CN111428365A - Method for distinguishing GEO target by using astronomical measurement data - Google Patents

Abstract

The invention discloses a method for judging a GEO target by utilizing astronomical measurement data, which establishes an optical measurement data declination, declination change rate, distance and distance change rate correlation model, establishes a declination and distance phase diagram equation, and obtains the conclusion that the astronomical measurement declination phase diagram of the GEO target is an ellipse.

Description

Method for distinguishing GEO target by using astronomical measurement data

Technical Field

The invention relates to the technical field of astronomical measurement, in particular to a method for judging a GEO target by using astronomical measurement data.

Background

The initial orbit determination is to determine the space target orbit by using short arc section orbit measurement data (single-station single-circle orbit measurement data in most cases) and adopting a simpler dynamic model under the condition of no prior information. And determining an initial orbit result, namely, rapidly providing orbit parameters for the spacecraft which is just launched or orbitally maneuvered to judge whether the spacecraft is in orbit according to the designed orbit or maneuvered to the designed orbit, and guiding and forecasting the tracking of the space target by the later-stage survey station, wherein the initial orbit parameter is used as an initial value of orbit improvement, namely, a prior orbit. The initial rail determining result is used as a prior rail for rail improvement, the initial rail with higher precision can reduce the calculation iteration times in the rail improvement process, and the rail determining time is saved. In addition, in the spatial target inventory management, the initial track is the basis for measuring data matching and track identification, and the initial track with poor precision can cause target matching result errors.

[1] Liqiang, Single star passive orbit determination and tracking key technology research on satellite targets [ D ]. Changsha, institute of electronic science and engineering of national defense science and technology university, 2007,14-64.

[2] A single star-to-satellite passive positioning and tracking method [ J ] space science report in Guo Fucheng, fan and space information confrontation, 2005,26(2): 196-.

When a high and medium orbit target, particularly a GEO target orbit, is determined by using optical angle measurement data of a single-station short arc section and adopting an L aplace method, the current situation of the target 'drilling ground' with the orbit height smaller than the earth radius or the ill-conditioned normal equation and the loss rank phenomenon can occur due to the 'static ground' characteristic of the GEO, particularly, the initial orbit determination is performed by using single space-based satellite angle measurement data, although Liqiang et al [1]]Theoretical derivation proves that the optical measurement system for the space target by using a single satellite is considerable, but in engineering application, due to the short observation arc section, sparse data and poor observation geometry, the observability of the system is weak, and the ill-conditioned phenomenon of the normal equation in the initial orbit determination process is more serious. Document [2]]The introduction of frequency measurement information while angle measurement is pointed out, so that the observability of the orbit determination system can be increased, and the orbit determination precision is improvedHowever, for spatial target inventory management, adding frequency information while measuring angles is not feasible. Through analysis, the reasons for the failure of the target orbit determination of the middle and high orbit mainly fall into two aspects: firstly, the ill-condition of the initial orbit determination equation is caused by short arc angle measurement data; another aspect is the initial ground offset ρ₀If p is selected₀Too large, iterative divergence or "earth boring" of the target may occur. In the prior art, the astronomical measurement data cannot be directly used for judging the type of the target orbit, so that the success rate of determining the initial orbit of the GEO target by using the short-arc astronomical measurement data is low.

Disclosure of Invention

In order to solve the above problems, an object of the present invention is to provide a method for discriminating a GEO target using astronomical measurement data.

The invention realizes the purpose through the following technical scheme:

the invention comprises the following steps:

the method comprises the following steps: and (3) carrying out preliminary discrimination on the GEO orbit by using astronomical measurement declination data magnitude:

the position vectors of the space target and the measuring station in the J2000 inertial coordinate system are respectively set as R (x, y, z) and R_s(X_R,Y_R,Z_R) And the distance between the measuring station and the space target is rho, then:

the spatial polar coordinates of the ranging vector ρ are then expressed as follows:

the expressions of the astronomical measurement right ascension α and declination according to the formulas (1) and (2) are as follows:

for GEO targets, the inertial system coordinate Z itself is a small quantity, the inertial system coordinate Z of the station_RAlso small, and compared to L EO, MEO, the distance p is at least about 36000km, much greater than the value of p for L EO, MEO, and, therefore, for GEO targets,

the declination is a small quantity, so that the measured value declination is a small quantity, and the utilized magnitude can preliminarily carry out orbit identification on the GEO target;

step two: and (3) discriminating the GEO orbit by using an astronomical measurement declination phase diagram:

the two sides of the theoretical calculation equation (4) are derived to obtain:

as can be seen from equation (5), for the GEO target, it rotates around the Z axis at almost the same angular velocity as the measuring station, while Z, Z_RIs small relative to ρ, and is therefore

