Triangular layout in-orbit visual axis pointing three-axis measurement system and method

Abstract

The invention relates to an in-orbit visual axis pointing three-axis measurement system and method for a triangular layout. The system comprises three included angle measurement instruments J1, J2 and J3 and three reflectors R1, R2 and R3, the reflecting mirror R1 and the reflecting mirror R2 are installed at a position A to be measured as a whole, the included angle measuring instrument J1 and the included angle measuring instrument J3 are installed at a position B to be measured as a whole, and the reflecting mirror R3 and the included angle measuring instrument J2 are installed at the position B to be measured as a whole; the to-be-measured positions A, B and C form a plane II; in an initial state, light beams emitted by the included angle measuring instrument Ji respectively and vertically enter the reflecting mirror Ri and are reflected back, three optical axes of the three included angle measuring instruments intersect at one point in pairs, the optical axis of the included angle measuring instrument J1 is parallel to the AB direction, the optical axis of the included angle measuring instrument J2 is parallel to the AC direction, and the optical axis of the included angle measuring instrument J3 is parallel to the BC direction. According to the invention, on-orbit monitoring of three-axis pointing change of the visual axis is realized, feedback control is implemented according to monitoring data, remote sensing data is corrected, and remote sensing imaging quality and target positioning precision are ensured.

Description

Technical Field

[0001] The invention belongs to the technical field of on-orbit monitoring of spacecraft, and relates to an on-orbit line of sight pointing three-axis measurement system and method with a triangular layout. Background Art

[0002] High resolution and high target positioning accuracy are the key features and core indicators of high-performance remote sensing satellites, and the change in the line of sight of the optical payload caused by structural deformation is an important factor affecting the quality of remote sensing imaging and target positioning accuracy. This is because the on-orbit structure will be deformed by complex factors such as gravity, extreme temperature changes, impact of space debris and fatigue, which will directly affect the spatial pointing of key components such as high-resolution remote sensing cameras and star sensors and their geometric relationships with each other, causing changes in the line of sight of the optical payload, which in turn has a serious impact on the quality of remote sensing imaging and target positioning accuracy. For remote sensing satellites with sub-meter resolution, changes in the line of sight caused by micron-level structural deformation can lead to meter-level imaging errors. This will seriously affect the accuracy of target positioning.

[0003] At present, the deformation of on-orbit structures is mainly reduced through methods such as thermal control and material structure optimization design to suppress the change in the line of sight of optical payloads. However, its application scope and effect are limited. The main problems are: although key structures such as the integrated bracket of the remote sensing camera and the payload mounting baseplate have high stability, there are differences in the thermodynamic parameters of the overall structure after assembly and connection with other structures. Even if the above-mentioned suppression methods are used, these key structures will still produce micron-level or even millimeter-level deformations under the action of micro-vibration and variable external heat flow. For some key structures, it is difficult to implement overall high-precision temperature control. These structures are easily affected by extreme temperature changes and gravity in space and are prone to super-threshold deformation. These factors will cause arc-second changes in the line of sight of remote sensing satellites.

[0004] As the requirements for remote sensing detection accuracy, range, and stability become increasingly high, suppressing deformation by methods such as thermal control and material structure optimization design alone can no longer meet the requirements for high-precision control of satellite boresight pointing. Taking effective measures to monitor changes in boresight pointing on-orbit, implementing feedback control based on monitoring data, and correcting remote sensing data have become the key to ensuring remote sensing imaging quality and target positioning accuracy. At the same time, on-orbit monitoring of boresight pointing is also the key to evaluating satellite design performance and inverting design parameters.

[0005] The angle measuring instrument based on the principle of autocollimation is a measurement method that uses the displacement of the image point at the conjugate image plane to solve the small changes of the system. Taking the parallel light emitted by the off-axis point as the reference, its working principle is as follows: Figure 1 Assume that the height of the object point is H, the focal length of the objective lens is f0, and the inclination angle of the reflector is θ, then H = f0·tan2θ. When the visual axis of the system rotates by Δω, the position of the image point on the image plane also shifts, which is recorded as the image point displacement ΔH. ωThe visual axis rotation Δω and the corresponding image point displacement ΔH ω The functional relationship between the two is obtained by recording the image point displacement ΔH ω The back calculation system Δω can monitor the line of sight in real time. The autocollimation principle can measure the angle change around two axes with high precision, while the satellite line of sight needs to measure the angle change around three axes. Generally, the three-axis angle change cannot be obtained by a single angle measuring instrument, and multiple angle measuring instruments are required for joint measurement. Summary of the invention

[0006] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art, to propose an on-orbit line of sight pointing three-axis measurement system and method with a triangular layout, to monitor the three-axis pointing changes of the line of sight on-orbit, to implement feedback control and correct remote sensing data based on the monitoring data, to ensure the remote sensing imaging quality and target positioning accuracy.

