitude data of the space-based platform to obtain a position vector and a speed vector under a J2000 coordinate system; selecting two space-based platform measuring arcs aiming at the GEO target from the screened measuring arcs, and respectively sampling the right ascension and declination data in the two arcs; for each arc section, determining the distance range from the space-based platform to the GEO target according to the right ascension and declination data of the sampling points to generate search grid points with slant distances, determining an initial orbit corresponding to each sampling point by adopting a bacterial foraging algorithm and a genetic algorithm in the search grid points to obtain a corresponding subsatellite point track, and further obtaining a longitude average value of each arc section; and calculating the difference value of the longitude average values of the two arc sections, and associating the two arc sections when the difference value is smaller than a preset threshold value.

Description

Space-based optical angle measurement arc section initial orbit determination method for GEO target and correlation method
Technical Field
The invention belongs to the technical field of aerospace, and relates to a space-based optical angle measurement arc initial orbit determination method for a GEO target and an association method.
Background
The problem faced in GEO (Geostationary Orbit) target space-based optical measurement arc identification engineering is that measurement data of hundreds of ultrashort arcs per day cannot be effectively utilized, resulting in resource waste. The full utilization of the data can directly increase the quantity of the space target cataloging and improve the early warning level of the space target cataloging in China. The main difficulty in tracking the space-based optical GEO target is that the measurement arc is short, generally less than 3 minutes. The shorter the arc segment is, the more prominent the orbit determination ill-conditioned behavior of the conventional laplacian method and gaussian method is, and especially the lower the semi-major axis precision in the initial track determination is, so that the correlation accuracy of a plurality of ultrashort arc segments based on the track characteristics is low. An effective approach for solving the problem is a relatively high-precision initial orbit determination method and a high-accuracy correlation method of multiple ultra-short arc sections of a GEO target based on the characteristics of the orbit. The high accuracy correlation of the multiple arc sections can realize the extension of the arc sections, and the observation data of the long arc section provides data support for the determination of the precise track. Therefore, a highly efficient correlation and high-precision initial orbit determination method for the space-based optical angle measurement arc section of the GEO target is needed.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an initial orbit determination method based on an improved bacterial foraging algorithm and a GEO target arc segment association method based on azimuth characteristics (longitude and latitude of points below a satellite) in order to solve the problems of determination of a space-based optical angle measurement ultra-short arc segment initial orbit and arc segment association of a GEO target.
A space-based optical goniometric arc segment initial orbit and associated method for GEO targets, the method comprising:
step 1) screening a measuring arc section of a space-based platform, and performing coordinate system conversion on height and longitude and latitude data of the space-based platform to obtain a position vector and a speed vector under a J2000 coordinate system;
step 2) selecting two space-based platform measuring arc sections aiming at the GEO target from the screened measuring arc sections, and respectively sampling the right ascension and declination data in the two arc sections;
step 3) determining the distance range from the space-based platform to the GEO target to generate search grid points with slant distances for each arc section according to the right ascension and declination data of the sampling points, and determining the initial orbit corresponding to each sampling point by adopting a bacterial foraging algorithm and a genetic algorithm in the search grid points to obtain the corresponding sub-satellite point track so as to obtain the longitude average value of each arc section;
and 4) calculating the difference value of the longitude average values of the two arc sections, and associating the two arc sections when the difference value is smaller than a preset threshold value.
As an improvement of the above method, the step 1) specifically includes:
screening the measuring arc section of the space-based platform, and discarding the arc section when the maximum value of declination data of the measuring data in the measuring arc section is greater than a threshold value; otherwise, the arc segment is reserved;
and converting the height and longitude and latitude data of the space-based platform under the earth-fixed coordinate system into position data and speed data under the J2000 coordinate system.
As an improvement of the above method, the step 2) specifically includes:
selecting two measuring arc sections with the length reaching the preset time and aiming at a space-based platform of the GEO target, and setting sampling point intervals for sampling;
respectively selecting right ascension data alpha of the ith sampling point for each arc segmentiAnd declination data deltai；
Generating a sight unit vector of the GEO target corresponding to the ith sampling point relative to the measuring platform according to the following formula
Figure BDA0003038136410000021
Comprises the following steps:
Figure BDA0003038136410000022
wherein N is the number of sampling points in the arc segment.
