CN111259310A - Thermal layer atmospheric density prediction method and system based on distributed sensing unit - Google Patents

Thermal layer atmospheric density prediction method and system based on distributed sensing unit Download PDF

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CN111259310A
CN111259310A CN202010036996.7A CN202010036996A CN111259310A CN 111259310 A CN111259310 A CN 111259310A CN 202010036996 A CN202010036996 A CN 202010036996A CN 111259310 A CN111259310 A CN 111259310A
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atmospheric density
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CN111259310B (en
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刘卫
刘四清
龚建村
罗冰显
王荣兰
师立勤
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National Space Science Center of CAS
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Abstract

The invention belongs to the technical field of atmospheric density sensing methods and space physics, and particularly relates to a thermal layer atmospheric density prediction method based on a distributed track atmospheric sensing unit, which comprises the following steps: obtaining P distributed track atmosphere sensing units; calculating the hot-layer atmospheric density correction ratio of the track surface where each distributed track atmospheric sensing unit is located by combining the energy dissipation rate or the semimajor axis attenuation; a plurality of space targets which are uniformly distributed in the P distributed track atmosphere sensing units when different places are periodically and dynamically selected; on all P distributed orbit atmosphere sensing units, calculating the atmosphere density of space points of space targets on corresponding orbit surfaces every 2-30 s, and further periodically acquiring a full-space atmosphere density data set { rho [ rho ] for 3-24 hOAnd calculating spherical harmonic coefficients, further calculating the corrected inflection point temperature and the corrected escape layer temperature to form a hot-layer atmospheric density correction model, and obtaining the dynamically corrected hot-layer atmospheric density by using the correction model to realize prediction of the atmospheric density at any position in future space.

Description

Thermal layer atmospheric density prediction method and system based on distributed sensing unit
Technical Field
The invention belongs to the technical field of atmospheric density sensing methods and space physics, and particularly relates to a thermal layer atmospheric density prediction method and system based on a distributed track atmospheric sensing unit.
Background
The high-precision orbit atmosphere prediction has important application value in aerospace activities such as spacecraft orbit determination prediction, reentry point prediction of a re-entry returning capsule and the like. At present, a thermal layer atmosphere model generally has an error of 15-30%, and a space weather event period is larger, so that the high-precision thermal layer atmosphere prediction requirement cannot be met.
In the aerospace engineering, the method for estimating the resistance coefficient to compensate the atmospheric model error can meet the high-precision requirement of the spacecraft with the orbit tracking data. Because the error of the atmosphere model of the thermal layer has the characteristics of local time, latitude and height, the method has no space expansibility and cannot be popularized to other orbit spacecrafts for application; the special detection space and time resolution for the atmosphere of the thermal layer are low, the cost is high and the like; the traditional track atmosphere compensation method has the defect of non-expandable space, and cannot meet the high-precision prediction of the atmosphere density of a thermal layer.
Disclosure of Invention
The invention aims to solve the defects of the existing thermal layer atmospheric density model, and provides a thermal layer atmospheric density prediction method based on a distributed track atmospheric sensing unit.
In order to achieve the above object, the present invention provides a hot-layer atmospheric density prediction method based on a distributed track atmospheric sensing unit, which includes:
dividing the atmosphere of the thermal layer into a plurality of tangent planes, and taking a plurality of space targets running in a track surface corresponding to each tangent plane as distributed track atmosphere sensing units to obtain P distributed track atmosphere sensing units;
calculating a hot-layer atmospheric density correction ratio of a track surface where each distributed track atmospheric sensing unit is located based on track data of each distributed track atmospheric sensing unit and by combining energy dissipation rate or semimajor axis attenuation;
a plurality of space targets which are uniformly distributed in the P distributed track atmosphere sensing units when different places are periodically and dynamically selected;
on all P distributed track atmosphere sensing units, calculating the atmosphere density of space points of a space target on a corresponding track surface every 2-30 s by using the corrected ratio and the atmosphere density of a hot-layer atmosphere density model, and further periodically acquiring a full-space atmosphere density data set { rho ] for 3-24 hO}；
The obtained full-space atmospheric density data set [ rho ]OTaking the thermal layer boundary temperature spherical harmonic coefficient expansion correction method as correction data, dynamically correcting the thermal layer atmospheric density model, and calculating the spherical harmonic coefficient by using a differential correction method;
and calculating the corrected inflection point temperature and the corrected escape layer temperature by using the calculated spherical harmonic coefficient to form a thermal layer atmospheric density correction model, and obtaining the dynamically corrected thermal layer atmospheric density by using the thermal layer atmospheric density correction model to realize the prediction of the atmospheric density of any position in the future space.
As one improvement of the technical scheme, in the plurality of space targets, each space target is located at an orbit height of less than 800km, has an inclination angle within a range of 90 +/-15 degrees, and has a spherical or square target configuration characteristic and a posture stability characteristic of a spin rate of less than 10 degrees/day.
