CN111578950B - Space-based optical monitoring-oriented GEO target autonomous arc segment association and orbit determination method - Google Patents

Space-based optical monitoring-oriented GEO target autonomous arc segment association and orbit determination method Download PDF

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CN111578950B
CN111578950B CN202010515802.1A CN202010515802A CN111578950B CN 111578950 B CN111578950 B CN 111578950B CN 202010515802 A CN202010515802 A CN 202010515802A CN 111578950 B CN111578950 B CN 111578950B
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CN111578950A (en
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黄剑
朱天林
王东亚
李朋远
张兵
王鲲鹏
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63921 Troops of PLA
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Abstract

The invention discloses a space-based optical monitoring-oriented GEO target autonomous arc segment association and orbit determination method, relates to the technical field of spaceflight, and has high association accuracy and orbit determination precision. Firstly, the method utilizes the position vectors corresponding to any two short arc primary tracks to carry out Lambert equation solution to obtain a primary track semi-major axis with higher precision, utilizes the assumption of a near-circular track to carry out distance assignment on angle measurement data points, further completes primary track improvement under the perturbation condition, compares the difference between the primary track improvement result and the original observation angle, and selects the observation residual slope as a judgment threshold to carry out correlation among primary track arc sections. And taking the initial orbit result of the correlation between the two arc sections as the initial root number of the inventory library, carrying out autonomous distance forecast on the newly observed arc section, combining actual angle measurement data, carrying out track improvement and correlation judgment, and realizing the updating and maintenance of the steady GEO target autonomous inventory track.

Description

Space-based optical monitoring-oriented GEO target autonomous arc segment association and orbit determination method
Technical Field
The invention relates to the technical field of spaceflight, in particular to a GEO-target autonomous arc segment association and orbit determination method for space-based optical monitoring.
Background
The normalized monitoring for realizing the global space target is based on the space, and world major countries such as America, Russia, France, Japan and the like successively build a space target monitoring 'national team', and undertake the tasks of detecting, cataloguing, reconnaissance and monitoring the space target. The GEO satellite has wide application in the fields of global communication, reconnaissance, early warning and the like, and belongs to scarce space strategic resources. The method has important significance for completely detecting and cataloging global GEO targets and determining the target rail positions and behavior intentions.
The space-based optical monitoring satellite has the characteristic of global inspection, can quickly search and scan or stare to track a plurality of GEO targets, and can effectively inhibit the influence of sunlight and terrestrial gas light and improve the detection capability if a sun synchronous orbit or a small-inclination-angle orbit is adopted. After the observation data of the GEO target is obtained, the most critical link of space-based optical monitoring is to perform arc-segment correlation orbit determination on the data to complete autonomous cataloguing maintenance. The general process of the automatic cataloging of the space targets is that on the basis of short arc orbit determination, the association orbit determination between every two short arcs is carried out on the targets without the historical orbit number to form a new target orbit number; for the target with the historical track number, track improvement and cataloguing maintenance are carried out on the historical track number by using short arc data. An autonomous cataloguing method of GEO target space-based observation data with high association success rate and orbit determination precision is established, and is a basis for supporting the technical application of new target discovery, transaction detection, approach warning and the like.
However, autonomous correlation and orbit determination of space-based optical observation data present some systematic difficult problems. Due to the fact that the satellite platform is high in operation speed, the observation arc section of each GEO target is short, and convergence and accuracy of the short arc initial orbit determination cannot be guaranteed. Meanwhile, the track surface direction of the space-based platform under the inertial system is relatively fixed, if large-amplitude attitude maneuver is not adopted, the position of the obtained observation arc section under the inertial system is relatively fixed, the geometric distribution is sparse, and autonomous association and high-precision orbit determination cataloging are very difficult to realize.