As an improvement of the above method, the step 3) specifically includes the following steps for each arc segment:
step 301) converting the right ascension and declination data of the sampling point into a direction vector;
step 302) estimating the distance range from the space-based platform to the GEO target, taking the distance range as an optimization variable, and generating a search grid point of the slant distance according to the limiting condition;
step 303) forecasting the orbital direction angle measurement sampling point according to the perturbation model, calculating the position of the GEO target relative to the measuring platform according to the forecasted position vector and the space-based platform position vector, and generating forecast data; calculating the mean square error of the measured data and the forecast data of each sampling point in the arc section;
step 304) in the search grid points, performing track search optimization by adopting a bacterial foraging algorithm and a genetic algorithm and taking the mean square error as an adaptability value to obtain a position vector and a speed vector of a GEO target so as to determine an initial track;
step 305) converting and calculating to obtain the longitude and latitude of the sub-satellite point track corresponding to the sampling point according to the position vector of the GEO target;
step 306), when the arc segment has the non-calculated sampling point, turning to step 301) to obtain the longitude and latitude of the sub-satellite point track of the next sampling point of the arc segment; otherwise, go to step 307);
step 307) the longitude of all the sampling points of the arc is summed to calculate the longitude average of the arc.
As a modification of the above method, the step 302) specifically includes:
determining the distance rho from the GEO target to the space-based measurement platformiAnd ρj，ρiAnd ρjAll values are within 38000-44000 kilometers, and | rhoi-ρjLess than or equal to 1000 kilometers; i and j are the arcsTwo sampling points within a segment;
according to rhoiAnd ρjThe value interval and the difference between the value interval and the value interval assume that a distance set from a space-based platform to a GEO target at a series of measuring point moments in an arc section meets the following formula:
{(ρi,ρj)|38000＜ρi＜44000,38000＜ρj＜44000,|ρi-ρj|＜1000}
according to p in each pair of combinationsiAnd ρjCalculated according to the following formula:
Figure BDA0003038136410000031
Figure BDA0003038136410000032
wherein r isiAnd rjPosition vectors, r, of sampling points i and J, respectively, with respect to the GEO target in the J2000 coordinate systemsite_miAnd rsite_mjRespectively, the position vectors of the sampling points i and J relative to the space-based platform under the J2000 coordinate system,
Figure BDA0003038136410000033
and
Figure BDA0003038136410000034
and respectively, the eye line unit vectors of the GEO target corresponding to the sampling points i and j relative to the measuring platform.
As an improvement of the above method, the step 303) specifically includes:
calculating velocity vectors v of sampling points i and j by adopting lambert methodiAnd vj，
Right ascension alpha of k-th angle measurement sampling point of track direction according to perturbation modelmkAnd declination deltamkForecasting to obtain a position vector r forecasted under a J2000 coordinate systemekAnd velocity vector vek；
According to the predicted position vector rekAnd a platform position vector rsite_mkCalculating the position r of the GEO target relative to the space-based platformrel_ekGenerating the predicted right ascension alphaekAnd declination deltaek；
The mean square error J in the arc is obtained according to the following formula:
Figure BDA0003038136410000035
as a modification of the above method, the step 304) specifically includes:
set { rho ] of pairs by bacterial foragingi,ρjPerforming chemotaxis operation, and selecting a mean square error J as an adaptability value:
Figure BDA0003038136410000036
obtaining the distance quantity which enables the fitness function to be minimum through the optimization process of the bacterial foraging combined genetic algorithm, and calculating to obtain the position vector r of the GEO targetiAnd velocity vector viThereby determining an initial trajectory.
Compared with the prior art, the invention has the advantages that:
1. compared with the prior art, the invention provides a method for converting the determination problem of the initial orbit of the short arc section of the GEO target into the parameter optimization problem, improves the global search capability of a bacterial foraging algorithm by improving the bacterial foraging algorithm, is applied to the determination of the initial orbit of the short arc section of the GEO target, and improves the determination precision of the initial orbit of the GEO target, particularly the semi-long axis precision;
2. the method of the invention converts the orbit of the initial orbit determination into the longitude and latitude in the sub-star point orbit to carry out the association between the arc sections, and can improve the success rate of the association of the target for most non-8-shaped sub-star point orbit GEO targets;
3. the method has the effects of improving the determination precision of the GEO target space-based angle measurement data track and improving the association success rate.