Is a minute quantity, from the above analysis, is a small quantity, which can be assumed

tan ≈ is. In this case, (5) can be simplified as follows:

converting equation (6) to:

for the GEO target, according to the analysis of the variation rule of ρ, it can be expressed as the sum of a constant term and a certain trigonometric function, assuming that the expression of ρ is:

ρ(t)≈l+c₁sin(ω_ρt+φ) (8)

let c₂＝c₁ω_ρ，θ＝ω_ρt + φ, the derivation of the equation (8) at both ends is given by:

obtained by the formula (8):

ρ-l≈c₁sinθ (10)

obtained by the formulae (9) and (10):

as can be seen from the formula (11),

the curve along with the change of rho-l is an ellipse, and the equation (7) and the equation (11) are compared, so that the phase diagram of the right ascension is an ellipse, and the center positions of two circles are different; by utilizing the characteristic of the GEO target, the type of the target track can be directly identified by utilizing the measurement data;

step three: the method for judging whether the target orbit is the GEO by utilizing the declination data is applied to initial orbit determination, and comprises the following steps:

1) preprocessing short-arc optical astronomical track measurement data for determining an initial track, and removing outliers;

2) statistically analyzing the maximum value of declination of measured value in the arc-segment rail measurement data_maxIf, if_maxLess than 15 deg., continue step 3);

3) calculating the declination change rate of the arc segment at different moments by using a difference method

4) Approximately equally dividing the observation arc into 4 small arcs, and extracting the sum of 1 group of targets in each arc

5) Using 4 groups extracted in step 4) and

solving an elliptic equation;

6) another 8 groups of the arc section are taken and

(in order to improve the efficiency, verification is not needed one by one, and 2 groups are taken for each 4 small arc segments), and whether the elliptic equation established in the step 5 is met or not is verified, so that the error of 10 percent is allowed. If yes, continuing to step 7);

7) taking rho₀Determining initial orbit by using an improved L aplace method (average value of ranging at elevation angles of 90 degrees and 3 degrees) 39000km, outputting a result if the initial orbit is successful, and continuing to the step 8 if the initial orbit is failed);

8) taking rho₀39000 ± 50nkm, where n is ρ₀The number of values is taken until the initial orbit is successfully determined, or rho₀< 36000km or rho₀Stopping taking values when the speed is more than 42000 km.

The invention has the beneficial effects that:

the invention relates to a method for judging a GEO target by utilizing astronomical measurement data, which is characterized in that an optical measurement data declination, declination change rate and distance, distance change rate correlation model is established, a declination and distance phase diagram equation is established, and the conclusion that the astronomical measurement declination phase diagram of the GEO target is an ellipse is obtained.

Drawings

FIG. 1 is a graph of the variation of target declination for L EO;

FIG. 2 is a graph of MEO target declination variation;

FIG. 3 is a graph of HEO target declination variation;

FIG. 4 is a graph of the change in IGSO target declination;

FIG. 5 is a graph of the change in declination for the GEO target;

FIG. 6 is a graph of the change in target declination at 34779;

FIG. 7 is a 34779 objective declination phase diagram;

FIG. 8 is an 21727 target declination phase diagram;

FIG. 9 is 30323 target declination phase diagram;

fig. 10 is an 36287 target declination phase diagram.

Detailed Description

The invention will be further described with reference to the accompanying drawings in which:

the invention comprises the following steps:

the method comprises the following steps: and (3) carrying out preliminary discrimination on the GEO orbit by using astronomical measurement declination data magnitude:

the position vectors of the space target and the measuring station in the J2000 inertial coordinate system are respectively set as R (x, y, z) and R_s(X_R,Y_R,Z_R) And the distance between the measuring station and the space target is rho, then:

the spatial polar coordinates of the ranging vector ρ are then expressed as follows:

the expressions of the astronomical measurement right ascension α and declination according to the formulas (1) and (2) are as follows:

for GEO targets, the inertial system coordinate Z itself is a small quantity, the inertial system coordinate Z of the station_RAlso small, and compared to L EO, MEO, the distance p is at least about 36000km, much greater than the value of p for L EO, MEO, and, therefore, for GEO targets,

the declination is a small quantity, so that the measured value declination is a small quantity, and the utilized magnitude can preliminarily carry out orbit identification on the GEO target;

simulation verification

The method comprises the steps of selecting a real orbit with an orbit type of L EO, MEO, HEO, IGSO and GEO respectively from a T L E orbit root database, carrying out simulation analysis by utilizing a certain measuring station in China, and verifying the assumptions and conclusions, wherein the orbit information of the selected target is shown in table 1.

