CN111291473B

CN111291473B - Double-sight observation design method for space target tracking

Info

Publication number: CN111291473B
Application number: CN202010055803.2A
Authority: CN
Inventors: 王奕迪; 李钊; 郑伟
Original assignee: National University of Defense Technology
Current assignee: National University of Defense Technology
Priority date: 2020-01-17
Filing date: 2020-01-17
Publication date: 2024-05-28
Anticipated expiration: 2040-01-17
Also published as: CN111291473A

Abstract

The invention discloses a double-sight observation design method for space target tracking, which comprises the steps of designing a track configuration of a detection platform, designing an installation angle of an optical camera, establishing an optimization problem model, optimizing the value of a design variable, and obtaining target covering capacity and target positioning accuracy. According to the method, the track configuration of the detection platform and the mounting angle of the cameras are designed, so that the fields of view of the two cameras are overlapped in the inertial space, and therefore, double-sight observation is realized in a scanning mode; under the condition of simultaneously considering satisfaction of the observation constraint condition and double-sight positioning equivalent ranging error, the design variable of the detection platform is optimized, and better coverage performance can be provided on the premise of ensuring the positioning accuracy of the detection system to the target.

Description

Double-sight observation design method for space target tracking

Technical Field

The invention relates to the technical field of space on-orbit positioning, in particular to a double-sight line observation design method for space target tracking.

Background

Space objects generally refer to man-made objects that orbit the earth, and mainly include normally orbiting spacecraft and space debris, etc., with space debris being over 76%. With the increasing number of space targets, the safe operation of an on-orbit spacecraft is greatly threatened. Thus, tracking and cataloging of spatial targets has become the basis for spatial resource utilization and has significant implications for spatial security.

Existing space-based target tracking systems typically use optical cameras carried by a single satellite to make line-of-sight angle measurements of a space target. For a low-rail target, the relative angular speed between the observation platform and the space object is high, the observation arc section is short, the accuracy of the target rail is low, and even the initial rail determination cannot be effectively completed. When the two detection platforms are used for double-sight observation of the space target, the required observation arc length of the target track can be effectively shortened, and the target positioning accuracy can be improved.

Dual line-of-sight observations require two optical cameras to detect the same spatial target simultaneously. The working modes of the space optical detection can be generally divided into a tracking mode and a scanning mode, wherein the tracking mode is used for detecting and tracking a target by adjusting the orientation of a sensor, and the scanning mode is used for observing the orientation of the sensor in an inertial space when the target passes through the field of view of a camera. In the prior disclosures, dual line-of-sight observation of a spatial target is typically achieved by adjusting the sensor orientation.

In the prior art: chinese patent CN201910372583.3 discloses a space target precision on-orbit positioning method based on angle measurement and ranging information, which uses a visible light camera to obtain angle information of space debris relative to a satellite, and at the same time obtains distance information of space debris through a microwave ranging radar, and then high precision positioning of space debris can be achieved through data fusion. Chinese patent CN201910049548.8 discloses a method for locating a spatial target by fusion of a heterogeneous optical platform, in which it is assumed that the spatial target can be found by a plurality of sensors of non-coaxial optical platforms at the same time, and by using the spatial fusion locating algorithm mentioned in the method, the two-dimensional position information of the target obtained by fusing a plurality of sensors can be calculated, so as to complete the target locating. The accuracy of target positioning is not mentioned in the prior art.

Therefore, it is significant to develop a dual-line-of-sight observation method with high detection efficiency and high target positioning accuracy.

SUMMARY OF THE PATENT FOR INVENTION

The invention provides a double-sight line observation design method for space target tracking, which aims at the space target tracking problem, and by designing the track configuration of an observation platform and the installation angles of optical cameras, the fields of view of the two optical cameras are overlapped in an inertial space, so that the double-sight line observation of the space target is realized in a scanning mode, and the high-precision positioning of the target is completed, and the specific technical scheme is as follows:

A dual line of sight observation design method for spatial target tracking, comprising the steps of:

Designing a detection platform track configuration, and selecting a solar synchronous morning and evening track as a platform deployment track;

designing an optical camera mounting angle, firstly providing definition of the optical camera mounting angle, and then defining the relation between the two platform optical camera mounting angles;

establishing an optimization problem model, which comprises defining design variables, objective functions and constraint conditions;

optimizing the value of the design variable;

Target coverage capability and target positioning accuracy are obtained to evaluate the performance of the resulting solution.