Aiming at the requirements of autonomous arc segment association and orbit determination of the GEO target monitored by the space-based optics, an inter-arc segment association and orbit determination method with high association accuracy and precision is found, which is necessary for improving the autonomous cataloguing efficiency of the space-based optics monitoring satellite on the GEO target.
Disclosure of Invention
In view of the above, the invention provides a GEO target autonomous arc segment association and orbit determination method for space-based optical monitoring, which can solve the difficult problems of autonomous association and high-precision orbit determination between space-based observation short arc segments only using optical angle measurement data.
In order to achieve the purpose, the technical scheme of the invention is as follows: a GEO target autonomous arc segment association and orbit determination method for space-based optical monitoring comprises the following steps:
step 1, acquiring observation data of a geosynchronous orbit GEO target, and selecting any two known arc sections.
Step 2, performing Lambert equation solution on the two currently selected known arc sections to obtain an initial orbit semi-major axis, so as to obtain a Lambert equation orbit determination result of the two currently selected known arc sections, namely an epoch initial time t0Initial orbital number of time σLambert(t0)；t0Is the epoch initial time;
step 3, constructing a first observation equation: [ rho ]i(ti),αi(ti),δi(ti)]＝H(σLambert(t0),ti-t0)+V；
Wherein t isiFor epoch i time, ρi(ti) Is tiDistance assumed value, alpha, of a target observed at a momenti(ti) Is tiTime of red channel observation, deltai(ti) Is tiDeclination at time, H (σ)Lambert(t0),ti-t0) Is given by σLambert(t0) Substituting the initial value into a theoretical observation function of the track forecast, wherein V is a measurement error;
the first observation equation is subjected to linearization treatment, and the orbit is improved based on the least square method to obtain t after the orbit is improved0Time orbit determination result sigmaχ(t0)；
Step 4, utilizing orbit determination result sigma after orbit improvementχ(t0) Forecasting the track to obtain the improved t of the trackiForecast value of time red channel
Figure BDA0002530054570000021
And tiDeclination prediction value at moment
Figure BDA0002530054570000022
Step 5, respectively calculating a fixed orbit residual error sequence of the right ascension observation predicted value and a fixed orbit residual error sequence of the declination observation predicted value for two currently selected known arc sections with successful track improvement, and resolving to obtain residual error coefficients, wherein the residual error coefficients comprise a first-order trend coefficient of the fixed orbit residual error sequence of the right ascension observation predicted value and a first-order trend coefficient of the fixed orbit residual error sequence of the declination observation predicted value;
step 6, setting a threshold of the residual error coefficient, and if each residual error coefficient accords with the threshold of the residual error coefficient, judging that the two selected known arc sections are related and are related to each other, wherein the two related arc sections belong to the same target;
two known arc sections are selected again, the step 2 is returned until the pairwise combination of all the known arc sections is judged to be finished;
for two related arc segments belonging to the same target, corresponding to the improved t of the track0Time orbit determination result sigmaχ(t0) Step 7 is executed as the number of the historical tracks;
step 7, constructing a second observation equation:
Figure BDA0002530054570000031
H(σχ(t0),ti-t0) For taking the number of historical orbits sigmaχ(t0) Substituting a theoretical observation function of the track forecast; according to tiForecast value of time-of-day right ascension observation
Figure BDA0002530054570000032
tiForecast value of declination observation at moment
Figure BDA0002530054570000033
Adopting a second observation equation to forecast the target distance of the new observation arc section to obtain the new observation arc section at tiForecast value of time target distance
Figure BDA0002530054570000034
Step 8, constructing a third observation equation:
Figure BDA0002530054570000035
H(σχ(t0),ti-t0) For taking the number of historical orbits sigmaχ(t0) And substituting the theoretical observation function of the orbit prediction.