TABLE 1 selected target track

Fig. 1 to 5 respectively show schematic diagrams of the declination variation curves of L EO, MEO, HEO, IGSO and GEO targets, and it can be seen from the diagrams that the declination variation amplitudes of L EO, MEO, HEO and IGSO targets are very large within 24 hours, are different from dozens of degrees to nearly hundred degrees, and the declination maximum value of the GEO target does not exceed 3 degrees, so that whether the target orbit is the GEO orbit can be easily judged by using the variation amplitude of the declination measurement value.

Step two: and (3) discriminating the GEO orbit by using an astronomical measurement declination phase diagram:

the two sides of the theoretical calculation equation (4) are derived to obtain:

as can be seen from equation (5), for the GEO target, it rotates around the Z axis at almost the same angular velocity as the measuring station, while Z, Z_RIs small relative to ρ, and is therefore

Is a minute quantity, from the above analysis, is a small quantity, which can be assumed

tan ≈ is. In this case, (5) can be simplified as follows:

converting equation (6) to:

for the GEO target, according to the analysis of the variation rule of ρ, it can be expressed as the sum of a constant term and a certain trigonometric function, assuming that the expression of ρ is:

ρ(t)≈l+c₁sin(ω_ρt+φ) (8)

let c₂＝c₁ω_ρ，θ＝ω_ρt + φ, the derivation of the equation (8) at both ends is given by:

obtained by the formula (8):

ρ-l≈c₁sinθ (10)

obtained by the formulae (9) and (10):

as can be seen from the formula (11),

the curve along with the change of rho-l is an ellipse, and the equation (7) and the equation (11) are compared, so that the phase diagram of the right ascension is an ellipse, and the center positions of two circles are different; by utilizing the characteristic of the GEO target, the type of the target track can be directly identified by utilizing the measurement data;

simulation verification

GEO target ranging rho and method thereof

Verification of characteristics of

FIG. 6 shows p, b, of the GEO target (NORAD No. 34779) over 24 hours,

As can be seen from the figure, ρ can be approximately expressed as equation (12) in km, and is assumed to be consistent with the expression of ρ of equation (8);

the curve is almost a strict trigonometric function, and the sum of the trigonometric functions of p

The periods are equal and the phases are different by 90 deg., further verifying the feasibility of the assumption of p.

ρ＝41200+740sinθ (12)

GEO target ranging declination phase diagram verification

Fig. 7 shows the declination phase diagram of the GEO target (NORAD 34779), and as can be seen, the declination phase diagram of 34779 is an ellipse, and the theoretical analysis results are consistent. Meanwhile, for comparison, fig. 8 shows the declination phase diagram of the measurement data of the HEO target 21727, and it can be seen that the phase diagrams of the two are significantly different. In order to further verify the above analysis results, FIGS. 9 and 10 show the declination phase diagrams of two other GEO targets (NORAD 30323 and 36287, respectively), and it can be seen that the declination phase diagrams of the two targets are bothThe ellipse is shown in fig. 7, 9 and 10, and the central points of the three ellipses are different, and the radii of the major axis and the minor axis are different, i.e. l and c in formula (8)₁And ω_ρThe values are different.

Step three: the method for judging whether the target orbit is the GEO by utilizing the declination data is applied to initial orbit determination, and comprises the following steps:

1) preprocessing short-arc optical astronomical track measurement data for determining an initial track, and removing outliers;

2) statistically analyzing the maximum value of declination of measured value in the arc-segment rail measurement data_maxIf, if_maxLess than 15 deg., continue step 3);

3) calculating the declination change rate of the arc segment at different moments by using a difference method

4) Approximately equally dividing the observation arc into 4 small arcs, and extracting the sum of 1 group of targets in each arc

5) Using 4 groups extracted in step 4) and

solving an elliptic equation;

6) another 8 groups of the arc section are taken and

(in order to improve the efficiency, verification is not needed one by one, and 2 groups are taken for each 4 small arc segments), and whether the elliptic equation established in the step 5 is met or not is verified, so that the error of 10 percent is allowed. If yes, continuing to step 7);

7) taking rho₀Determining initial orbit by using an improved L aplace method (average value of ranging at elevation angles of 90 degrees and 3 degrees) 39000km, outputting a result if the initial orbit is successful, and continuing to the step 8 if the initial orbit is failed);

8) taking rho₀39000 ± 50nkm, where n is ρ₀Number of values until the initial orbit is successfully determinedTo a total of, or ρ₀< 36000km or rho₀Stopping taking values when the speed is more than 42000 km.