As one improvement of the above technical solution, the hot-layer atmospheric density correction ratio of the track surface where each distributed track atmospheric sensing unit is located is calculated based on the track data of each distributed track atmospheric sensing unit and by combining with semimajor axis attenuation; the method specifically comprises the following steps:
the orbit data of the distributed orbit atmosphere sensing unit comprises: track semi-major axis data; wherein the track semi-major axis data comprises: the change rate of the satellite orbit semimajor axis and the satellite orbit semimajor axis caused by atmospheric resistance perturbation acceleration and atmospheric damping;
obtaining atmospheric resistance perturbation acceleration adrag：
Figure BDA0002366387650000021
Wherein the ballistic coefficient BC ═ CDA/m；CDIs the satellite drag coefficient; a and m are the windward area and mass of the satellite respectively; v. ofrIs the velocity vector of the satellite relative to the atmosphere;
obtaining the change rate of the semi-major axis of the satellite orbit caused by atmospheric damping
Figure BDA0002366387650000022
Figure BDA0002366387650000023
Wherein a is a satellite orbit semi-major axis; v is the satellite velocity; mu is an earth gravity constant;
integration can obtain two track data epoch times t1,t2In the interval, calculating the average atmospheric density of the track surface where the distributed track atmosphere sensing unit is located
Figure BDA0002366387650000024
Figure BDA0002366387650000031
wherein ,
Figure BDA0002366387650000032
is a time t1,t2In the interval, the variation of the semi-major axis of the track caused by atmospheric damping; mu is an earth gravity constant;
Figure BDA0002366387650000033
the square of the semi-major axis of the track corresponding to the moment t; vt is the satellite speed corresponding to the moment t;
Figure BDA0002366387650000034
is the square of the satellite's relative atmospheric velocity;
mean value of density of hot layer model on orbit surface of distributed orbit atmospheric sensing unit at the same time
Figure BDA0002366387650000035
Expressed as:
Figure BDA0002366387650000036
wherein ,ρMAtmospheric density of the thermal layer atmospheric density model;
in the period, the atmospheric density correction ratio lambda of the P-th distributed track atmospheric sensing unitpNamely, the corrected ratio of the atmospheric density on the track surface where the distributed track atmospheric sensing unit is located is expressed as:
Figure BDA0002366387650000037
as one improvement of the above technical solution, on all the P distributed track atmosphere sensing units, the atmospheric density of the spatial point of the spatial target on the corresponding track surface is calculated every 2 to 30s by using the corrected ratio and the atmospheric density of the thermal layer atmospheric density model, and then the full-space atmospheric density data set { ρ is periodically acquired for 3 to 24hO}; the method specifically comprises the following steps:
on all P distributed track atmosphere sensing units, calculating the atmospheric density of a space target at a space point on a corresponding track surface every 2-30 s by using the corrected ratio and the atmospheric density of the hot-layer atmospheric density model:
ρO＝λpρM(6)
wherein ,ρOThe atmospheric density of a space point of a space target on a track surface corresponding to the P-th distributed track atmosphere sensing unit is obtained;
and then periodically obtaining a full-space atmospheric density data set { rho ] within 3-24 hO}：
{ρO}＝{λ1ρM,λ2ρM,...λpρM} (7)
Wherein p is 1,2, … N; lambda [ alpha ]1Correcting the ratio for the atmospheric density of the 1 st distributed track atmospheric sensing unit; lambda [ alpha ]2And correcting the ratio for the atmospheric density of the 2 nd distributed track atmospheric sensing unit.
As one improvement of the technical scheme, the full-space atmospheric density data set { rho ] to be obtainedOTaking the thermal layer boundary temperature spherical harmonic coefficient expansion correction method as correction data, dynamically correcting the thermal layer atmospheric density model, and calculating the spherical harmonic coefficient by using a differential correction method; the method specifically comprises the following steps:
the obtained full-space atmospheric density data set [ rho ]OThe method comprises the following steps of (1) dynamically correcting a hot-layer atmospheric density model Jacchia70 by adopting a hot-layer boundary temperature spherical harmonic coefficient expansion correction method as correction data, wherein the method comprises the following specific steps:
inflection temperature T at 125km height for thermal layer atmospheric density model Jacchia70xAnd temperature T of escaping layercRespectively carrying out spherical harmonic coefficient expansion to respectively obtain inflection point temperature correction quantity delta TxAnd escaping layer temperature correction quantity delta Tc：
Figure BDA0002366387650000041
Figure BDA0002366387650000042
wherein ：
Figure BDA0002366387650000043
is an orthogonal normalized l × m order connected Legendre polynomial;
Figure BDA0002366387650000044
is the latitude; θ is local time;
Figure BDA0002366387650000045
spherical harmonic coefficient corresponding to temperature for thermal layer correction, for Δ Tx and ΔTcIn a word
Figure BDA0002366387650000046
The values of (a) are different, and the order of l, m is also different; l and m are positive integers;
wherein, spherical harmonic coefficient corresponding to the correction temperature of the thermal layer is obtained
Figure BDA0002366387650000047
The method specifically comprises the following steps:
the obtained full-space atmospheric density data set [ rho ]OAs correction data, the density residual vector b is calculated:
b＝ρo-ρM(10)
and solving the spherical harmonic coefficient corresponding to the correction temperature of the thermal layer by using b minimization as an optimization target
Figure BDA0002366387650000048
Since the calculated function of the density of the thermal layer and the spherical harmonic coefficient are nonlinear, the spherical harmonic coefficient corresponding to the corrected temperature of the thermal layer
Figure BDA0002366387650000049
When solving, firstly, carrying out linearization processing on a calculation function of the thermal layer density by using a differential correction method, and then carrying out iterative calculation on a processed result, wherein the method specifically comprises the following steps:
model equation ρ to be correctedm(X) at X0And (3) treating Taylor expansion:
Figure BDA00023663876500000410
wherein ,ρm(X) a hot layer density calculation function for the Jacchia70 model; x is a spherical harmonic coefficient vector; x0A reference value for X; rhom(X0) Function for hot layer density calculation for the Jacchia70 model at X0The specific value of (d);
Figure BDA00023663876500000411
is rhomA matrix of partial derivatives for X; x is the vector of the spherical harmonic coefficient vector correction value; o (| X-X)0|)kA small quantity of order k; x → X0Denotes that X tends to X0When the current is over;
order:
Figure BDA0002366387650000051
Figure BDA0002366387650000052
wherein ,
Figure BDA0002366387650000053
calculating a corresponding model value for the nth hot layer density measurement; xi+1The i +1 th iteration value vector of X;
Xithe ith iteration value vector of X;
Figure BDA0002366387650000054
is an element in the spherical harmonic coefficient vector X;
Figure BDA0002366387650000055
is an element in the vector x of the spherical harmonic coefficient vector correction value;
spherical harmonic coefficient corresponding to thermal layer correction temperature
Figure BDA0002366387650000056
The solution becomes:
Ax＝b (14)
wherein ,
Figure BDA0002366387650000057
is the spherical harmonic coefficient vector SH (1-13) to be estimated; a is an n × 13 partial derivative matrix (n is the number of measured data n > 13); x is the vector of the spherical harmonic coefficient vector correction value;
and taking the state quantity correction value of the spherical harmonic coefficient as the spherical harmonic coefficient corresponding to the hot layer correction temperature, namely the spherical harmonic coefficient.
