Triangular layout on-orbit boresight pointing three-axis measurement system and method

Abstract

The present application relates to a triangle layout on-orbit visual axis pointing three-axis measurement system and method, comprising three angle measuring instruments J1, J2, J3 and three mirrors R1, R2, R3; the mirrors R1, R2 are installed as a whole at the measured position A, the angle measuring instruments J1, J3 are installed as a whole at the measured position B, the mirror R3 and the angle measuring instrument J2 are installed as a whole at the measured position B; the three points A, B, C form a plane Pi; in the initial state, the angle measuring instruments J i The emitted light beams are perpendicularly incident on the mirrors R i And are reflected back, the three optical axes of the three angle measuring instruments intersect at a point, 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. The present application realizes the three-axis pointing change of the on-orbit monitoring visual axis, implements feedback control and corrects remote sensing data according to the monitoring data, and ensures the remote sensing imaging quality and target positioning accuracy.

Description

Technical Field

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

[0002] High resolution and high target positioning accuracy are key characteristics and core indicators of high-performance remote sensing satellites. However, changes in the line-of-sight (LAS) pointing of optical payloads due to structural deformation are a significant factor affecting remote sensing imaging quality and target positioning accuracy. This is because on-orbit structures are subject to deformation due to complex factors such as gravity, extreme temperature changes, space debris impacts, and fatigue. This deformation directly affects the spatial pointing of key components such as high-resolution remote sensing cameras and star sensors, as well as their geometric relationships, causing changes in the LAS pointing of optical payloads. Consequently, this severely impacts remote sensing imaging quality and target positioning accuracy. For sub-meter resolution remote sensing satellites, even micrometer-level structural deformation can lead to meter-level imaging errors. This will significantly affect target positioning accuracy.

[0003] Currently, methods such as thermal control and optimized material structure design are mainly used to reduce on-orbit structural deformation and thus suppress changes in the line-of-sight pointing of optical payloads. However, their application scope and effectiveness are limited. The main problems include: although key structures such as the integrated support for remote sensing cameras and the payload mounting substrate possess high stability, their overall thermodynamic parameters differ after assembly and connection with other structures. Even with the aforementioned suppression methods, these key structures can still experience micrometer-level or even millimeter-level deformations under the influence of micro-vibrations and variable external heat flows. For some key structures, it is difficult to implement high-precision overall temperature control. These structures are prone to exceeding the threshold deformation due to extreme temperature changes and gravity in space. All these factors can lead to arcsecond-level changes in the line-of-sight pointing of remote sensing satellites.

[0004] As the performance requirements for remote sensing detection, such as accuracy, range, and stability, become increasingly stringent, simply suppressing deformation through methods like thermal control and optimized material structure design is no longer sufficient to meet the high-precision control requirements of satellite line-of-sight pointing. Taking effective measures to monitor line-of-sight pointing changes in orbit, implementing feedback control based on the monitoring data, and correcting remote sensing data have become crucial to ensuring remote sensing imaging quality and target positioning accuracy. Simultaneously, on-orbit monitoring of line-of-sight pointing is also key to evaluating satellite design performance and retrieving design parameters.

[0005] Angle measuring instruments based on the self-collimation principle are measurement methods that use the displacement of image points at conjugate image planes to solve for minute changes in a system. Using parallel light emitted from off-axis points as a reference, its working principle is as follows: Figure 1 As shown. Let the height of the object point be H, the focal length of the objective lens be f0, and the tilt angle of the reflecting mirror be θ. Then we have H = f0 · tan2θ. When the line of sight of the system rotates by Δω, the position of the image point on the image plane also shifts, denoted as the image point displacement ΔH. ωThe rotation of the line of sight Δω and the corresponding image point displacement ΔH ω The functional relationship between them is determined by recording the image point displacement ΔH. ω The inverse calculation system Δω enables real-time monitoring of the line of sight. The autocollimation principle can measure the angular changes around two axes with high precision, while the satellite line of sight needs to measure the angular changes around three axes. Generally, the angular changes around three axes cannot be obtained by a single angular measuring instrument, and multiple angular measuring instruments need to be used in conjunction for measurement. Summary of the Invention

[0006] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose an on-orbit line-of-sight pointing triaxial measurement system and method with a triangular layout. This system monitors the triaxial pointing changes of the line of sight on-orbit, implements feedback control based on the monitoring data, and corrects the remote sensing data to ensure the quality of remote sensing imaging and the accuracy of target positioning.