Drawings
FIG. 1 is a flow chart of a space-based optical angle measurement arc initial orbit determination and correlation method for a GEO target according to embodiment 1 of the present invention;
FIG. 2 is a graph of a simulation example low orbit solar synchronous orbit satellite platform versus GEO measurement arc segment distribution;
FIG. 3 is a longitude profile calculated 5 days after orbit determination of GEO measurement data by a simulation example low orbit solar synchronous orbit satellite platform;
fig. 4 is a correlation success rate calculated by a simulation example for different time intervals.
Detailed Description
The basic implementation process of the invention is as follows:
the method comprises the steps of firstly, processing data measured by a space-based platform, converting a coordinate system, and screening the GEO target right ascension and declination data.
And step two, converting the right ascension angle data into a direction vector.
Step three, measuring the distance rho between the space-based platform and the GEO target in the measuring point in the arc sectioniAnd ρjAnd as an optimization variable, generating a search grid point of the skew distance according to a limiting condition.
And fourthly, calculating the number of the orbits according to the two points, and forecasting and counting the mean square error of the measured data.
And fifthly, performing track search optimization by adopting a bacterial foraging algorithm and a genetic algorithm to determine an initial track.
Step six, calculating the position vector r of the GEO targetiTransforming and calculating to obtain longitude and latitude parameters (lat) of the track of the points under the satelliteiloni)。
Step seven, judging whether to return to the second step or not, repeating the steps to calculate the latitude and longitude parameter (lat) of the track of the point under the satellite of the (i + 1) th pointi+1 loni+1)
Step eight, averaging the longitudes of the N points,
Figure BDA0003038136410000051
and calculating the longitude average value of the second arc segment by adopting the method.
And step nine, setting correlation between longitude threshold arc sections, and judging whether the two arc sections are correlated when the longitude error is less than 0.015 degree.
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 1, embodiment 1 of the present invention provides a method for tracking and associating a space-based optical angle measurement arc segment for a GEO target, which includes the following specific steps:
the method comprises the steps of firstly, processing data measured by a space-based platform, converting a coordinate system, and screening the GEO target right ascension and declination data. In this embodiment, the first step may include the following steps S11 to S13, specifically:
s11: screening the measuring arc sections of the space-based platform, and if the maximum value delta of declination data of the measured value in a certain measuring arc section ismaxAbove 15 deg., discard the arc segment.
S12: converting the height and longitude and latitude data of the space-based measuring platform under the earth-fixed coordinate system into position and speed data r under the J2000 coordinate systemsite_miAnd vsite_mi。
And step two, converting the right ascension angle data into a direction vector. In this embodiment, the second step may include the following steps S21 to S23, specifically:
s21: selecting two measuring arc sections aiming at the GEO target space-based platform, wherein the length of the measuring arc section is about 1-3 minutes, and the interval between sampling points is 3 seconds.
S22: each sampling point corresponds to a pair of right ascension and declination data, and the t-th of the arc segment is selectediRight ascension and declination measurement data (alpha) of timei,δi)。
S23: and aiming at each arc segment, generating a sight line unit vector of the GEO target relative to the measuring platform at the measuring time point:
Figure BDA0003038136410000061
wherein N is the number of data points in the arc segment, alphatiAnd deltatiThe data of the right ascension and the declination of the ith sampling point are respectively shown.
Step three, measuring the distance rho between the space-based platform and the GEO target in the measuring point in the arc sectioniAnd ρjAnd as an optimization variable, generating a search grid point of the skew distance according to the limiting condition.
In the present embodiment, the third step may include the following steps S31 to S34, specifically:
s31: the space-based platform selects a low-orbit sun synchronous near-circular orbit.
S32: estimating a distance ρ from a GEO target to a space-based measurement platformiAnd ρj，ρiAnd ρjThe value is in 38000-44000 kilometers range, | rhoi-ρjLess than or equal to 1000 kilometers.