As one improvement of the above technical solution, the modified inflection point temperature and the external escapement layer temperature are calculated by using the calculated spherical harmonic coefficient, two boundary temperatures of the inflection point temperature and the external escapement layer temperature of the original thermal layer large air density model are replaced to form a thermal layer atmospheric density modification model, and the thermal layer atmospheric density modification model is used to obtain the dynamically modified thermal layer atmospheric density, so as to predict the atmospheric density of any position in the future space; the method specifically comprises the following steps:
correction amount of inflection point temperature Delta TxInflection temperature T added to thermal layer atmospheric density model Jacchia70xTo obtain a corrected inflection point temperature T'x：
T′x＝Tx+ΔTx(15)
Correcting escape layer temperature by delta TcEscape layer temperature T into thermal layer atmospheric Density model Jacchia70cTo obtain a corrected escape layer temperature T'c：
T′c＝Tc+ΔTc(16)
Corrected inflection point temperature T'xAnd corrected escape layer temperature T'cReplacing two boundary temperatures of inflection point temperature and escape layer temperature of the original hot layer large air density model to form a hot layer atmospheric density correction model, and correcting the corrected inflection point temperature Tx' and corrected escape layer temperature TcSubstituting the atmospheric density of the thermal layer into the thermal layer atmospheric density correction model to obtain the atmospheric density of the thermal layer after dynamic correction, and realizing prediction of the atmospheric density of any position in the future space.
The invention also provides a hot-layer atmospheric density prediction system based on the distributed track atmospheric sensing unit, which comprises:
the sensing unit acquisition module is used for dividing the hot-layer atmosphere into a plurality of tangent planes, and a plurality of space targets running in a track plane corresponding to each tangent plane are used as distributed track atmosphere sensing units to acquire P distributed track atmosphere sensing units;
the first calculation module is used for calculating a hot-layer atmospheric density correction ratio of a track surface where each distributed track atmospheric sensing unit is located based on track data of each distributed track atmospheric sensing unit and by combining energy dissipation rate or semi-major axis attenuation;
the dynamic selection module is used for periodically and dynamically selecting a plurality of space targets which are uniformly distributed in the P distributed track atmosphere sensing units when different places are selected;
the data acquisition module is used for calculating the atmospheric density of a space target at a space point on a corresponding track surface every 2-30 s by using the corrected ratio and the atmospheric density of the thermal layer atmospheric density model on all P distributed track atmospheric sensing units, and further periodically acquiring a full-space atmospheric density data set { rho within 3-24 hO}；
A second calculation module for calculating the acquired full-space atmospheric density data set { rho }OTaking the thermal layer boundary temperature spherical harmonic coefficient expansion correction method as correction data, dynamically correcting the thermal layer atmospheric density model, and calculating the spherical harmonic coefficient by using a differential correction method; and
and the prediction module is used for calculating the corrected inflection point temperature and the corrected escape layer temperature by using the calculated spherical harmonic coefficient to form a thermal layer atmospheric density correction model, obtaining the dynamically corrected thermal layer atmospheric density by using the thermal layer atmospheric density correction model, and realizing the prediction of the atmospheric density of any position in the future space.
Compared with the prior art, the invention has the beneficial effects that: in the aspect of sensing the atmospheric change of the thermal layer, the invention selects low orbit targets which are distributed in a reasonable quantity and a full space from the existing space targets as sensing units, overcomes the defects of low space and time resolution, high cost and the like of the special detection space for the thermal layer atmosphere, adopts a dynamic correction method of a thermal layer atmospheric model, breaks through the space expansibility compared with the prior art, and can be popularized to other orbital spacecrafts for application. In addition, based on the distributed track atmosphere sensing unit, the atmosphere density change on different track surfaces is sensed. And generating thermal layer atmosphere density correction data of the whole space by combining the thermal layer model, dynamically correcting the thermal layer atmosphere model, breaking through the defect that the space of the traditional track atmosphere compensation method cannot be expanded, and meeting the high-precision requirement of the thermal layer atmosphere.
Drawings
Fig. 1 is a schematic diagram of a track surface for obtaining P distributed track atmosphere sensing units in step 1) of a method for predicting the hot-layer atmosphere density of the distributed track atmosphere sensing units according to the present invention;
FIG. 2 is a distribution diagram of inflection point temperature correction amount based on a hot-layer atmospheric density prediction method of a distributed track atmospheric sensing unit according to the present invention;
FIG. 3 is a comparison graph of relative error before and after correction of a method for predicting hot-layer atmospheric density based on a distributed track atmospheric sensing unit according to the present invention;
FIG. 4 is a flowchart of a hot-layer atmospheric density prediction method based on a distributed track atmospheric sensing unit according to the present invention.