[0007] The solution to the technical problem of this invention is: a triangular layout on-orbit line-of-sight pointing triaxial measurement system, including 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 to be measured A, angle measuring instruments J1 and J3 are installed as a whole at the position to be measured B, and reflector R3 and angle measuring instrument J2 are installed as a whole at the position to be measured B; the three points to be measured A, B, and C form a plane Π; in the initial state, angle measuring instrument J... i The emitted beams are perpendicularly incident on the reflecting mirror R. i And reflect back, i = 1, 2, 3; the three optical axes of the three angle measuring instruments intersect at a point in pairs, where the optical axis of angle measuring instrument J1 is parallel to the AB direction, the optical axis of angle measuring instrument J2 is parallel to the AC direction, and the optical axis of angle measuring instrument J3 is parallel to the BC direction.

[0008] A triangular layout method for on-orbit line-of-sight pointing triaxial measurement includes the following steps:

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

[0010] S2. Establish a planar coordinate system in the same way on the photosensitive surfaces of the angle measuring instruments J1, J2, and J3: with the optical axis direction as z′. i The axis is defined by the frame of the measuring instrument's photosensitive chip as x′. i y′ i Axis, i=1,2,3;

[0011] S3. Calculate the vector v2 after rotation at position A. 23 And v2 and v 23 The included angle: The reading (x2, y2) of the included angle measuring instrument J2 is determined by the attitude change (a1, b1, c1) of position A. When position A rotates, the transformation of vector v2 is decomposed into three rotations, namely, counterclockwise rotations a1, b1, and c1 around the negative x, y, and z axes of the world coordinate system. The vector v2 after rotation by position A is obtained using the Rodrigues rotation formula. 23 And obtain v2 and v 23 The included angle;

[0012] S4. Let point p2 be the intersection of the reflected ray on the x′2y′2 plane of the angle measuring instrument J2. Calculate the coordinates of point p2, i.e., the reading (x2, y2) of the angle measuring instrument J2: based on v2 and v 23 The distance h from the angle calculation point p2 to the origin of the angle measuring instrument J2 plane coordinate system, and the direction vector v′ from the origin of the angle measuring instrument J2 plane coordinate system to point p2. 23 Then calculate vector v′ 23 The angle θ between the coordinate axes x′2 and y′2 2x θ 2y Based on the distance h and the included angle θ 2x θ 2y The angle measuring instrument J2 reading (x2, y2) is calculated.

[0013] S5. The angle measuring instrument J3 reading (x3, y3) is determined by the attitude 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 angle measuring instrument J1 reading (x1,y1) is determined by the attitude changes (a1,b1,c1) and (a2,b2,c2) of positions A and B. The angle measuring instrument J1 reading (x1,y1) is obtained by subtracting (x3,y3) from (x2,y2).

[0015] S7, x1, x2, x3, y1, y2, y3 approximate a1, b1, c1, a2, b2, c2 in one step, and can be represented in matrix form as 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 Given the coordinate transformation n of the angle measuring instrument, the triaxial pointing change s of the line of sight is s = M. -1 ×n.

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

[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 The axis is defined by the frame of the measuring instrument's photosensitive chip as x′. i y′ i The axes, i = 1, 2, 3, are 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 vector v2 after rotation at position A is calculated. 23 And v2 and v 23 The included angle is as follows:

[0024] Let the negative x, y, and z axis vectors of the world coordinate system be k1 = {-1, 0, 0}, k2 = {0, -1, 0}, and k3 = {0, 0, -1}, respectively. Calculate the state of vector v2 after rotating it around vectors k1, k2, and k3 in turn:

[0025] The vector v2 after rotation around vector k1 is represented as:

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

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

[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, it becomes:

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

[0031] Finally, after rotating v2 at position A, we obtain vector v. 23 Vectors v2 and v 23 The included angle is expressed as:

[0032]

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

[0034] h=2fθ2

[0035] v′ 23 =v 23 -v2cos(θ2)

[0036] In the formula, f is the focal length of the included angle measuring instrument.