S33: according to rhoiAnd ρjThe value range and the difference between the value range and the value range assume a distance set from a space-based platform to a GEO target at a measuring point moment in a series of arc sections
{(ρi,ρj)|38000＜ρi＜44000,38000＜ρj＜44000,|ρi-ρj|＜1000}
S34: according to rho in each pair of combinationsiAnd ρjCalculating the position vector of the corresponding time of two points
Figure BDA0003038136410000062
Figure BDA0003038136410000063
Wherein r isiAnd rjPosition vectors, r, of sampling points i and J, respectively, with respect to the GEO target in the J2000 coordinate systemsite_miAnd rsite_mjRespectively, the position vectors of the sampling points i and J relative to the space-based platform under the J2000 coordinate system,
Figure BDA0003038136410000064
and
Figure BDA0003038136410000065
is respectively adoptedAnd (4) viewing unit vectors of GEO targets corresponding to the sampling points i and j relative to the measuring platform.
And fourthly, calculating the number of the orbits according to the two points, and forecasting and counting the mean square error of the measured data.
In the present embodiment, the step four may include the following steps S41 to S43, specifically:
s41: calculating the velocity vector v of the two selected points by using a lambert methodiAnd vj，
S42: after the position and the velocity vector of the arc segment point are obtained, the track direction angle measurement sampling point (alpha) is measured according to the perturbation modelmk,δmk) Forecasting to obtain a position vector r which represents a measurement sampling point under a J2000 coordinate systemekAnd velocity vector vek。
S43: according to the predicted position vector rekAnd a platform position vector rsite_mkCalculating the position r of the target relative to the measuring platformrel_ekGenerating the forecast right ascension and declination angle measurement data (alpha)ek,δek)。
Calculating the mean square deviations of the measured right ascension and declination and the forecast right ascension and declination of N-1 points:
Figure BDA0003038136410000071
and fifthly, performing track search optimization by adopting a bacterial foraging algorithm and a genetic algorithm to determine an initial track. In the present embodiment, the step four may include the following steps S51 to S56, specifically:
s51: set { rho ] of pairs by bacterial foragingi,ρjAnd performing chemotaxis operation. In the chemotaxis operation, bacteria randomly select a direction to swim, and the bacteria individual fitness value is calculated once when the bacteria swim. The fitness value is selected as:
Figure BDA0003038136410000072
s52: and in the case of less than the limited walking step number, if the fitness of the new position is better, storing and updating the fitness value of the new position.
If the adaptability of the new position is poor or the limited step length of the swimming is reached, the swimming is finished, the swimming direction of the bacteria is reversed, and the bacteria swim to the other direction.
S53: and (3) searching a local optimal solution, setting P (i, n) as the position of the bacteria individual, and representing the nth chemotaxis operation by n. The equation for the movement of bacteria in the confined area is:
P(i,n+1)＝P(i,n)+C(i)φ(i,n)
wherein
Figure BDA0003038136410000073
Is a unit random vector, C (i) is a chemotaxis step size of the bacteria, and delta (i) is a unit direction random vector with the size between-1 and 1.
S54: in the process of bacteria swimming and overturning, the bacteria individuals can judge whether to deviate from the optimal fitness area according to the interaction with other bacteria, so that the occurrence of dispersion is avoided, and the aggregation characteristic of the bacteria is kept. Particularly the attractive and repulsive forces between bacteria. The interaction between individual bacteria and other bacteria is represented by the following formula:
Figure BDA0003038136410000081
s means the number of bacteria, m means the dimension of individual bacteria,
Figure BDA0003038136410000082
represents the m-th component of the i-th bacterium. dattAnd wattDistance and range, h, representing the action of bacterial attractionrepAnd wrepBacterial repulsion action distance and range.
S55: and (4) coding, crossing, mutating and decoding the current bacterial sample, and screening out a new bacterial sample. Different from the copying and transferring operation of the traditional bacterial foraging method, the genetic algorithm is introduced into the traditional bacterial foraging copying and transferring operation, and the global searching capacity of the bacterial foraging method is improved.
S56: obtaining the distance quantity which enables the fitness function to be minimum through the optimization process of the bacterial foraging combined genetic algorithm, and calculating the position vector riVelocity vector vi。
Step six, calculating the position vector r of the GEO targetiTransforming and calculating to obtain longitude and latitude parameters (lat) of the track of the points under the satelliteiloni)。
Step seven, judging whether to return to the second step or not, repeating the steps to calculate the latitude and longitude parameter (lat) of the track of the point under the satellite of the (i + 1) th pointi+1 loni+1)
Step eight, averaging the longitudes of the N points,
Figure BDA0003038136410000083
and calculating the longitude average value of the second arc segment by adopting the method.