Detailed Description
The invention will now be further described with reference to the accompanying drawings.
As shown in FIG. 4, the invention provides a hot-layer atmosphere density prediction method based on a distributed track atmosphere sensing unit, which dynamically corrects a hot-layer atmosphere model based on atmosphere sensing data acquired by the distributed track atmosphere sensing unit, overcomes the defect of non-expandable space of the traditional track atmosphere compensation method, and meets the high-precision prediction of the hot-layer atmosphere density.
The method comprises the following steps:
step 1) dividing the atmosphere of the heat layer into a plurality of tangent planes, and taking a plurality of space targets running in a track surface corresponding to each tangent plane as distributed track atmosphere sensing units to obtain P distributed track atmosphere sensing units; the multiple space targets in each track surface correspond to each distributed track atmosphere sensing unit;
in other specific embodiments, one space target running in the track plane corresponding to each tangent plane may also be used as a distributed track atmosphere sensing unit to obtain P distributed track atmosphere sensing units; the space target in each track surface corresponds to each distributed track atmosphere sensing unit one by one; and the hot-layer atmospheric density prediction method based on the distributed track atmospheric sensing unit is carried out as an alternative technical scheme. Step 2) calculating a hot-layer atmospheric density correction ratio of a track surface where each distributed track atmospheric sensing unit is located based on track data of each distributed track atmospheric sensing unit and by combining energy dissipation rate or semi-major axis attenuation;
specifically, the orbit data of the distributed orbit atmosphere sensing unit includes: track semi-major axis data; wherein the track semi-major axis data comprises: the change rate of the satellite orbit semimajor axis and the satellite orbit semimajor axis caused by atmospheric resistance perturbation acceleration and atmospheric damping;
obtaining atmospheric resistance perturbation acceleration adrag：
Figure BDA0002366387650000071
Wherein the ballistic coefficient BC ═ CDA/m；CDIs the satellite drag coefficient; a and m are the windward area and mass of the satellite respectively; v. ofrIs the velocity vector of the satellite relative to the atmosphere;
obtaining the change rate of the semi-major axis of the satellite orbit caused by atmospheric damping
Figure BDA0002366387650000081
Figure BDA0002366387650000082
Wherein a is a satellite orbit semi-major axis; v is the satellite velocity; mu is an earth gravity constant;
integration can obtain two track data epoch times t1,t2In the interval, calculating the average atmospheric density of the track surface where the distributed track atmosphere sensing unit is located
Figure BDA0002366387650000083
Figure BDA0002366387650000084
wherein ,
Figure BDA0002366387650000085
is a time t1,t2In the interval, the variation of the semi-major axis of the track caused by atmospheric damping; mu is an earth gravity constant;
Figure BDA0002366387650000086
the square of the semi-major axis of the track corresponding to the moment t; v. oftThe satellite speed corresponding to the moment t;
Figure BDA0002366387650000087
is the square of the satellite's relative atmospheric velocity;
mean value of density of hot layer model on orbit surface of distributed orbit atmospheric sensing unit at the same time
Figure BDA0002366387650000088
Expressed as:
Figure BDA0002366387650000089
wherein ,ρMAtmospheric density of the thermal layer atmospheric density model;
in the period, the atmospheric density correction ratio lambda of the P-th distributed track atmospheric sensing unitpNamely, the corrected ratio of the atmospheric density on the track surface where the distributed track atmospheric sensing unit is located is expressed as:
Figure BDA00023663876500000810
in other specific embodiments, based on the orbit data of each distributed orbit atmosphere sensing unit and in combination with an Energy Dissipation Ratio (EDR), a hot layer atmosphere density correction ratio of the orbit surface where each distributed orbit atmosphere sensing unit is located is calculated.
Step 3) periodically and dynamically selecting a plurality of space targets which are uniformly distributed in the P distributed track atmosphere sensing units at different places; wherein, 2-3d is set as a period;
selecting a plurality of space targets of a near-polar orbit and a low-earth orbit (200-800 km) distributed at different places, wherein the number of the space targets is 100, 60 space targets are used for correction, and 40 space targets are used for standby.
In the plurality of space targets, the orbit height of each space target is less than 800km, the inclination angle is within the range of 90 +/-15 degrees, and the space targets have spherical or square target configuration characteristics and attitude stabilization characteristics with the spin rate of less than 10 degrees/day.