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

[0038]

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

[0040] x² = 2f²θ²cos(θ) 2x )

[0041] y2=2*f*θ2*cos(θ 2y ).

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

[0043] Let ∠BAC=α, ∠CBA=β, ∠BCA=γ,

[0044]

[0045] Furthermore, matrix M is specifically as follows:

[0046]

[0047] The beneficial effects of this invention compared to the prior art are:

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

[0049] (2) The measurement accuracy of the triangular layout on-orbit line-of-sight pointing triaxial measurement system proposed in this invention can reach 0.3 arcseconds, which improves the remote sensing imaging quality and target positioning accuracy. Attached Figure Description

[0050] Figure 1 This is a schematic diagram illustrating the measurement principle of an angle measuring instrument based on the self-collimation principle.

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

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

[0053] Figure 4 An example of an on-orbit high-precision triaxial measurement system for a satellite with a triangular layout. Detailed Implementation

[0054] The triangular layout on-orbit line-of-sight triaxial measurement system proposed in this invention is based on... Figure 2 The layout shown includes three angle measuring instruments J1, J2, and J3, and three reflectors R1, R2, and R3. Reflectors R1 and R2 are installed as a unit at the measurement location A, angle measuring instruments J1 and J3 are installed as a unit at the measurement location B, and reflector R3 and angle measuring instrument J2 are installed as a unit at the measurement location B. The three points A, B, and C form a plane Π. In the initial state, angle measuring instrument J... i The emitted beams are perpendicularly incident on the reflecting mirror R. i And reflect back, i = 1, 2, 3; the three optical axes of the three angle measuring instruments intersect at a point in pairs, where the optical axis of angle measuring instrument J1 is parallel to the AB direction, the optical axis of angle measuring instrument J2 is parallel to the AC direction, and the optical axis of angle measuring instrument J3 is parallel to the BC direction.

[0055] Based on the above-mentioned on-orbit line-of-sight pointing triaxial measurement system, the method for measuring changes in the triaxial pointing of the line of sight in orbit is as follows:

[0056] Let ∠BAC = α, ∠CBA = β, ∠BCA = γ, and establish a world coordinate system with point C as the origin: the positive x-axis is along the BC direction, the positive z-axis is upward and perpendicular to the x-axis, both the x and z axes lie in plane Π, and the positive y-axis is perpendicular to plane Π and inward, satisfying the right-hand rule; v1, v2, and v3 are the unit direction vectors of the reflected beams from angle measuring instrument J1 through mirror R1, angle measuring instrument J2 through mirror R2, and angle measuring instrument J3 through mirror R3, respectively, 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] Establish a planar coordinate system on the photosensitive surfaces of the angle measuring instruments J1, J2, and J3 in the same manner: with the optical axis direction as z′. i The axis is defined by the frame of the measuring instrument's photosensitive chip as x′. i y′ i Axes, including:

[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) at position A, the reading (x3, y3) of the angle measuring instrument J3 is determined by the attitude change (a2, b2, c2) at position B, and the reading (x1, y1) of the angle measuring instrument J1 is jointly determined by the attitude changes (a1, b1, c1) and (a2, b2, c2) at positions A and B. When position A rotates, the transformation of vector v2 can be decomposed into three rotations, namely counterclockwise rotations a1, b1, and c1 around the negative x, y, and z axes of the world coordinate system. Let the negative x, y, and z axis vectors of the world coordinate system be k1 = {-1, 0, 0}, k2 = {0, -1, 0}, and k3 = {0, 0, -1}, respectively. The states of vector v2 after rotation around vectors k1, k2, and k3 are calculated in turn. According to Rodrigues' rotation formula, the vector v2 rotated around 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 of vectors v2 and k1, and Cross[k1,v2] represents the cross product of vectors k1 and v2. Similarly, v 21 After rotating around k2, it becomes

[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, it becomes

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

[0076] Finally, after rotating v2 at position A, we obtain vector v. 23 Vectors v2 and v 23 The included angle can be expressed as

[0077]

[0078] After mirror reflection, the angle between the incident ray and the reflected ray is the angle between vector v2 and vector v. 23 Twice the included angle is 2θ². The intersection point of the reflected rays in the x′2y′2 plane of the J2 plane coordinate system of the angle measuring instrument is point p2, as shown below. Figure 3 As shown, the coordinates of point p2 are (x2, y2), and the desired reading is obtained. Based on the included angle, the distance from point p2 to the origin of the J2 plane coordinate system of the angle measuring instrument is 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 using Taylor expansion.