And step nine, setting correlation between longitude and latitude threshold arc sections, and judging that the two arc sections are correlated when the longitude error is less than 0.015 degree.
A specific simulation example is given below to illustrate the method, in which a simulated satellite platform is located in a morning and evening orbit of a sun-synchronized orbit at an orbit height of about 500 km, and an optical detection device points to the sun-back surface of the satellite, i.e., the Y-axis of the satellite body coordinate system, and points to the GEO orbit band. The orbital long period term of the satellite platform is: the semi-major axis a is 6871.902km, the track eccentricity e is 0.0014714, and the track inclination angle i is 97.428 °. The angle measurement accuracy of the optical measuring device was 3 arcsec. The simulation generated 5 days of optical measurements as shown in fig. 2, which shows the distribution of simulated arcs characterized by short arcs, since the optical device may also detect large elliptical and low orbit satellites. The overall arc segment distribution is centered at less than 150 seconds.
The method of the present invention is used for orbit determination and is converted into the latitude and longitude information of the sub-satellite point, as shown in fig. 3, which shows the latitude and longitude information of the sub-satellite point at different times of the detection target calculated by the method. It can be seen that the distribution of longitude information is substantially linear with time, which lays a good foundation for the next step of correlation.
As shown in fig. 4, we correlate the measurement arcs of different time intervals, and it can be seen from the correlation result that the initial correlation success rate is greater than 85%. Since most of the error correlation results are that a plurality of arc segments are correlated with one target, if the condition is further screened, the correlation success rate can reach more than 90%.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (7)

1. A space-based optical goniometric arc segment initial orbit and associated method for GEO targets, the method comprising:
step 1) screening a measuring arc section of a space-based platform, and performing coordinate system conversion on height and longitude and latitude data of the space-based platform to obtain a position vector and a speed vector under a J2000 coordinate system;
step 2) selecting two space-based platform measuring arc sections aiming at the GEO target from the screened measuring arc sections, and respectively sampling the right ascension and declination data in the two arc sections;
step 3) determining the distance range from the space-based platform to the GEO target to generate search grid points with slant distances for each arc section according to the right ascension and declination data of the sampling points, and determining the initial orbit corresponding to each sampling point by adopting a bacterial foraging algorithm and a genetic algorithm in the search grid points to obtain the corresponding sub-satellite point track so as to obtain the longitude average value of each arc section;
and 4) calculating the difference value of the longitude average values of the two arc sections, and associating the two arc sections when the difference value is smaller than a preset threshold value.
2. The space-based optical goniometric arc segment initial orbit determination and correlation method for the GEO-target according to claim 1, wherein the step 1) specifically includes:
screening the measuring arc section of the space-based platform, and discarding the arc section when the maximum value of declination data of the measuring data in the measuring arc section is greater than a threshold value; otherwise, the arc segment is reserved;
and converting the height and longitude and latitude data of the space-based platform under the earth-fixed coordinate system into a position vector and a speed vector under the J2000 coordinate system.
3. The space-based optical goniometric arc segment initial orbit determination and correlation method for the GEO target of claim 2, wherein the step 2) specifically comprises:
selecting two measuring arc sections with the length reaching the preset time and aiming at a space-based platform of the GEO target, and setting sampling point intervals for sampling;
respectively selecting right ascension data alpha of the ith sampling point for each arc segmentiAnd declination data deltai；
Generating a sight unit vector of the GEO target corresponding to the ith sampling point relative to the measuring platform according to the following formula
Figure FDA0003038136400000011
Comprises the following steps:
Figure FDA0003038136400000012
wherein N is the number of sampling points in the arc segment.