[0007] The solution to the technical problem of the present invention is: an on-track line-of-sight pointing three-axis measurement system with a triangular layout, comprising three angle measuring instruments J1, J2, and J3 and three reflectors R1, R2, and R3; the reflectors R1 and R2 are installed as a whole at the position to be measured A, the angle measuring instruments J1 and J3 are installed as a whole at the position to be measured B, and the reflector R3 and the angle measuring instrument J2 are installed as a whole at the position to be measured B; the three points of the positions to be measured A, B, and C constitute a plane Π; the angle measuring instrument J1 is installed at the position to be measured B, and the reflector R3 and the angle measuring instrument J2 are installed at the position to be measured B; the three points of the positions to be measured A, B, and C constitute a plane Π; the angle measuring instrument J1 is installed at the position to be measured B, and the reflector R3 and the angle measuring instrument J2 are installed at the position to be measured C, and the reflector R3 and the angle measuring instrument J2 are installed at the position to be measured B ... i The emitted light beams are incident vertically on the reflector R i , and reflected back, i=1,2,3; the three optical axes of the three angle measuring instruments intersect at one point, among which the optical axis of the angle measuring instrument J1 is parallel to the AB direction, the optical axis of the angle measuring instrument J2 is parallel to the AC direction, and the optical axis of the angle measuring instrument J3 is parallel to the BC direction.

[0008] An on-orbit line-of-sight pointing three-axis measurement method with a triangular layout comprises the following steps:

[0009] S1. Establish a world coordinate system with position C as the origin: the BC direction is the positive direction of the x-axis, the positive direction of the z-axis is upward and perpendicular to the x-axis, the x-axis and the z-axis are both in the plane Π, the positive direction of the y-axis is perpendicular to the plane Π and inward, and the right-hand rule is satisfied; let v1, v2 and v3 be the unit direction vectors of the reflected light of the angle measuring instrument J1 through the reflector R1, the angle measuring instrument J2 through the reflector R2, and the angle measuring instrument J3 through the reflector R3 respectively;

[0010] S2. On the photosensitive surfaces of angle measuring instruments J1, J2, and J3, plane coordinate systems are established in the same way: the optical axis direction is z′ i Axis, with the frame of the measuring instrument's photosensitive chip as x' i , y′ i Axis, i=1,2,3;

[0011] S3, calculate the vector v after v2 is rotated by position A 23 and v2 and v 23 Angle: The angle measuring instrument J2 reading (x2, y2) is determined by the posture change (a1, b1, c1) of position A. When position A rotates, the transformation of vector v2 is decomposed into three rotations, which are a1, b1, and c1 counterclockwise rotations around the negative axis of x, y, and z of the world coordinate system. The vector v after v2 is rotated by position A is obtained using the Rodrigues rotation formula. 23 , and get v2 and v 23 The angle of

[0012] S4. Assume that the intersection of the reflected light on the x′2y′2 plane of the angle measuring instrument J2 plane coordinate system is point p2, and calculate the coordinate value of point p2, that is, the angle measuring instrument J2 reading (x2, y2): According to v2 and v 23 The distance h from the angle calculation point p2 to the origin of the plane coordinate system of the angle measuring instrument J2 and the direction vector v′ from the origin of the plane coordinate system of the angle measuring instrument J2 to point p2 23 , and then calculate the vector v′ 23 The angle θ between the same coordinate axes x′2 and y′2 2x ,θ 2y , according to the distance h and the angle θ 2x ,θ 2y , calculate and obtain the angle measuring instrument J2 reading (x2, y2);

[0013] S5. The angle measuring instrument J3 reading (x3, y3) is determined by the posture change (a2, b2, c2) of position B. The angle measuring instrument J3 reading (x3, y3) is calculated according to the method of steps S3 to S4.