In the above technical solution, it is preferable to design a track configuration of the detection platform, specifically, to design a track configuration of two detection platforms, where the two detection platforms are disposed on two sun synchronous tracks with the same track height, and one detection platform is correspondingly provided with an optical camera; the track configuration of the detection system depends on three variables of track height H, intersection point elevation right angle difference delta omega and latitude amplitude angle difference delta u.

In the above technical solution, preferably, the installation angle of the optical camera is represented by two angles α and β, wherein: alpha is an included angle between R _oxz and R _o1, beta is an included angle between R _oxz and the negative direction of the z ₁ axis, R _o1 is a unit vector indicating the direction of the optical axis of the optical camera, and R _oxz is the projection of R _o1 on the xoz plane; the mounting angles of the first optical camera are represented by two angles of alpha ₁ and beta ₁, and the mounting angles of the second optical camera are represented by two angles of alpha ₂ and beta ₂, and then the relation of the mounting angles of the two optical cameras is as follows: α ₁＝-α₂ =α and β ₁＝β₂ =β.

In the above technical solution, the specific process of establishing the optimization problem model is as follows:

Firstly defining design variables, and taking H, delta omega, delta u, alpha and beta as the design variables;

And then selecting an objective function, and selecting the observation constraint satisfaction MD as the objective function, wherein the expression 4 is as follows:

Wherein: K is the total number of simulation time discrete points;

Finally, defining constraint conditions, and selecting an equivalent ranging error Deltaρ ₁ smaller than 1km as the constraint conditions, wherein the equivalent ranging error Deltaρ ₁ is expressed by adopting expression 6):

wherein: ρ ₁₂ is the distance between the two detection platforms, R _e is the earth radius.

In the above technical solution, preferably, the optimizing the value of the design variable specifically includes:

The values of H and beta are optimized firstly, and specifically: the method comprises the steps that the satisfaction degree of a simulation single detection platform for a specific space target set is restrained, and the change of H and beta under different values is determined; and optimizing the values of delta omega, delta u and alpha, wherein the values are specifically as follows: based on the determination of H and beta, the values of delta omega, delta u and alpha are determined by restraining satisfaction of the simulated dual-detection platform on a specific space target set and changing under different values of delta omega, delta u and alpha.

In the above technical solution, preferably, the target coverage capability is represented by the number of detected targets and the average detected arc length, and the target positioning accuracy is represented by the average positioning accuracy of all detected targets.

The scheme of the invention has the following effects: by designing the track configuration of the detection platform and the mounting angle of the cameras, the fields of view of the two cameras are overlapped in the inertial space, so that double-sight observation is realized in a scanning mode, frequent camera pointing adjustment can be avoided, and the detection efficiency of the system is improved; under the condition of simultaneously considering satisfaction of the observation constraint condition and double-sight positioning equivalent ranging error, the design variable of the detection platform is optimized, and better coverage performance can be provided on the premise of ensuring the positioning accuracy of the detection system to the target.

Drawings

The accompanying drawings, which are included to provide a further understanding of the present application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and not to limit the application. In the drawings:

FIG. 1 is a flow chart of a dual line of sight observation method in an embodiment of the invention;

FIG. 2 is a schematic view of a track configuration of a detection platform in an embodiment of the present invention;

FIG. 3 is a schematic view of the mounting angle of an optical camera in an embodiment of the invention;

FIG. 4 is a dual line-of-sight observation geometry in an embodiment of the invention;

FIG. 5 is a graph showing the variation of constraint satisfaction with H and beta for a single detection platform in an embodiment of the present invention;

FIG. 6 is a graph showing the constraint satisfaction of a dual detection platform as a function of Deltau, deltaomega, alpha in an embodiment of the present invention.