4. The space-based optical goniometric arc segment initial orbit determination and correlation method for the GEO-target according to claim 3, characterized in that said step 3) specifically comprises, for each arc segment, the following steps:
step 301) converting the right ascension and declination data of the sampling point into a direction vector;
step 302) estimating the distance range from the space-based platform to the GEO target, taking the distance range as an optimization variable, and generating a search grid point of the slant distance according to the limiting condition;
step 303) forecasting the orbital direction angle measurement sampling point according to the perturbation model, calculating the position of the GEO target relative to the measuring platform according to the forecasted position vector and the space-based platform position vector, and generating forecast data; calculating the mean square error of the measured data and the forecast data of each sampling point in the arc section;
step 304) in the search grid points, performing track search optimization by adopting a bacterial foraging algorithm and a genetic algorithm and taking the mean square error as an adaptability value to obtain a position vector and a speed vector of a GEO target so as to determine an initial track;
step 305) converting and calculating to obtain the longitude and latitude of the sub-satellite point track corresponding to the sampling point according to the position vector of the GEO target;
step 306), when the arc segment has the non-calculated sampling point, turning to step 301) to obtain the longitude and latitude of the sub-satellite point track of the next sampling point of the arc segment; otherwise, go to step 307);
step 307) the longitude of all the sampling points of the arc is summed to calculate the longitude average of the arc.
5. The space-based optical goniometric arc segment initial orbit determination and correlation method for the GEO-target of claim 4, wherein the step 302) specifically comprises:
determining the distance rho from the GEO target to the space-based measurement platformiAnd ρj，ρiAnd ρjAll values are within 38000-44000 kilometers, and | rhoi-ρjLess than or equal to 1000 kilometers; i and j are two sampling points in the arc segment;
according to rhoiAnd ρjThe value interval and the difference between the value interval and the value interval assume that a distance set from a space-based platform to a GEO target at a series of measuring point moments in an arc section meets the following formula:
{(ρi,ρj)|38000＜ρi＜44000,38000＜ρj＜44000,|ρi-ρj|＜1000}
according to p in each pair of combinationsiAnd ρjCalculated according to the following formula:
Figure FDA0003038136400000021
Figure FDA0003038136400000022
wherein r isiAnd rjPosition vectors, r, of sampling points i and J, respectively, with respect to the GEO target in the J2000 coordinate systemsite_miAnd rsite_mjRespectively, the position vectors of the sampling points i and J relative to the space-based platform under the J2000 coordinate system,
Figure FDA0003038136400000023
and
Figure FDA0003038136400000024
and respectively, the eye line unit vectors of the GEO target corresponding to the sampling points i and j relative to the measuring platform.
6. The space-based optical goniometric arc segment initial orbit determination and correlation method for the GEO-target of claim 5, wherein the step 303) specifically includes:
calculating velocity vectors v of sampling points i and j by adopting lambert methodiAnd vj，
Right ascension alpha of k-th angle measurement sampling point of track direction according to perturbation modelmkAnd declination deltamkForecasting to obtain a position vector r forecasted under a J2000 coordinate systemekAnd velocity vector vek；
According to the predicted position vector rekAnd a platform position vector rsite_mkCalculating the position r of the GEO target relative to the space-based platformrel_ekGenerating the predicted right ascension alphaekAnd declination deltaek；
The mean square error J in the arc is obtained according to the following formula:
Figure FDA0003038136400000031
7. the space-based optical goniometric arc segment initial orbit determination and correlation method for GEO targets of claim 6, wherein the step 304) specifically comprises:
set { rho ] of pairs by bacterial foragingi,ρjPerforming chemotaxis operation, and selecting a mean square error J as an adaptability value:
Figure FDA0003038136400000032
obtaining the distance quantity which enables the fitness function to be minimum through the optimization process of the bacterial foraging combined genetic algorithm, and calculating to obtain the position vector r of the GEO targetiAnd velocity vector viThereby determining an initial trajectory.
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CN114396953A (en) * 2021-11-30 2022-04-26 中国西安卫星测控中心 Correlation method for space-based short arc optical track measurement data
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CN115790607B (en) * 2023-01-31 2023-05-12 南京航空航天大学 Non-cooperative target maneuvering characteristic detection method based on short arc historical data
CN116224379A (en) * 2023-05-06 2023-06-06 中国科学院国家空间科学中心 NBRCS correction method and device, electronic equipment and storage medium
CN116224379B (en) * 2023-05-06 2023-09-12 中国科学院国家空间科学中心 NBRCS correction method and device, electronic equipment and storage medium

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