[0014] S6. The reading (x1, y1) of the angle measuring instrument J1 is determined by the posture changes (a1, b1, c1) and (a2, b2, c2) of positions A and B. The calculated (x2, y2) is subtracted from (x3, y3) to obtain the reading (x1, y1) of the angle measuring instrument J1.

[0015] S7, x1, x2, x3, y1, y2, y3 are first approximated to a1, b1, c1, a2, b2, c2, and the matrix form is M×s=n, where M is a 6×6 matrix and s=[a1, b1, c1, a2, b2, c2] T , n = [x1,x2,x3,y1,y2,y3] T , then the coordinate transformation n of the angle measuring instrument is known to calculate the three-axis pointing change s of the visual axis as s = M -1 ×n.

[0016] Furthermore, v1, v2 and v3 are:

[0017] v1={cos(180-∠CBA),0,-sin(180-∠CBA)}、

[0018] v2={cos(∠BCA),0,-sin(∠BCA)}, v3={-1,0,0}.

[0019] Furthermore, the optical axis direction is z′ i Axis, with the frame of the measuring instrument's photosensitive chip as x' i , y′ i Axis, i = 1, 2, 3, as follows:

[0020] x′1={sin(180-∠CBA),0,cos(180-∠CBA)}, y′1={0,1,0}, z′1=-v1;

[0021] x′2={sin(∠BCA),0,cos(∠BCA)}, y′2={0,1,0}, z′2=-v2;

[0022] x′3={0,0,-1}, y′3={0,1,0}, z′3=-v3.

[0023] Furthermore, the calculation of the vector v after v2 is rotated by position A 23 and v2 and v 23 The angles are as follows:

[0024] Assume that the negative axis vectors of the x, y, and z axes of the world coordinate system are k1 = {-1, 0, 0}, k2 = {0, -1, 0}, and k3 = {0, 0, -1}, respectively. Calculate the state of vector v2 after rotating around vectors k1, k2, and k3:

[0025] The vector v2 rotated around vector k1 is expressed as:

[0026] v 21 =cos(a1)*v2+(1-cos(a1))*(Dot[v2,k1])*k1+sin(a1)*Cross[k1,v2]

[0027] Where Dot[v2,k1] represents the dot product of vector v2 and k1, Cross[k1,v2] represents the cross product of vector k1 and v2; vector v 21 After rotating around k2:

[0028] v 22 =cos(b1)*v 21+(1-cos(b1))*(Dot[v 21 ,k2])*k2+sin(b1)*Cross[k2,v 21 ]

[0029] Vector v 22 After rotating around k3:

[0030] v 23 =cos(c1)*v 22 +(1-cos(c1))*(Dot[v 22 ,k3])*k3+sin(c1)*Cross[k3,v 22 ]

[0031] Finally, v2 is rotated by position A to obtain vector v 23 , vector v2 and v 23 The angle is expressed as:

[0032]

[0033] Furthermore, the distance h and the vector v′ 23 They are:

[0034] h=2fθ2

[0035] v′ 23 =v 23 -v2cos(θ2)

[0036] Where f is the focal length of the angle measuring instrument.

[0037] Furthermore, the angle θ 2x ,θ 2y They are:

[0038]

[0039] Furthermore, the angle measuring instrument J2 reading (x2, y2) is:

[0040] x2=2*f*θ2*cos(θ 2x )

[0041] y2=2*f*θ2*cos(θ 2y ).

[0042] Furthermore, the angle measuring instrument J2 readings (x2, y2), the angle measuring instrument J3 readings (x3, y3), and the angle measuring instrument J1 readings (x1, y1) are respectively organized into the following forms:

[0043] Let ∠BAC=α, ∠CBA=β, ∠BCA=γ,

[0044]

[0045] Furthermore, the matrix M is specifically:

[0046]

[0047] The beneficial effects of the present invention compared with the prior art are:

[0048] (1) In the prior art, the angle measuring instrument based on the principle of autocollimation can only measure the angle change around two axes with high precision, while the satellite line of sight needs to measure the angle change around three axes. Generally, the three-axis angle change cannot be obtained by a single angle measuring instrument. The triangular layout of the on-orbit line of sight pointing high-precision three-axis measurement system of the present invention realizes the on-orbit monitoring of the three-axis pointing change of the line of sight.