Wherein each space target is selected to meet the requirements that the track height is less than 800km and the inclination angle is within the range of 90 +/-15 degrees, and each space target also comprises the following components: simple target configuration features and attitude stabilization features; wherein simple target configuration features are square or spherical; wherein, the shape is preferably spherical, and the prolate space target is avoided; attitude stabilization is characterized by a spin rate of less than 10 degrees per day (deg/day);
and 4) calculating the atmospheric density of a space target at a space point on a corresponding track surface every 2-30 s on all P distributed track atmospheric sensing units by using the corrected ratio and the atmospheric density of the thermal-layer atmospheric density model, and further periodically acquiring a full-space atmospheric density data set { rho (rho) } within 3-24 hO}；
Step 5) obtaining a full-space atmospheric density data set { rhoOTaking the thermal layer boundary temperature spherical harmonic coefficient expansion correction method as correction data, dynamically correcting the thermal layer atmospheric density model, and calculating the spherical harmonic coefficient by using a differential correction method;
specifically, the full-space atmospheric density data set { ρ is to be obtainedODo itIn order to correct data, a thermal-layer boundary temperature spherical harmonic coefficient expansion correction method is adopted to dynamically correct a thermal-layer atmospheric density model Jacchia70, and the method specifically comprises the following steps:
inflection temperature T at 125km height for thermal layer atmospheric density model Jacchia70xAnd temperature T of escaping layercRespectively carrying out spherical harmonic coefficient expansion to respectively obtain inflection point temperature correction quantity delta TxAnd escaping layer temperature correction quantity delta Tc：
Figure BDA0002366387650000091
Figure BDA0002366387650000092
wherein ：
Figure BDA0002366387650000093
is an orthogonal normalized l × m order connected Legendre polynomial;
Figure BDA0002366387650000094
is the latitude; θ is local time;
Figure BDA0002366387650000095
spherical harmonic coefficient corresponding to temperature for thermal layer correction, for Δ Tx and ΔTcIn a word
Figure BDA0002366387650000096
The values of (a) are different, and the order of l, m is also different; l and m are positive integers; wherein the inflection point temperature TxAnd temperature T of escaping layercTwo atmospheric boundary temperatures for the thermal layer atmospheric density model Jacchia 70;
wherein, spherical harmonic coefficient corresponding to the correction temperature of the thermal layer is obtained
Figure BDA0002366387650000097
The method specifically comprises the following steps:
the obtained full-space atmospheric density data set [ rho ]OAs a correctionPositive data, compute density residual vector b:
b＝ρo-ρM(10)
and solving the spherical harmonic coefficient corresponding to the correction temperature of the thermal layer by using b minimization as an optimization target
Figure BDA0002366387650000098
Since the calculated function of the density of the thermal layer and the spherical harmonic coefficient are nonlinear, the spherical harmonic coefficient corresponding to the corrected temperature of the thermal layer
Figure BDA0002366387650000099
When solving, firstly, carrying out linearization processing on a calculation function of the thermal layer density by using a differential correction method, and then carrying out iterative calculation on a processed result, wherein the method specifically comprises the following steps:
model equation ρ to be correctedm(X) at X0And (3) treating Taylor expansion:
Figure BDA0002366387650000101
wherein ,ρm(X) a hot layer density calculation function for the Jacchia70 model; x is a spherical harmonic coefficient vector; x0A reference value for X; ρ m (X)0) Function for hot layer density calculation for the Jacchia70 model at X0The specific value of (d);
Figure BDA0002366387650000102
is rhomA matrix of partial derivatives for X; x is the vector of the spherical harmonic coefficient vector correction value; o (| X-X)0|)kA small quantity of order k; x → X0Denotes that X tends to X0When the current is over;
order:
Figure BDA0002366387650000103
Figure BDA0002366387650000104
wherein ,
Figure BDA0002366387650000105
calculating a corresponding model value for the nth hot layer density measurement; xi+1The i +1 th iteration value vector of X;
Xithe ith iteration value vector of X;
Figure BDA0002366387650000106
is an element in the spherical harmonic coefficient vector X;
Figure BDA0002366387650000107
is an element in the vector x of the spherical harmonic coefficient vector correction value;
spherical harmonic coefficient corresponding to thermal layer correction temperature
Figure BDA0002366387650000108
The solution becomes:
Ax＝b (14)
wherein ,
Figure BDA0002366387650000109
is the spherical harmonic coefficient vector SH (1-13) to be estimated; a is an n × 13 partial derivative matrix (n is the number of measured data n > 13); x is the vector of the spherical harmonic coefficient vector correction value;
and taking the state quantity correction value of the spherical harmonic coefficient as the spherical harmonic coefficient corresponding to the hot layer correction temperature, namely the spherical harmonic coefficient.
And 6) calculating the corrected inflection point temperature and the corrected escape layer temperature by using the calculated spherical harmonic coefficient, replacing two boundary temperatures of the inflection point temperature and the escape layer temperature of the original hot layer large air density model to form a hot layer atmospheric density correction model, and obtaining the dynamically corrected hot layer atmospheric density by using the hot layer atmospheric density correction model to realize the prediction of the atmospheric density of any position of a future space.
Specifically, the inflection point temperature correction amount Δ T is correctedxInflection temperature T added to thermal layer atmospheric density model Jacchia70xIn the step (2), the corrected inflection point temperature is obtainedDegree T'x：
T′x＝Tx+ΔTx(15)
Correcting escape layer temperature by delta TcEscape layer temperature T into thermal layer atmospheric Density model Jacchia70cTo obtain a corrected escape layer temperature T'c：
T′c＝Tc+ΔTc(16)
Corrected inflection point temperature T'xAnd corrected escape layer temperature T'cReplacing two boundary temperatures of inflection point temperature and escape layer temperature of the original hot layer atmospheric density model to form a hot layer atmospheric density correction model, and correcting the corrected inflection point temperature T'xAnd corrected escape layer temperature T'cAnd substituting the atmospheric density of the thermal layer into a thermal layer atmospheric density correction model to obtain the dynamically corrected thermal layer atmospheric density, thereby realizing the prediction of the atmospheric density at any position in the future space.
The invention also provides a hot-layer atmospheric density prediction system based on the distributed track atmospheric sensing unit, which comprises:
the sensing unit acquisition module is used for dividing the hot-layer atmosphere into a plurality of tangent planes, and a plurality of space targets running in a track plane corresponding to each tangent plane are used as distributed track atmosphere sensing units to acquire P distributed track atmosphere sensing units; the multiple space targets in each track surface correspond to each distributed track atmosphere sensing unit;
in other specific embodiments, one space target running in the track plane corresponding to each tangent plane may also be used as a distributed track atmosphere sensing unit to obtain P distributed track atmosphere sensing units; the space target in each track surface corresponds to each distributed track atmosphere sensing unit one by one; and to use it as an alternative solution.