Detailed Description

Embodiments of the present invention are described in detail below with reference to the attached drawing figures, but the present invention can be implemented in a number of different ways, which are defined and covered by the claims.

Examples:

A double-sight line observation design method for space target tracking is shown in fig. 1 in detail, and comprises the following steps:

step 1), designing a track configuration of a detection platform, and selecting a solar synchronous morning and evening track as a platform deployment track;

Step 2), designing an optical camera mounting angle, firstly defining the camera mounting angle, and then defining the relation between the two platform camera mounting angles;

step 3), establishing an optimization problem model, which comprises defining design variables, objective functions and constraint conditions;

Step 4), optimizing the value of the design variable, namely optimizing the value of the design variable by simulating the size of an objective function under the values of different design variables and considering the limitation of constraint conditions;

Step 5), evaluating the performance of the obtained design scheme, including target covering capacity and target positioning accuracy.

The specific scheme of the embodiment is as follows:

first, design and survey platform track configuration:

In order to ensure good sun illumination conditions during the detection process, the space-based optical detection system is generally located in a solar synchronous morning and evening orbit. The track configuration of designing two detection platforms is shown in fig. 2, the two detection platforms are deployed on two solar synchronous tracks with the same track height, and the relation between the track height and the track inclination angle is shown by expression 1):

Wherein: h is track height; Is the angular velocity of the sun relative to the geocentric inertial coordinate system (i.e., ECI coordinate system); mu _e is the gravitational constant, J ₂ is the gravitational perturbation constant, R _e is the earth radius, e is the orbital eccentricity, and i is the orbital tilt.

Assuming that the track where the detection platform is located is a circular track, the right ascent point and descent (RAAN, omega) are located near the morning and evening line, and the influence of the respective track phase angles of the detection platform on the system coverage performance is not obvious. The track configuration of the detection system is mainly dependent on three variables of the track height H, RAAN difference (ΔΩ, ΔΩ=Ω ₂-Ω₁) and the latitude amplitude difference (Δu, Δu=u ₁-u₂).

The second step, design the installation angle of the optical camera, specifically:

① Defining camera mounting angles

The optical camera is fixedly connected to the detection platform, and the platform keeps the coordinate system of the platform body coincident with the local horizontal and local vertical coordinate system (LVLH) by adopting a three-axis stable attitude control method. For convenience of the following description, camera pointing is defined in an LVLH coordinate system. As shown in fig. 3, R _o1 is a unit vector indicating the direction of the camera optical axis, and R _oxz is the projection of R _o1 on the xoz plane.

As can be seen from fig. 3, the camera mounting angle is represented by two angles α and β. Where α is the angle between R _oxz and R _o1, and β is the angle between R _oxz and the negative z ₁ axis. When α and β are determined, the camera pointing R _o1 is given by expression 2):

R_o1＝cosαsinβx₁-sinαy₁-cosαcosβz₁ 2)；

wherein: x ₁、y₁、z₁ is the coordinate;

② Given the two-camera mounting angle relationship:

in order to overlap the two camera fields of view and simplify the design problem, the mounting angles of the two sensors are required to satisfy the relation as in expression 3):

α₁＝-α₂＝α,β₁＝β₂＝β 3)。

Thirdly, establishing an optimization problem model, which specifically comprises the following steps:

① Definition of design variables

From the first and second steps, the design variables of the dual line-of-sight observation scheme include H, ΔΩ, Δu, α, and β.

② Defining an objective function

The satisfaction (MATCHING DEGREE, MD) of the observation constraint is selected as an objective function, which is defined as the total number of discrete points which simultaneously satisfy all the observation constraint in the simulation process, namely the total length of the observable arc segment, and is mainly used for representing the target coverage performance of the detection system. The observed constraint satisfaction can be calculated by expression 4): wherein: /(I) K is the total number of simulation time discrete points.