According to t of the new observation arc segmentiTime-of-day right ascension observed value alphai(ti) And a new observation arc segment tiDeclination observed value delta at momenti(ti)，tiForecast value of time target distance
Figure BDA0002530054570000036
Using least square method to measure sigma in third observation equationχ(t0) Carrying out orbit improvement, if the orbit improvement is successful, obtaining the orbit improvement result of the new observation arc section, and using the orbit improvement result of the new observation arc section to carry out the historical orbit number sigmaχ(t0) And maintaining the catalogues corresponding to the targets.
Further, in step 2, performing Lambert equation solving on the two currently selected known arc segments to obtain an initial orbit semi-major axis, so as to obtain a Lambert equation orbit determination result of the two selected known arc segments, namely the epoch initial time t0Initial orbital number of time σLambert(t0) (ii) a The method specifically comprises the following steps:
for two currently selected known arc segments, the orbit determination result of the first arc segment is an epoch t1Number of tracks at time σinitial(t1)，t1Calculating to obtain a first arc section t according to the two-body problem1The position vector of the time is
Figure BDA0002530054570000041
The result of the second arc is epoch t2Number of tracks at time σinitial(t2)，t2Calculating a second arc segment t for the epoch time corresponding to the second arc segment and taking the value of the epoch time as the observation time corresponding to the second arc segment2The position vector of the time is
Figure BDA0002530054570000042
Establishing a Lambert equation:
t2-t1＝(a3/μ)1/2[(ψ-sinψ)-(ε-sinε)]；
where a is the orbital semimajor axis, μ is the gravitational constant, and ψ is about the first arc segment t1Position vector of time
Figure BDA0002530054570000043
Is related to the second arc segment t2Position vector of time
Figure BDA0002530054570000044
Function of (c):
Figure BDA0002530054570000045
Figure BDA0002530054570000046
has a two-norm of
Figure BDA0002530054570000047
Has a two-norm of
Figure BDA0002530054570000048
The vector between the first arc segment and the second arc segment has a second norm of
Figure BDA0002530054570000049
||·||2Representing the two-norm of the vector.
Through iterative solution of the Lambert equation to the semi-major axis a of the track, the track fixing result of the Lambert equation of two known arc sections is selected, namely the initial epoch timet0Initial orbital number of time σLambert(t0)；t0Is the epoch initial time.
Further, in step 5, specifically: the two selected known arc sections are A and B;
using orbit determination results sigma after orbit improvementχ(t0) Forecasting the track to obtain the improved t of the trackiForecast value of time red channel
Figure BDA00025300545700000410
And tiDeclination prediction value at moment
Figure BDA00025300545700000411
In a time Slot corresponding to a currently selected known arc segment, forenotice values of the red meridians observation at S observation moments are respectively taken
Figure BDA00025300545700000412
And declination observation prediction value
Figure BDA00025300545700000413
Thus obtaining the orbit determination residual error sequence { delta alpha ] of the right ascension observation predicted values at S observation momentss,s＝1,2,...,S}，
Figure BDA0002530054570000051
And orbital residual sequence of declination observation prediction value { deltas,s＝1,2,...,S}，
Figure BDA0002530054570000052
s is the s-th observation time in the Slot; alpha is alphasIs the red channel observed value delta at the s-th observation time in the SlotsIs the declination observed value at the s-th observation time in the time interval Slot.
And (3) constructing an equation system:
Figure BDA0002530054570000053
wherein a is0Is the coefficient of deviation of the right ascension system, a1Is a first-order trend coefficient of the right ascension orbit determination error, b0Is the coefficient of declination system deviation, b1The first-order trend quantity of the declination orbit determination error is shown.
Solving residual error coefficient a corresponding to arc sections A and B through least square estimation0、a1、b0And b1。
Wherein the first-order trend coefficient of the right ascension orbit determination error corresponding to the arc segment A is recorded as
Figure BDA0002530054570000054
Declination orbit determination error first-order trend quantity
Figure BDA0002530054570000055
The first-order trend coefficient of the right ascension orbit determination error corresponding to the arc segment B is recorded as
Figure BDA0002530054570000056
Declination orbit determination error first-order trend quantity
Figure BDA0002530054570000057
Step 6, setting a threshold of the residual error coefficient, and if each residual error coefficient accords with the threshold of the residual error coefficient, judging that the two selected known arc sections are related and are related to each other, wherein the two related arc sections belong to the same target, and the method specifically comprises the following steps:
setting a residual coefficient threshold as 5 arc seconds/minute; if the following conditions are met:
Figure BDA0002530054570000058
then the arc sections A and B are judged to be related and are related to each other, and the two related arc sections belong to the same target.