The method is used for processing the optical astronomical measurement data of 204 GEO targets to determine the initial orbit, and the orbit determination success rate is greatly improved.

Interpretation of terms:

the foregoing shows and describes the general principles and features of the present invention, together with the advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (1)

1. A method for distinguishing a GEO target by using astronomical measurement data is characterized by comprising the following steps:

the method comprises the following steps: and (3) carrying out preliminary discrimination on the GEO orbit by using astronomical measurement declination data magnitude:

the position vectors of the space target and the measuring station in the J2000 inertial coordinate system are respectively set as R (x, y, z) and R_s(X_R,Y_R,Z_R) And the distance between the measuring station and the space target is rho, then:

the spatial polar coordinates of the ranging vector ρ are then expressed as follows:

the expressions of the astronomical measurement right ascension α and declination according to the formulas (1) and (2) are as follows:

for GEO targets, the inertial system coordinate Z itself is a small quantity, the inertial system coordinate Z of the station_RAlso small, and compared to L EO, MEO, the distance p is at least about 36000km, much greater than the value of p for L EO, MEO, and, therefore, for GEO targets,

the declination is a small quantity, so that the measured value declination is a small quantity, and the utilized magnitude can preliminarily carry out orbit identification on the GEO target;

step two: and (3) discriminating the GEO orbit by using an astronomical measurement declination phase diagram:

the two sides of the theoretical calculation equation (4) are derived to obtain:

as can be seen from equation (5), for the GEO target, it rotates around the Z axis at almost the same angular velocity as the measuring station, while Z, Z_RIs small relative to ρ, and is therefore

Is a minute quantity, from the above analysis, is a small quantity, which can be assumed

tan ≈ is. In this case, (5) can be simplified as follows:

converting equation (6) to:

for the GEO target, according to the analysis of the variation rule of ρ, it can be expressed as the sum of a constant term and a certain trigonometric function, assuming that the expression of ρ is:

ρ(t)≈l+c₁sin(ω_ρt+φ) (8)

let c₂＝c₁ω_ρ，θ＝ω_ρt + φ, the derivation of the equation (8) at both ends is given by:

obtained by the formula (8):

ρ-l≈c₁sinθ (10)

obtained by the formulae (9) and (10):

as can be seen from the formula (11),

the curve along with the change of rho-l is an ellipse, and the equation (7) and the equation (11) are compared, so that the phase diagram of the right ascension is an ellipse, and the center positions of two circles are different; by utilizing the characteristic of the GEO target, the type of the target track can be directly identified by utilizing the measurement data;

step three: the method for judging whether the target orbit is the GEO by utilizing the declination data is applied to initial orbit determination, and comprises the following steps:

1) preprocessing short-arc optical astronomical track measurement data for determining an initial track, and removing outliers;

2) statistically analyzing the arc track measurement dataMaximum value of declination of measured value_maxIf, if_maxLess than 15 deg., continue step 3);

3) calculating the declination change rate of the arc segment at different moments by using a difference method

4) Approximately equally dividing the observation arc into 4 small arcs, and extracting the sum of 1 group of targets in each arc

5) Using 4 groups extracted in step 4) and

solving an elliptic equation;

6) another 8 groups of the arc section are taken and

(in order to improve the efficiency, verification is not needed one by one, and 2 groups are taken for each 4 small arc segments), and whether the elliptic equation established in the step 5 is met or not is verified, so that the error of 10 percent is allowed. If yes, continuing to step 7);

7) taking rho₀Determining initial orbit by using an improved L aplace method (average value of ranging at elevation angles of 90 degrees and 3 degrees) 39000km, outputting a result if the initial orbit is successful, and continuing to the step 8 if the initial orbit is failed);

8) taking rho₀39000 ± 50nkm, where n is ρ₀The number of values is taken until the initial orbit is successfully determined, or rho₀< 36000km or rho₀Stopping taking values when the speed is more than 42000 km.

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