[0049] (2) The triangular layout of the on-orbit line-of-sight pointing three-axis measurement system proposed in the present invention has a measurement accuracy of up to 0.3 arc seconds, which improves the remote sensing imaging quality and target positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic diagram of the measuring principle of the angle measuring instrument based on the principle of self-collimation;

[0051] Figure 2 A schematic diagram of the on-orbit line-of-sight pointing three-axis measurement system of the present invention with a triangular layout;

[0052] Figure 3 This is a schematic diagram of imaging of the angle measuring instrument of the present invention;

[0053] Figure 4 This is an example of a high-precision three-axis measurement system for on-orbit line of sight pointing of a certain satellite with a triangular layout. DETAILED DESCRIPTION

[0054] The triangular layout on-orbit line-of-sight pointing three-axis measurement system proposed in the present invention is Figure 2 The layout shown in the figure includes three angle measuring instruments J1, J2 and J3 and three reflectors R1, R2 and R3; the reflectors R1 and R2 are installed as a whole at the position A to be measured, the angle measuring instruments J1 and J3 are installed as a whole at the position B to be measured, and the reflector R3 and the angle measuring instrument J2 are installed as a whole at the position B to be measured; the three points of the positions A, B and C to be measured form a plane Π; in the initial state, the angle measuring instrument J i The emitted light beams are incident vertically on the reflector R i , and reflected back, i=1,2,3; the three optical axes of the three angle measuring instruments intersect at one point, among which the optical axis of the angle measuring instrument J1 is parallel to the AB direction, the optical axis of the angle measuring instrument J2 is parallel to the AC direction, and the optical axis of the angle measuring instrument J3 is parallel to the BC direction.

[0055] Based on the above-mentioned on-orbit line of sight pointing three-axis measurement system, the on-orbit monitoring line of sight three-axis pointing change measurement method is as follows:

[0056] Let ∠BAC=α, ∠CBA=β, ∠BCA=γ, and establish the world coordinate system with point C as the origin: the BC direction is the positive direction of the x-axis, the positive direction of the z-axis is upward and perpendicular to the x-axis, the x-axis and the z-axis are both in the plane Π, the positive direction of the y-axis is perpendicular to the plane Π and points inward, and the right-hand rule is satisfied; v1, v2 and v3 are the unit direction vectors of the reflected light beams of the angle measuring instrument J1 through the reflector R1, the angle measuring instrument J2 through the reflector R2, and the angle measuring instrument J3 through the reflector R3, respectively, which are calculated based on the actual coordinates of points A, B and C:

[0057] v1={cos(180-∠CBA),0,-sin(180-∠CBA)}={-cos(β),0,-sin(β)},

[0058] v2={cos(∠BCA),0,-sin(∠BCA)}={cos(γ),0,-sin(γ)},

[0059] v3 = {-1, 0, 0};

[0060] On the photosensitive surfaces of the angle measuring instruments J1, J2, and J3, a plane coordinate system is established in the same way: the optical axis direction is z′ i Axis, with the frame of the measuring instrument's photosensitive chip as x' i , y′ i Axis, with:

[0061] x′1={sin(180-∠CBA),0,cos(180-∠CBA)}={sin(β),0,-cos(β)},

[0062] y′1={0,1,0},

[0063] z′1=-v1={cos(β),0,sin(β)};

[0064] x′2={sin(∠BCA),0,cos(∠BCA)}={sin(γ),0,cos(γ)},

[0065] y′2={0,1,0}、

[0066] z′2=-v2={-cos(γ),0,sin(γ)};

[0067] x′3={0,0,-1},

[0068] y′3={0,1,0},

[0069] z′3=-v3={1,0,0};

[0070] The reading (x2, y2) of the angle measuring instrument J2 is determined by the attitude change (a1, b1, c1) of position A, the reading (x3, y3) of the angle measuring instrument J3 is determined by the attitude change (a2, b2, c2) of position B, and the reading (x1, y1) of the angle measuring instrument J1 is determined by the attitude changes (a1, b1, c1) and (a2, b2, c2) of positions A and B. When position A rotates, the transformation of vector v2 can be decomposed into three rotations, which are a1, b1, and c1 counterclockwise rotations around the negative x, y, and z axes of the world coordinate system. Assume that the negative x, y, and z axis vectors of the world coordinate system are k1 = {-1, 0, 0}, k2 = {0, -1, 0}, and k3 = {0, 0, -1}, respectively. The following calculates the states of vector v2 after rotating around vectors k1, k2, and k3. According to the Rodriguez rotation formula, the vector v2 rotated around the vector k1 can be expressed as