Further, if the current known arc segment is related to more than one other known arc segment, the one with the smallest first-order trend quantity coefficient is preferably selected from the more than one other known arc segment as the related arc segment of the current known arc segment.
Further, in step 8, if the track improvement of the newly observed arc segment for more than one historical track number is successful, the target corresponding to the more than one historical track number is preferably sorted and maintained for which the corresponding first-order trend coefficient of the associated arc segment is the smallest.
Has the advantages that:
the invention provides a GEO target autonomous arc segment association and orbit determination method based on space-based optical monitoring. The method has the core that the Lambert equation is solved for any two short arcs, the precision of the initial orbit semi-long axis is improved, the distance initial value assumption is carried out on angle measurement data points, the initial orbit improvement under the perturbation condition is completed, the difference between the initial orbit improvement result and the original observation angle is compared, and the observation residual slope is selected as a judgment threshold to carry out the association between arc sections. The initial orbit result of the association between the two arc sections is used as the initial root number of the inventory library, autonomous distance prediction of a new observation arc section is carried out, and the stable inventory track updating and maintaining are realized by combining angle measurement data, so that the problems of autonomous association and high-precision orbit determination between space-based observation short arc sections only using optical angle measurement data in the traditional technology are solved.
Drawings
Fig. 1 is a flowchart of a GEO-target autonomous arc segment association and orbit determination method for space-based optical monitoring according to an embodiment of the present invention;
FIG. 2 is a diagram of the multi-arc segment correlation accuracy and orbit determination accuracy variation of the optical sky-based surveillance.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
As shown in fig. 1, the invention provides a GEO-target autonomous arc segment association and orbit determination method facing space-based optical monitoring, which is characterized by comprising the following steps:
step 1, acquiring observation data of a geosynchronous orbit GEO target, selecting any two known arc sections, and performing random grouping on all the known arc sections related to the observation data in pairs in a group when the random grouping is performed, wherein the step 2 to the step 6 are performed for each group.
Step 2, performing Lambert equation solution on the two currently selected known arc sections,obtaining the semi-major axis of the initial orbit, thus obtaining the orbit determination result of the Lambert equation of the two selected known arc sections, namely the initial time t of the epoch0Initial orbital number of time σLambert(t0)；t0Is the epoch initial time.
The method specifically comprises the following steps:
for two currently selected known arc segments, the orbit determination result of the first arc segment is an epoch t1Number of tracks at time σinitial(t1)，t1Is the epoch time, t, corresponding to the first arc segment1The value of (a) is an observation time interval corresponding to the first arc section, and the first arc section t is obtained by resolving according to the two-body problem1The position vector of the time is
Figure BDA0002530054570000071
The result of the second arc is epoch t2Number of tracks at time σinitial(t2)，t2Calculating a second arc segment t for the epoch time corresponding to the second arc segment and taking the value of the epoch time as the observation time corresponding to the second arc segment2The position vector of the time is
Figure BDA0002530054570000072
Establishing a Lambert equation:
t2-t1＝(a3/μ)1/2[(ψ-sinψ)-(ε-sinε)]formula (1)
Where a is the orbital semimajor axis, μ is the gravitational constant, and ψ is about the first arc segment t1Position vector of time
Figure BDA0002530054570000073
Is related to the second arc segment t2Position vector of time
Figure BDA0002530054570000074
The functions of ψ and ε are as follows
Figure BDA0002530054570000075
Figure BDA0002530054570000076
Has a two-norm of
Figure BDA0002530054570000077
Has a two-norm of
Figure BDA0002530054570000078
The vector between the first arc segment and the second arc segment has a second norm of
Figure BDA0002530054570000079
||·||2Representing the two-norm of the vector.