The first calculation module is used for calculating a hot-layer atmospheric density correction ratio of a track surface where each distributed track atmospheric sensing unit is located based on track data of each distributed track atmospheric sensing unit and by combining energy dissipation rate or semi-major axis attenuation;
the dynamic selection module is used for periodically and dynamically selecting a plurality of space targets which are uniformly distributed in the P distributed track atmosphere sensing units when different places are selected; wherein, 2-3d is set as a period;
the data acquisition module is used for calculating the atmospheric density of a space target at a space point on a corresponding track surface every 2-30 s by using the corrected ratio and the atmospheric density of the thermal layer atmospheric density model on all P distributed track atmospheric sensing units, and further periodically acquiring a full-space atmospheric density data set { rho within 3-24 hO}；
A second calculation module for calculating the acquired full-space atmospheric density data set { rho }OTaking the thermal layer boundary temperature spherical harmonic coefficient expansion correction method as correction data, dynamically correcting the thermal layer atmospheric density model, and calculating the spherical harmonic coefficient by using a differential correction method; and
and the prediction module is used for calculating the corrected inflection point temperature and the corrected escape layer temperature by using the calculated spherical harmonic coefficient, replacing two boundary temperatures of the inflection point temperature and the escape layer temperature of the original hot layer large air density model to form a hot layer atmospheric density correction model, and obtaining the dynamically corrected hot layer atmospheric density by using the hot layer atmospheric density correction model to realize the prediction of the atmospheric density of any position of a future space.
In the method, about 60 near-polar orbit low-space targets which are uniformly distributed when a place with the height of 200-800 km and have simple configuration and stable postures are selected to form a distributed orbit atmosphere sensing unit; calculating the hot-layer atmospheric density correction ratio of the track surface where each distributed track atmospheric sensing unit is located by utilizing TLE track data of the sensing unit and attenuation of a semimajor axis, obtaining the density of each 20s (not limited to) atmospheric point on the track surface by combining with a corresponding atmospheric model, and further periodically obtaining a full-space atmospheric density data set { rho ] within 3-24 hOTaking the thermal layer boundary temperature spherical harmonic coefficient as a correction data set, dynamically correcting the thermal layer atmospheric density model by adopting a thermal layer boundary temperature spherical harmonic coefficient expansion correction method, and calculating the spherical harmonic coefficient by using a differential correction method; calculating the corrected inflection point temperature and the corrected escape layer temperature by using the calculated spherical harmonic coefficient to replace the large air density of the original thermal layerThe inflection point temperature and the escape layer temperature of the model form a thermal layer atmospheric density correction model, the thermal layer atmospheric density correction model is utilized to obtain the thermal layer atmospheric density after dynamic correction, the atmospheric density at any position of a future space is predicted, the high-precision thermal layer atmospheric demand is met, and the implementation effect is shown in figure 2.
As shown in fig. 1, the atmospheric thermal layer is divided into a plurality of track surfaces according to the track surface distribution of the selected track atmospheric sensing units, and each track surface is used as a corresponding distributed track atmospheric sensing unit to obtain P distributed track atmospheric sensing units; and each track surface corresponds to each distributed track atmosphere sensing unit one to one.
As shown in fig. 2, the distribution of the global inflection point temperature correction amount calculated on the spherical surface of 125km height, and the shade of the color bar on the right side represents the temperature correction amount of a specific point on the spherical surface. Such as
Figure BDA0002366387650000121
When θ is 3, Δ T x50 degrees celsius.
As shown in fig. 3, for an example of a magnetic storm event of 10 months in 2003, the correction effects of the relative errors before and after the thermal layer atmosphere model is dynamically corrected are compared. The results of the correction using the data on both orbital planes: mean before dynamic correction-94.43%, standard deviation 65.87%, mean after dynamic correction-6.96%, standard deviation 39.37%, mean of MSIS00 model-86.11%, and standard deviation 58.13%. If the 60-track sensing unit is combined with the method, the corrected average value can be reduced to 3%.
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 thermal-layer atmospheric density prediction method based on a distributed track atmospheric sensing unit is characterized by comprising the following steps:
dividing the atmosphere of the thermal layer into a plurality of tangent planes, and taking a plurality of space targets running in a track surface corresponding to each tangent plane as distributed track atmosphere sensing units to obtain P distributed track atmosphere sensing units;
calculating a hot-layer atmospheric density correction ratio of a track surface where each distributed track atmospheric sensing unit is located based on track data of each distributed track atmospheric sensing unit and by combining energy dissipation rate or semimajor axis attenuation;
a plurality of space targets which are uniformly distributed in the P distributed track atmosphere sensing units when different places are periodically and dynamically selected;
on all P distributed track atmosphere sensing units, calculating the atmosphere density of space points of a space target on a corresponding track surface every 2-30 s by using the corrected ratio and the atmosphere density of a hot-layer atmosphere density model, and further periodically acquiring a full-space atmosphere density data set { rho ] for 3-24 hO}；
The obtained full-space atmospheric density data set [ rho ]OTaking the thermal layer boundary temperature spherical harmonic coefficient expansion correction method as correction data, dynamically correcting the thermal layer atmospheric density model, and calculating the spherical harmonic coefficient by using a differential correction method;
and calculating the corrected inflection point temperature and the corrected escape layer temperature by using the calculated spherical harmonic coefficient to form a thermal layer atmospheric density correction model, and obtaining the dynamically corrected thermal layer atmospheric density by using the thermal layer atmospheric density correction model to realize the prediction of the atmospheric density of any position in the future space.