[0071] v 21 =cos(a1)*v2+(1-cos(a1))*(Dot[v2,k1])*k1+sin(a1)*Cross[k1,v2] (1)

[0072] In the formula, Dot[v2,k1] represents the dot product operation of vector v2 and k1, and Cross[k1,v2] represents the cross product operation of vector k1 and v2. 21 After rotating around k2,

[0073] v 22 =cos(b1)*v 21 +(1-cos(b1))*(Dot[v 21 ,k2])*k2+sin(b1)*Cross[k2,v 21 ] (2)

[0074] v 22 After rotating around k3,

[0075] v 23 =cos(c1)*v 22 +(1-cos(c1))*(Dot[v 22 ,k3])*k3+sin(c1)*Cross[k3,v 22 ] (3)

[0076] Finally, v2 is rotated by position A to obtain vector v 23 . The vector v2 is equal to v 23 The angle can be expressed as

[0077]

[0078] After mirror reflection, the angle between the incident light and the reflected light is the angle between vector v2 and vector v 23 The intersection point of the reflected light on the x′2y′2 plane of the plane coordinate system of the angle measuring instrument J2 is point p2, as shown in Figure 3 As shown, the coordinate value of point p2 is the required reading (x2, y2). According to the angle, the distance from point p2 to the origin of the plane coordinate system of the angle measuring instrument J2 can be obtained as h = 2f tan(θ2), where f is the focal length of the angle measuring instrument and is a given constant. Since the angle θ2 is particularly small, the equation can be approximated as h = 2fθ2 according to Taylor expansion.

[0079] x2 and y2 are the projection lengths of point p2 on the x′2 axis and y′2 axis respectively. First, calculate the direction vector from the origin to point p2, as Figure 3 The vector v′ shown 23 . The vector v2 is equal to v 23 are all unit vectors. To obtain the vector v′ 23 , use angle θ2 to scale vector v2, vector v′ 23 It can be expressed as

[0080] v′ 23 =v 23 -v2cos(θ2) (5)

[0081] According to the vector angle formula, we can obtain the vector v′ 23 The angle between the same coordinate axes x′2 and y′2

[0082]

[0083] In the formula, v′ 23 The modulus is sin(θ2). According to the distance h from point p2 to the origin, and the angle θ 2x With θ 2y , we can get the horizontal and vertical coordinates of point p2

[0084]

[0085] Combining equations (1) to (7) we get the coordinates of p2 (x2, y2), and make a first approximation of a1, b1, c1, a2, b2, and c2, specifically:

[0086]

[0087] Similarly, the coordinates (x1, y1) and (x3, y3) can be calculated (the values ​​of the coordinates (x1, y1) are related to the posture transformation of positions A and B, and the values ​​obtained from the two calculations can be subtracted), and a1, b1, c1, a2, b2, and c2 can be approximated once, as shown below:

[0088]

[0089] And written in matrix form as:

[0090] M×s=n (11)

[0091] Where M is a 6×6 matrix,

[0092]

[0093] s=[a1,b1,c1,a2,b2,c2] T ,

[0094] n=[x1,y1,x2,y2,x3,y3] T ;

[0095] The coordinate transformation n of the angle measuring instrument is known, and the three-axis pointing change s of the visual axis is calculated as follows:

[0096] s=M -1 ×n (12)

[0097] The present invention will be further described below in conjunction with the embodiments.