Through iterative solution of the Lambert equation to the semi-major axis a of the track, the track fixing result of the Lambert equation of two known arc sections is selected, namely the initial epoch time t0Initial orbital number of time σLambert(t0)；t0Is the epoch initial time.
Step 3, constructing a first observation equation:
[ρi(ti),αi(ti),δi(ti)]＝H(σLambert(t0),ti-t0) + V formula (3)
Wherein t isiFor epoch i time, ρi(ti) Is tiDistance assumed value, alpha, of a target observed at a momenti(ti) Is tiTime of red channel observation, deltai(ti) Is tiDeclination at time, H (σ)Lambert(t0),ti-t0) Is given by σLambert(t0) And (3) substituting the initial value into a theoretical observation function of the orbit prediction, wherein V is a measurement error, and H (×) and V are functions and error expressions commonly used in the field.
The first observation equation is subjected to linearization treatment, and the orbit is improved based on the least square method to obtain t after the orbit is improved0Time orbit determination result sigmaχ(t0)。
Step 4, utilizing orbit determination result sigma after orbit improvementχ(t0) Forecasting the track to obtain the improved t of the trackiForecast value of time red channel
Figure BDA0002530054570000081
And tiDeclination prediction value at moment
Figure BDA0002530054570000082
The orbit prediction adopts an orbit prediction mode commonly used in the field, and prediction values at all times can be obtained.
And 5, respectively calculating a fixed orbit residual sequence of the right ascension observation predicted value and a fixed orbit residual sequence of the declination observation predicted value for two currently selected known arc sections with successful track improvement, and calculating to obtain residual coefficients including a first-order trend coefficient of the fixed orbit residual sequence of the right ascension observation predicted value and a first-order trend coefficient of the fixed orbit residual sequence of the declination observation predicted value.
The method specifically comprises the following steps: the two selected known arc segments are denoted as a and B, respectively.
Using orbit determination results sigma after orbit improvementχ(t0) Forecasting the track to obtain the improved t of the trackiForecast value of time red channel
Figure BDA0002530054570000083
And tiDeclination prediction value at moment
Figure BDA0002530054570000084
In a time Slot corresponding to a currently selected known arc segment, forenotice values of the red meridians observation at S observation moments are respectively taken
Figure BDA0002530054570000085
And declination observation prediction value
Figure BDA0002530054570000086
Thereby obtaining the right ascension observation at S observation timesOrbit determination residual error sequence of prediction value [ delta alpha ]s,s＝1,2,...,S}，
Figure BDA0002530054570000087
And orbital residual sequence of declination observation prediction value { deltas,s＝1,2,...,S}，
Figure BDA0002530054570000088
s is the s-th observation time in the Slot; alpha is alphasIs the red channel observed value delta at the s-th observation time in the SlotsIs the declination observed value at the s-th observation time in the time interval Slot.
And (3) constructing an equation system:
Figure BDA0002530054570000089
wherein a is0Is the coefficient of deviation of the right ascension system, a1Is a first-order trend coefficient of the right ascension orbit determination error, b0Is the coefficient of declination system deviation, b1The first-order trend quantity of the declination orbit determination error is shown.
Solving residual error coefficient a corresponding to arc sections A and B through least square estimation0、a1、b0And b1。
Wherein the first-order trend coefficient of the right ascension orbit determination error corresponding to the arc segment A is recorded as
Figure BDA00025300545700000810
Declination orbit determination error first-order trend quantity
Figure BDA00025300545700000811
The first-order trend coefficient of the right ascension orbit determination error corresponding to the arc segment B is recorded as
Figure BDA00025300545700000812
Declination orbit determination error first-order trend quantity
Figure BDA0002530054570000091
And 6, setting a threshold of the residual error coefficient, and if each residual error coefficient accords with the threshold of the residual error coefficient, judging that the two selected known arc sections are related and are related to each other, wherein the two related arc sections belong to the same target.