2. The method of claim 1, wherein each of the plurality of spatial objects has an orbit height of less than 800km, a tilt angle in the range of 90 ± 15 degrees, a configuration feature with a spherical or square object, and an attitude stabilization feature with a spin rate of less than 10 degrees/day.
3. The method according to claim 1, wherein the hot layer atmospheric density correction ratio of the track surface where each distributed track atmosphere sensing unit is located is calculated based on the track data of each distributed track atmosphere sensing unit and combined with semimajor axis attenuation; the method specifically comprises the following steps:
the orbit data of the distributed orbit atmosphere sensing unit comprises: track semi-major axis data; wherein the track semi-major axis data comprises: the change rate of the satellite orbit semimajor axis and the satellite orbit semimajor axis caused by atmospheric resistance perturbation acceleration and atmospheric damping;
obtaining atmospheric resistance perturbation acceleration adrag：
Figure FDA0002366387640000011
Wherein the ballistic coefficient BC ═ CDA/m；CDIs the satellite drag coefficient; a and m are the windward area and mass of the satellite respectively; v. ofrIs the velocity vector of the satellite relative to the atmosphere;
obtaining the change rate of the semi-major axis of the satellite orbit caused by atmospheric damping
Figure FDA0002366387640000021
Figure FDA0002366387640000022
Wherein a is a satellite orbit semi-major axis; v is the satellite velocity; mu is an earth gravity constant;
integration can obtain two track data epoch times t1,t2In the interval, calculating the average atmospheric density of the track surface where the distributed track atmosphere sensing unit is located
Figure FDA0002366387640000023
Figure FDA0002366387640000024
wherein ,
Figure FDA0002366387640000025
is a time t1,t2In the interval, the variation of the semi-major axis of the track caused by atmospheric damping; mu is an earth gravity constant;
Figure FDA0002366387640000026
the square of the semi-major axis of the track corresponding to the moment t; v. oftThe satellite speed corresponding to the moment t;
Figure FDA0002366387640000027
is the square of the satellite's relative atmospheric velocity;
mean value of density of hot layer model on orbit surface of distributed orbit atmospheric sensing unit at the same time
Figure FDA0002366387640000028
Expressed as:
Figure FDA0002366387640000029
wherein ,ρMAtmospheric density of the thermal layer atmospheric density model;
in the period, the atmospheric density correction ratio lambda of the P-th distributed track atmospheric sensing unitpNamely, the corrected ratio of the atmospheric density on the track surface where the distributed track atmospheric sensing unit is located is expressed as:
Figure FDA00023663876400000210
4. the method as claimed in claim 1, wherein the atmospheric density of the space target at the corresponding space point on the orbit surface is calculated every 2-30 s by using the corrected ratio and the atmospheric density of the hot-layer atmospheric density model on all the P distributed orbit atmospheric sensing units, and then the full-space atmospheric density data set { P is acquired periodically for 3-24 hO}; the method specifically comprises the following steps:
on all P distributed track atmosphere sensing units, calculating the atmospheric density of a space target at a space point on a corresponding track surface every 2-30 s by using the corrected ratio and the atmospheric density of the hot-layer atmospheric density model:
ρO＝λpρM(6)
wherein ,ρOThe atmospheric density of a space point of a space target on a track surface corresponding to the P-th distributed track atmosphere sensing unit is obtained;
and then periodically obtaining a full-space atmospheric density data set { rho ] within 3-24 hO}：
{ρO}＝{λ1ρM,λ2ρM,...λpρM} (7)
Wherein p is 1,2, … N; lambda [ alpha ]1Correcting the ratio for the atmospheric density of the 1 st distributed track atmospheric sensing unit; lambda [ alpha ]2And correcting the ratio for the atmospheric density of the 2 nd distributed track atmospheric sensing unit.