[0098] Example 1

[0099] In order to monitor the change of the three-axis angle between the star sensor and the camera external reference, a satellite arranges reflectors R1 and R2 on the star sensor bracket (together mounted on a rigid bracket), angle measuring instruments J1 and J2 are mounted on a rigid bracket, and angle measuring instrument J3 and reflector R3 are mounted on a rigid bracket. Reflectors R1 and R2; angle measuring instruments J1 and J2; angle measuring instruments J3 and reflector R3 form a triangle layout as shown in the figure. Figure 4 After the layout, ∠BAC=α=46.8145°, ∠CBA=β=111.894°, ∠BCA=γ=21.2917°, f=220.048mm is the focal length of the angle measuring instrument, and substituting it into M in formula (11), we get:

[0100] Ms=n

[0101]

[0102] According to the maximum error, the reading deviation of the angle measuring instrument is set, and it is set to Δx1 = 6.8e-5mm, Δy1 = -6.8e-5mm, Δx2 = 6.8e-5mm, Δy2 = 6.8e-5mm, Δx3 = 6.8e-5mm, Δy3 = 6.8e-5mm. In addition, the attitude parameters (a1, b1, c1) and (a2, b2, c2) are assigned one by one. Each rotation amount changes within ±50”, with an interval of 5”. The rotation amount of a2 is different. It changes within ±0.19”, with an interval of 0.019”. Each rotation amount changes 21 times. The six rotation amount combinations change a total of 216 cases, which are used as the true value of the simulation experiment. According to formula (12), the result is inverted and the calculated error is compared with the true value. The experimental data shows that the maximum calculation error of each rigid body attitude rotation amount is reflected in the rotation amount a2, but it is still less than 0.302”.

[0103] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

[0104] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. The triangular layout of the on-orbit line-of-sight pointing three-axis measurement system is characterized by: It includes three angle measuring instruments J1, J2 and J3 and three reflectors R1, R2 and R3; reflectors R1 and R2 are installed as a whole at the position A to be measured, angle measuring instruments J1 and J3 are installed as a whole at the position B to be measured, and reflector R3 and angle measuring instrument J2 are installed as a whole at the position B to be measured; the three points A, B and C to be measured form a plane Π; in the initial state, the angle measuring instrument J i The emitted light beams are incident vertically on the reflector R i , and reflected back, i=1,2,3; the three optical axes of the three angle measuring instruments intersect at one point, among which the optical axis of the angle measuring instrument J1 is parallel to the AB direction, the optical axis of the angle measuring instrument J2 is parallel to the AC direction, and the optical axis of the angle measuring instrument J3 is parallel to the BC direction.

2. An on-track line-of-sight pointing three-axis measurement method based on the triangular layout of the system of claim 1, characterized in that: The following steps are involved: S1. Establish a world coordinate system with position C as the origin: the BC direction is the positive direction of the x-axis, the positive direction of the z-axis is upward and perpendicular to the x-axis, the x-axis and the z-axis are both in the plane Π, the positive direction of the y-axis is perpendicular to the plane Π and inward, and the right-hand rule is satisfied; let v1, v2 and v3 be the unit direction vectors of the reflected light of the angle measuring instrument J1 through the reflector R1, the angle measuring instrument J2 through the reflector R2, and the angle measuring instrument J3 through the reflector R3 respectively; S2. On the photosensitive surfaces of angle measuring instruments J1, J2, and J3, plane coordinate systems are established in the same way: the optical axis direction is z i 'axis, with the frame of the photosensitive chip of the measuring instrument as x' i , y′ i Axis, i=1,2,3; S3, calculate the vector v after v2 is rotated by position A 23 and v2 and v 23 Angle: The angle measuring instrument J2 reading (x2, y2) is determined by the posture change (a1, b1, c1) of position A. When position A rotates, the transformation of vector v2 is decomposed into three rotations, which are a1, b1, and c1 counterclockwise rotations around the negative axis of x, y, and z of the world coordinate system. The vector v after v2 is rotated by position A is obtained using the Rodrigues rotation formula. 23 , and get v2 and v 23 The angle of S4. Assume that the intersection of the reflected light on the x'2y'2 plane of the angle measuring instrument J2 plane coordinate system is point p2, and calculate the coordinate value of point p2, that is, the angle measuring instrument J2 reading (x2, y2): According to v2 and v 23 The distance h from the angle calculation point p2 to the origin of the plane coordinate system of the angle measuring instrument J2 and the direction vector v' from the origin of the plane coordinate system of the angle measuring instrument J2 to point p2 23 , and then calculate the vector v' 23 The angle θ between the same coordinate axes x'2 and y'2 2x ,θ 2y , according to the distance h and the angle θ 2x ,θ 2y , calculate and obtain the angle measuring instrument J2 reading (x2, y2); S5. The angle measuring instrument J3 reading (x3, y3) is determined by the posture change (a2, b2, c2) of position B. The angle measuring instrument J3 reading (x3, y3) is calculated according to the method of steps S3 to S4. S6. The reading (x1, y1) of the angle measuring instrument J1 is determined by the posture changes (a1, b1, c1) and (a2, b2, c2) of positions A and B. The calculated (x2, y2) is subtracted from (x3, y3) to obtain the reading (x1, y1) of the angle measuring instrument J1. S7, x1, x2, x3, y1, y2, y3 are first approximated to a1, b1, c1, a2, b2, c2, and the matrix form is M×s=n, where M is a 6×6 matrix and s=[a1, b1, c1, a2, b2, c2] T , n = [x1,x2,x3,y1,y2,y3] T , then the coordinate transformation n of the angle measuring instrument is known to calculate the three-axis pointing change s of the visual axis as s = M -1 ×n.