③ Defining constraints

In existing research, target coverage performance is often the only factor considered in the design of the detection system. However, the accuracy of the initial track determination of the target is also an important indicator affecting the system performance. Therefore, in this embodiment, the equivalent ranging error of the dual-line-of-sight positioning is used as a constraint condition for ensuring the initial track determination accuracy, and the definition and calculation processes are as follows:

Assuming that the spatial target is located at the intersection point of the optical axes of the two sensors, the simplified geometric relationship of the dual-line-of-sight measurement is schematically shown as 4, and R _o1 and R _o2 are unit vectors respectively representing the directions of the optical axes of the sensors 1 and 2; ρ ₁ and ρ ₂ are the distances between the detection stages 1 and 2 and the target, respectively, ρ ₁₂ is the distance between the two stages According to the sine theorem, the distance between the target and the platform 1 is/>The equivalent range error Δρ ₁ caused by the sensor angular error is expression 5):

wherein: delta theta is the sensor measurement error;

Derived expression 6):

in order to ensure the positioning accuracy of the target, the present embodiment sets the equivalent ranging error Δρ ₁ to be less than 1km.

The fourth step, optimizing the value of the design variable, specifically:

in order to reduce the search space of design variables, the optimization process is divided into two steps:

① Optimizing the values of H and beta: the method comprises the steps that the satisfaction degree of a simulation single detection platform for a specific space target set is restrained, and the change of H and beta under different values is determined; ② Optimizing the values of ΔΩ, Δu, and α: based on the determination of H and beta, the values of delta omega, delta u and alpha are determined by restraining satisfaction of the simulated dual-detection platform on a specific space target set and changing under different values of delta omega, delta u and alpha.

And fifthly, acquiring target covering capacity and target positioning accuracy, and evaluating the performance of the obtained design scheme.

The target coverage capability is characterized by the number of detected targets and the average detected arc length, and the target positioning accuracy is characterized by the average positioning accuracy of all detected targets.

The simulation is performed by applying the scheme of the embodiment, and the details are as follows:

(1) Simulation conditions

The space target of the low earth orbit is mainly concentrated near the sun synchronous orbit, especially in the region with orbit height of 600-900km and orbit inclination angle of 80-100 deg. Because the area has a plurality of space targets and has high socioeconomic value, a simulated detection target set is selected to be generated in the area. The initial track distribution of space objects in the set is shown in table 1 and the simulated initial conditions are shown in table 2.

TABLE 1 initial trajectory distribution of simulation space object set (100 objects)

TABLE 2 simulation initial conditions

(2) Simulation results

As shown in fig. 5, the upper sub-graph depicts design variable values for alternative detection platforms having different numbers, and the lower sub-graph shows constraint satisfaction values corresponding thereto, with a set of five alternative platforms having the same track height. As can be seen from fig. 5, the constraint satisfaction is maximum when the track heights H and β are 1100km and 16deg, respectively. Therefore, the parameter is set as a value of the scheme design.

As shown in fig. 6, the upper sub-graph shows the parameter settings of the differently numbered dual detector platoon, and the lower sub-graph gives the corresponding constraint satisfaction. The alternative formations with the same amplitude angle difference every five latitudes are a group. As can be seen from fig. 6, as au increases, the constraint satisfaction decreases. Considering the constraint of the equivalent ranging error of the double-sight line positioning, when the angle measurement error of the optical camera is 5 angular seconds, the equivalent ranging error under different values of the design variable can be obtained according to an error calculation formula, and the result is shown in Table 3.

Table 3 equivalent range error at different values of the design variables

As can be seen from table 3, the equivalent ranging error decreases with increasing au, whereas the effect of ΔΩ on the equivalent ranging error is insignificant. In order to maximize the constraint satisfaction on the premise of satisfying the equivalent range error constraint, the values of Δu, ΔΩ, and α should be 3deg, 5deg, and 2deg, respectively. In summary, the optimization results of the system design variables are shown in table 4:

table 4 results of optimization of probing system design variables

H[km]	β[deg]	Δu[deg]	ΔΩ[deg]	α[deg]
					1100	16	3	2	5

The detection performances of different schemes are compared, including the coverage performance of a target set and the track determination precision of the target, so as to verify the rationality of the scheme obtained by optimization, and the details are as follows:

The initial conditions for simulation are shown in table 2, the initial track numbers of the detection platforms are given in table 5, and the platform compositions and sensor mounting angles of different designs are given in table 6. Among them, scheme 1 was the result obtained by optimization, and the other schemes were used for comparative analysis.