In the embodiment of the invention, the residual coefficient threshold is set to be 5 arc seconds/minute, namely if the residual coefficient threshold meets the following conditions:
Figure BDA0002530054570000092
then the arc sections A and B are judged to be related and are related to each other, and the two related arc sections belong to the same target. If the current known arc segment is related to more than one other known arc segment, the one with the smallest first-order trend quantity coefficient is preferably selected from the more than one other known arc segment as the related arc segment of the current known arc segment.
And (3) reselecting two known arc sections, or selecting the next group of known arc sections, and returning to the step (2) until the combination of every two known arc sections is judged to be finished.
For two related arc segments belonging to the same target, corresponding to the improved t of the track0Time orbit determination result sigmaχ(t0) Step 7 is executed as the number of the historical tracks;
step 7, constructing a second observation equation:
Figure BDA0002530054570000093
H(σχ(t0),ti-t0) For taking the number of historical orbits sigmaχ(t0) Substituting a theoretical observation function of the track forecast; according to tiForecast value of time-of-day right ascension observation
Figure BDA0002530054570000094
tiForecast value of declination observation at moment
Figure BDA0002530054570000095
Adopting a second observation equation to forecast the target distance of the new observation arc section to obtain the new observation arc section at tiForecast value of time target distance
Figure BDA0002530054570000096
Step 8, constructing a third observation equation:
Figure BDA0002530054570000097
H(σχ(t0),ti-t0) For taking the number of historical orbits sigmaχ(t0) Substituting a theoretical observation function of the track forecast;
according to t of the new observation arc segmentiTime-of-day right ascension observed value alphai(ti) And a new observation arc segment tiDeclination observed value delta at momenti(ti)，tiForecast value of time target distance
Figure BDA0002530054570000098
Using least square method to measure sigma in third observation equationχ(t0) Carrying out orbit improvement, if the orbit improvement is successful, obtaining the orbit improvement result of the new observation arc section, and using the orbit improvement result of the new observation arc section to carry out the historical orbit number sigmaχ(t0) And maintaining the catalogues corresponding to the targets.
If the track improvement of the newly observed arc section aiming at more than one historical track number is successful, preferably, the target with the minimum first-order trend coefficient corresponding to the associated arc section is catalogued and maintained from more than one target corresponding to the historical track number.
In fig. 2, with the increase of the track improvement times, the target with association errors at the initial stage of autonomous cataloging is gradually removed, the association accuracy is rapidly improved, and when the improvement times reach more than 3 times, the association accuracy can be stabilized at more than 90%, which means that the autonomous stable cataloging of the target is basically realized. Meanwhile, as the number of arc sections adopted by target orbit determination is continuously increased, the orbit determination precision is increased from more than 120 kilometers associated with the initial two arc sections to 15 kilometers, and the higher precision level of sparse short arc orbit determination of the GEO target by the space-based optical monitoring satellite is basically achieved.