3. The on-track line-of-sight pointing three-axis measurement method of angular layout according to claim 2, characterized in that: v1, v2 and v3 are: v1={cos(180-∠CBA),0,-sin(180-∠CBA)}、 v2={cos(∠BCA),0,-sin(∠BCA)}, v3={-1,0,0}.

4. The on-track line-of-sight pointing three-axis measurement method of angular layout according to claim 3 is characterized in that: The optical axis direction is z i 'axis, with the frame of the photosensitive chip of the measuring instrument as x' i , y′ i Axis, i = 1, 2, 3, as follows: x1'={sin(180-∠CBA),0,cos(180-∠CBA)}, y1'={0,1,0}, z1'=-v1; x'2={sin(∠BCA),0,cos(∠BCA)}, y'2={0,1,0}, z'2=-v2; x'3={0,0,-1}, y'3={0,1,0}, z'3=-v3.

5. The on-track line-of-sight pointing three-axis measurement method of angular layout according to claim 4, characterized in that: The calculation v2 is the vector v after the position A is rotated 23 and v2 and v 23 The angles are as follows: Assume that the negative axis vectors of the x, y, and z axes of the world coordinate system are k1 = {-1, 0, 0}, k2 = {0, -1, 0}, and k3 = {0, 0, -1}, respectively. Calculate the state of vector v2 after rotating around vectors k1, k2, and k3: The vector v2 rotated around vector k1 is expressed as: <h2 style=";text-align:left;direction:ltr">v<h2 style=";text-align:left;direction:ltr"> 21 <h2 style=";text-align:left;direction:ltr"> = cos(a1)*v2+(1-cos(a1))*(Dot[v2,k1])*k1+sin(a1)*Cross[k1,v2] Where Dot[v2,k1] represents the dot product of vector v2 and k1, Cross[k1,v2] represents the cross product of vector k1 and v2; vector v 21 After rotating around k2: in 22 =cos(b1)*v 21 +(1-cos(b1))*(Dot[v 21 ,k2])*k2+sin(b1)*Cross[k2,v 21 ] Vector v 22 After rotating around k3: v 23 =cos(c1)*v 22 +(1-cos(c1))*(Dot[v 22 ,k3])*k3+sin(c1)*Cross[k3,v 22 ] Finally, v2 is rotated by position A to obtain vector v 23 , vector v2 and v 23 The angle is expressed as:

6. The on-track line-of-sight pointing three-axis measurement method of angular layout according to claim 5, characterized in that: Distance h, vector v′ 23 They are: h=2fθ2 v' 23 =v 23 -v2cos(θ2) Where f is the focal length of the angle measuring instrument.

7. The on-track line-of-sight pointing three-axis measurement method of angular layout according to claim 6, characterized in that: Angle θ 2x ,θ 2y They are:

8. The on-track line-of-sight pointing three-axis measurement method of angular layout according to claim 7, characterized in that: The angle measuring instrument J2 reading (x2, y2) is:

9. The on-track line-of-sight pointing three-axis measurement method of angular layout according to claim 8, characterized in that: Arrange the angle measuring instrument J2 readings (x2, y2), angle measuring instrument J3 readings (x3, y3), and angle measuring instrument J1 readings (x1, y1) into the following forms: Let ∠BAC=α, ∠CBA=β, ∠BCA=γ, 10. The on-track line-of-sight pointing three-axis measurement method of angular layout according to claim 9, characterized in that: The matrix M is specifically:

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