Table 5 initial track count for detection platform

Table 6 platform composition and sensor mounting angles for different schemes

First, the coverage performance of different schemes is analyzed, and the related indexes comprise the total number of detected targets, average observation duration and the like. The simulation duration is 24h, and the sampling step length is set to be 1s. The simulation focuses on comparing the influence of different detection methods on the coverage performance, so that only the observation arc segments of the target visible to all detection platforms in the scheme are calculated. The coverage types include: single Coverage (SC), double Coverage (DC), and Triple Coverage (TC). The simulation results are shown in table 7.

TABLE 7 covering Properties of different versions

From table 7 above, it can be seen that the number of spatial targets detected by scheme 0 is significantly greater than that of the other schemes, since multiple line-of-sight measurements need to satisfy more viewing constraints than single line-of-sight measurements at the same time. Both schemes 1 and 2 contain two detection platforms but different design variables, and comparing the same total number of targets detected by schemes 1 and 2, the average observation time of scheme 2 is greater than that of scheme 1.

Secondly, the positioning errors of the targets under different schemes are analyzed to evaluate the initial orbit determination performance of the different schemes. The observation arc for tracking is shown in table 7 and the remaining simulation conditions are listed in table 2. The average positioning errors of targets of different schemes after 100 times of target shooting simulation are shown in table 8.

Table 8 target positioning errors for different schemes

Scheme numbering	Number of platforms	Total number of detected targets	Average observation duration [ s ]	Average positioning error [ m ]
					1	2	45	261	64.73
2	2	45	294	89.12
					3	3	44	225	60.85

As can be seen from table 8 above, for the design scheme that also includes two detection platforms, scheme 1 has better average target positioning error than scheme 2 with the average observation time shorter than scheme 2. This illustrates that the equivalent range error has a greater impact on the tracking accuracy. This conclusion illustrates the necessity of considering equivalent ranging errors in the design process of the detection system, which can effectively ensure the initial track determination accuracy of the target.

The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1.A dual line of sight observation design method for spatial target tracking, comprising the steps of:

optimizing the value of the design variable;

Obtaining a target coverage capability and a target positioning accuracy to evaluate performance of the obtained scheme;

the specific process for establishing the optimization problem model is as follows:

Wherein: K is the total number of simulation time discrete points;

2. The dual line-of-sight observation design method for spatial target tracking of claim 1, wherein: the track configuration of the designed detection platform is specifically a track configuration of two detection platforms, the two detection platforms are deployed on two sun synchronous tracks with the same track height, and one optical camera is correspondingly arranged on one detection platform; the track configuration of the detection system depends on three variables of track height H, intersection point elevation right angle difference delta omega and latitude amplitude angle difference delta u.

3. The dual line-of-sight observation design method for spatial target tracking of claim 2, wherein: the mounting angle of the optical camera is represented by two angles α and β, wherein: alpha is an included angle between R _oxz and R _o1, beta is an included angle between R _oxz and the negative direction of the z ₁ axis, R _o1 is a unit vector indicating the direction of the optical axis of the optical camera, and R _oxz is the projection of R _o1 on the xoz plane; the mounting angles of the first optical camera are represented by two angles of alpha ₁ and beta ₁, and the mounting angles of the second optical camera are represented by two angles of alpha ₂ and beta ₂, and then the relation of the mounting angles of the two optical cameras is as follows: α ₁＝-α₂ =α and β ₁＝β₂ =β.

4. A dual line of sight observation design method for spatial target tracking according to claim 3, wherein: the value of the optimal design variable specifically comprises:

5. A dual line of sight observation design method for spatial target tracking according to claim 3, wherein: the target coverage capability is characterized by the number of detected targets and the average detected arc length, and the target positioning accuracy is characterized by the average positioning accuracy of all detected targets.