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 (5)

1. A GEO target autonomous arc segment association and orbit determination method for space-based optical monitoring is characterized by comprising the following steps:
step 1, acquiring observation data of a geosynchronous orbit GEO target, and selecting any two known arc sections;
step 2, performing Lambert equation solution on the two currently selected known arc sections to obtain an initial orbit semi-major axis, so as to obtain a Lambert equation orbit determination result of the two currently selected known arc sections, namely an epoch initial time t0Initial orbital number of time σLambert(t0)；t0Is the epoch initial time;
step 3, constructing a first observation equation: [ rho ]i(ti),αi(ti),δi(ti)]＝H(σLambert(t0),ti-t0)+V；
Wherein t isiFor epoch i time, ρi(ti) Is tiDistance assumed value, alpha, of a target observed at a momenti(ti) Is tiTime of red channel observation, deltai(ti) Is tiDeclination at time, H (σ)Lambert(t0),ti-t0) Is given by σLambert(t0) Substituting the initial value into a theoretical observation function of the track forecast, wherein V is a measurement error;
the first observation equation is subjected to linearization treatment, and the two selected known arc sections are subjected to orbit improvement based on a least square method to obtain t after the orbit improvement0Time orbit determination result sigmaχ(t0)；
Step 4, utilizing the orbit determination result sigma after the orbit improvementχ(t0) Forecasting the track to obtain the improved t of the trackiForecast value of time red channel
Figure FDA0003203431090000011
And tiDeclination prediction value at moment
Figure FDA0003203431090000012
Step 5, respectively calculating a fixed orbit residual error sequence of the right ascension observation predicted value and a fixed orbit residual error sequence of the declination observation predicted value for two currently selected known arc sections with successful track improvement, and resolving to obtain residual error coefficients, wherein the residual error coefficients comprise a first-order trend coefficient of the fixed orbit residual error sequence of the right ascension observation predicted value and a first-order trend coefficient of the fixed orbit residual error sequence of the declination observation predicted value;
step 6, setting a threshold of the residual error coefficient, and if each residual error coefficient accords with the threshold of the residual error coefficient, judging that the two selected known arc sections are related and are related to each other, wherein the two related arc sections belong to the same target;
two known arc sections are selected again, the step 2 is returned until the pairwise combination of all the known arc sections is judged to be finished;
for two related arc segments belonging to the same target, corresponding to the improved t of the track0Time orbit determination result sigmaχ(t0) Step 7 is executed as the number of the historical tracks;
step 7, constructing a second observation equation:
Figure FDA0003203431090000021
H(σχ(t0),ti-t0) For taking the number of historical orbits sigmaχ(t0) Substituting a theoretical observation function of the track forecast; according to tiForecast value of time-of-day right ascension observation
Figure FDA0003203431090000022
tiForecast value of declination observation at moment
Figure FDA0003203431090000023
Adopting a second observation equation to forecast the target distance of the new observation arc section to obtain the new observation arc section at tiForecast value of time target distance
Figure FDA0003203431090000024
Step 8, constructing a third observation equation:
Figure FDA0003203431090000025
H(σχ(t0),ti-t0) For taking the number of historical orbits sigmaχ(t0) Substituting a theoretical observation function of the track forecast;
according to t of the new observation arc segmentiTime-of-day right ascension observed value alphai(ti) And a new observation arc segment tiDeclination observed value delta at momenti(ti)，tiForecast value of time target distance
Figure FDA0003203431090000026
Using least square method to measure sigma in third observation equationχ(t0) Carrying out orbit improvement, if the orbit improvement is successful, obtaining the orbit improvement result of the new observation arc section, and using the orbit improvement result of the new observation arc section to carry out the historical orbit number sigmaχ(t0) And maintaining the catalogues corresponding to the targets.