5. The method of claim 1, wherein the full-space atmospheric density dataset { p ] to be obtainedOTaking the thermal layer boundary temperature spherical harmonic coefficient expansion correction method as correction data, dynamically correcting the thermal layer atmospheric density model, and calculating the spherical harmonic coefficient by using a differential correction method; the method specifically comprises the following steps:
the obtained full-space atmospheric density data set [ rho ]OThe method comprises the following steps of (1) dynamically correcting a hot-layer atmospheric density model Jacchia70 by adopting a hot-layer boundary temperature spherical harmonic coefficient expansion correction method as correction data, wherein the method comprises the following specific steps:
inflection temperature T at 125km height for thermal layer atmospheric density model Jacchia70xAnd temperature T of escaping layercRespectively carrying out spherical harmonic coefficient expansion to respectively obtain inflection point temperature correction quantity delta TxAnd escaping layer temperature correction quantity delta Tc：
Figure FDA0002366387640000031
Figure FDA0002366387640000032
wherein ：
Figure FDA0002366387640000033
is an orthogonal normalized l × m order connected Legendre polynomial;
Figure FDA0002366387640000034
is the latitude; θ is local time;
Figure FDA0002366387640000035
spherical harmonic coefficient corresponding to temperature for thermal layer correction, for Δ Tx and ΔTcIn a word
Figure FDA0002366387640000036
The values of (a) are different, and the order of l, m is also different; l and m are positive integers;
wherein, spherical harmonic coefficient corresponding to the correction temperature of the thermal layer is obtained
Figure FDA0002366387640000037
The method specifically comprises the following steps:
the obtained full-space atmospheric density data set [ rho ]OAs correction data, the density residual vector b is calculated:
b＝ρo-ρM(10)
and solving the spherical harmonic coefficient corresponding to the correction temperature of the thermal layer by using b minimization as an optimization target
Figure FDA0002366387640000038
Since the calculated function of the density of the thermal layer and the spherical harmonic coefficient are nonlinear, the spherical harmonic coefficient corresponding to the corrected temperature of the thermal layer
Figure FDA0002366387640000039
In advance ofWhen the line is solved, firstly, the calculation function of the thermal layer density is linearized by using a differential correction method, and then, the iteration calculation is carried out on the processed result, which specifically comprises the following steps:
model equation ρ to be correctedm(X) at X0And (3) treating Taylor expansion:
Figure FDA00023663876400000310
wherein ,ρm(X) a hot layer density calculation function for the Jacchia70 model; x is a spherical harmonic coefficient vector; x0A reference value for X; rhom(X0) Function for hot layer density calculation for the Jacchia70 model at X0The specific value of (d);
Figure FDA00023663876400000311
is rhomA matrix of partial derivatives for X; x is the vector of the spherical harmonic coefficient vector correction value; o (| X-X)0|)kA small quantity of order k; x → X0Denotes that X tends to X0When the current is over;
order:
Figure FDA0002366387640000041
Figure FDA0002366387640000042
wherein ,
Figure FDA0002366387640000043
calculating a corresponding model value for the nth hot layer density measurement; xi+1The i +1 th iteration value vector of X; xiThe ith iteration value vector of X;
Figure FDA0002366387640000044
is an element in the spherical harmonic coefficient vector X;
Figure FDA0002366387640000045
is an element in the vector x of the spherical harmonic coefficient vector correction value;
spherical harmonic coefficient corresponding to thermal layer correction temperature
Figure FDA0002366387640000046
The solution becomes:
Ax＝b (14)
wherein ,
Figure FDA0002366387640000047
is the spherical harmonic coefficient vector SH (1-13) to be estimated; a is a n × 13 partial derivative matrix, n is the number of measured data n > 13; x is the vector of the spherical harmonic coefficient vector correction value;
and taking the state quantity correction value of the spherical harmonic coefficient as the spherical harmonic coefficient corresponding to the hot layer correction temperature, namely the spherical harmonic coefficient.
6. The method as claimed in claim 5, wherein the corrected inflection point temperature and the outer escape layer temperature are calculated by using the calculated spherical harmonic coefficient to replace two boundary temperatures of the inflection point temperature and the outer escape layer temperature of the original thermal layer large air density model to form a thermal layer atmospheric density correction model, and the thermal layer atmospheric density correction model is used to obtain the dynamically corrected thermal layer atmospheric density to realize prediction of atmospheric density at any position of a future space; the method specifically comprises the following steps:
correction amount of inflection point temperature Delta TxInflection temperature T added to thermal layer atmospheric density model Jacchia70xTo obtain a corrected inflection point temperature T'x：
T′x＝Tx+ΔTx(15)
Correcting escape layer temperature by delta TcEscape layer temperature T into thermal layer atmospheric Density model Jacchia70cTo obtain a corrected escape layer temperature T'c：
T′c＝Tc+ΔTc(16)
Corrected inflection point temperature T'xAnd corrected temperature of the escaping layerT′cReplacing two boundary temperatures of inflection point temperature and escape layer temperature of the original hot layer atmospheric density model to form a hot layer atmospheric density correction model, and correcting the corrected inflection point temperature T'xAnd corrected escape layer temperature T'cAnd substituting the atmospheric density of the thermal layer into a thermal layer atmospheric density correction model to obtain the dynamically corrected thermal layer atmospheric density, thereby realizing the prediction of the atmospheric density at any position in the future space.
7. A thermal layer atmospheric density prediction system based on a distributed track atmospheric sensing unit is characterized by comprising:
the sensing unit acquisition module is used for dividing the hot-layer atmosphere into a plurality of tangent planes, and a plurality of space targets running in a track plane corresponding to each tangent plane are used as distributed track atmosphere sensing units to acquire P distributed track atmosphere sensing units;
the first calculation module is used for calculating a hot-layer atmospheric density correction ratio of a track surface where each distributed track atmospheric sensing unit is located based on track data of each distributed track atmospheric sensing unit and by combining energy dissipation rate or semi-major axis attenuation;
the dynamic selection module is used for periodically and dynamically selecting a plurality of space targets which are uniformly distributed in the P distributed track atmosphere sensing units when different places are selected;
the data acquisition module is used for calculating the atmospheric density of a space target at a space point on a corresponding track surface every 2-30 s by using the corrected ratio and the atmospheric density of the thermal layer atmospheric density model on all P distributed track atmospheric sensing units, and further periodically acquiring a full-space atmospheric density data set { rho within 3-24 hO}；
A second calculation module for calculating the acquired full-space atmospheric density data set { rho }OTaking the thermal layer boundary temperature spherical harmonic coefficient expansion correction method as correction data, dynamically correcting the thermal layer atmospheric density model, and calculating the spherical harmonic coefficient by using a differential correction method; and
and the prediction module is used for calculating the corrected inflection point temperature and the corrected escape layer temperature by using the calculated spherical harmonic coefficient to form a thermal layer atmospheric density correction model, obtaining the dynamically corrected thermal layer atmospheric density by using the thermal layer atmospheric density correction model, and realizing the prediction of the atmospheric density of any position in the future space.
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