2. The method as claimed in claim 1, wherein in step 2, Lambert's equation solution is performed for the two currently selected known arc segments to obtain the semi-major axis of the initial track, so as to obtain the result of the Lambert's equation orbit determination of the two selected known arc segments, that is, the initial epoch time t0Initial orbital number of time σLambert(t0) (ii) a The method specifically comprises the following steps:
for two currently selected known arc segments, the orbit determination result of the first arc segment is an epoch t1Number of tracks at time σinitial(t1)，t1Calendar corresponding to the first arc segmentAnd (3) calculating the meta-time to obtain a first arc section t according to the two-body problem1The position vector of the time is
Figure FDA0003203431090000027
The result of the second arc is epoch t2Number of tracks at time σinitial(t2)，t2Calculating a second arc segment t for the epoch time corresponding to the second arc segment and taking the value of the epoch time as the observation time corresponding to the second arc segment2The position vector of the time is
Figure FDA0003203431090000028
Establishing a Lambert equation:
t2-t1＝(a3/μ)1/2[(ψ-sinψ)-(ε-sinε)]；
where a is the orbital semimajor axis, μ is the gravitational constant, and ψ is about the first arc segment t1Position vector of time
Figure FDA0003203431090000031
Is related to the second arc segment t2Position vector of time
Figure FDA0003203431090000032
Function of (c):
Figure FDA0003203431090000033
Figure FDA0003203431090000034
has a two-norm of
Figure FDA0003203431090000035
Figure FDA0003203431090000036
Has a two-norm of
Figure FDA0003203431090000037
The vector between the first arc segment and the second arc segment has a second norm of
Figure FDA0003203431090000038
||·||2A two-norm representing a vector;
and iteratively solving the semi-major axis a of the track by the Lambert equation, so that the track fixing result of the Lambert equation of the two known arc sections is selected, namely the initial epoch time t0Initial orbital number of time σLambert(t0)；t0Is the epoch initial time.
3. The method according to claim 1, wherein in step 5, specifically: the two selected known arc sections are A and B;
using said improved orbit determination result sigmaχ(t0) Forecasting the track to obtain the improved t of the trackiForecast value of time red channel
Figure FDA0003203431090000039
And tiDeclination prediction value at moment
Figure FDA00032034310900000310
In a time Slot corresponding to a currently selected known arc segment, forenotice values of the red meridians observation at S observation moments are respectively taken
Figure FDA00032034310900000311
And declination observation prediction value
Figure FDA00032034310900000312
Thus obtaining the orbit determination residual error sequence { delta alpha ] of the right ascension observation predicted values at S observation momentss,s＝1,2,...,S}，
Figure FDA00032034310900000313
And orbital residual sequence of declination observation prediction value { deltas,s＝1,2,...,S}，
Figure FDA00032034310900000314
s is the s-th observation time in the time Slot; alpha is alphasIs the red channel observation value delta at the s-th observation time in the SlotsThe declination observed value is the s-th observation time in the Slot of the time period;
and (3) constructing an equation system:
Figure FDA00032034310900000315
wherein a is0Is the coefficient of deviation of the right ascension system, a1Is a first-order trend coefficient of the right ascension orbit determination error, b0Is the coefficient of declination system deviation, b1The first-order trend quantity of the declination orbit determination error is obtained;
solving residual error coefficient a corresponding to arc sections A and B through least square estimation0、a1、b0And b1；
Wherein the first-order trend coefficient of the right ascension orbit determination error corresponding to the arc segment A is recorded as
Figure FDA0003203431090000041
Declination orbit determination error first-order trend quantity
Figure FDA0003203431090000042
The first-order trend coefficient of the right ascension orbit determination error corresponding to the arc segment B is recorded as
Figure FDA0003203431090000043
Declination orbit determination error first-order trend quantity
Figure FDA0003203431090000044
In the step 6, by setting a threshold of the residual coefficient, if each residual coefficient meets the threshold of the residual coefficient, it is determined that the two selected known arc segments are related to each other and are related to each other, and the two related arc segments belong to the same target, specifically:
setting a residual coefficient threshold as 5 arc seconds/minute; if the following conditions are met:
Figure FDA0003203431090000045
then the arc sections A and B are judged to be related and are related to each other, and the two related arc sections belong to the same target.
4. The method of claim 3, wherein if the current known arc segment is related to more than one other known arc segment, then the one with the smallest first order trend magnitude coefficient is preferred from the more than one other known arc segment as the related arc segment of the current known arc segment.
5. The method according to claim 4, wherein in step 8, if the track improvement of the new observation arc segment for more than one historical track number is successful, the one with the smallest first-order trend coefficient of the associated arc segment is preferably maintained in the catalog from the more than one historical track number corresponding targets.
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