[0079] x2 and y2 are the projection lengths of point p2 onto the x′2 axis and y′2 axis, respectively. First, calculate the direction vector from the origin to point p2, as follows: Figure 3 The vector v′ shown 23 Vectors v2 and v 23 All are unit vectors; to obtain vector v′ 23 By scaling vector v2 using angle θ2, vector v′ 23 It can be represented as

[0080] v′ 23 =v 23 -v2cos(θ2) (5)

[0081] Calculate vector v′ using the formula for the angle between vectors. 23 Angle between the coordinate axes x′2 and y′2

[0082]

[0083] In the formula, v′ 23 The modulus is sin(θ2). Based on the distance h from point p2 to the origin, and the angle θ... 2x With θ 2y We can obtain the x and y coordinates of point p2.

[0084]

[0085] Combining equations (1) to (7), we obtain the coordinates (x2, y2) of p2, and approximate a1, b1, c1, a2, b2, and c2 in one step, specifically as follows:

[0086]

[0087] Similarly, coordinates (x1, y1) and (x3, y3) can be calculated (where the value of coordinate (x1, y1) is related to the attitude transformations at positions A and B; the difference between the two calculated values ​​is sufficient). Then, approximate a1, b1, c1, a2, b2, and c2 once, as shown below:

[0088]

[0089] And expressed in matrix form as follows:

[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] Given the coordinate transformation n of the angle measuring instrument, the three-axis pointing changes s of the line of sight are as follows:

[0096] s=M -1 ×n (12)

[0097] The present invention will be further described below with reference to the embodiments.

[0098] Example 1

[0099] To monitor the three-axis angle changes between a star sensor and an external reference point of a camera, a satellite has two reflectors, R1 and R2 (both mounted on a rigid support), mounted on a star sensor support. Angle measuring instruments J1 and J2 are mounted on one rigid support, and angle measuring instrument J3 and reflector R3 are mounted on another rigid support. The reflectors R1 and R2, angle measuring instruments J1 and J2, and angle measuring instrument J3 and reflector R3 form a triangular arrangement as shown in the diagram. Figure 4 As shown. After 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, which is substituted into M in formula (11) to obtain,

[0100] Ms=n

[0101]

[0102] The deviation of the angle measuring instrument reading was set according to the maximum error, and was 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 sequence. In addition, the attitude parameters (a1,b1,c1) and (a2,b2,c2) were assigned values ​​one by one. Each rotation amount changed within ±50”, with an interval of 5”. However, the rotation amount of a2 was different. It changed within ±0.19”, with an interval of 0.019”. Each rotation amount changed 21 times. There were a total of 216 possible combinations of the six rotation amounts, which were used as the true values ​​of the simulation experiment. The results were calculated by reverse calculation according to formula (12) and compared with the true values ​​to calculate the error. The experimental data showed that the maximum calculation error of each rigid body attitude rotation amount was reflected in the rotation amount a2, but it was still less than 0.302”.

[0103] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0104] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A triangle layout on-orbit boresight pointing triaxial measurement method, realized by a triangle layout on-orbit boresight pointing triaxial measurement system, the system comprising three goniometers and three reflectors; the reflectors are installed as a whole at a to-be-measured position A, the goniometers are installed as a whole at a to-be-measured position B, the reflectors , the goniometers are installed as a whole at the to-be-measured position B; the three points of the to-be-measured positions A, B and C form a plane . Clamp angle measuring instrument in initial state The emitted light beams are each normally incident on the mirror and reflected back, ; The three optical axes of the three goniometers intersect at a point, wherein the optical axis of the goniometer is parallel to the AB direction, the optical axis of the goniometer is parallel to the AC direction, and the optical axis of the goniometer is parallel to the BC direction; characterized in that the method comprises the following steps: S1, establish a world coordinate system with position C as the origin: the x-axis positive direction is along the BC direction, the z-axis positive direction is upward perpendicular to the x-axis, both the x-axis and the z-axis are in the plane , , , , , , , , , , the unit direction vectors of the reflected light rays of the reflector, the angle measuring instrument, the reflector, the angle measuring instrument, the reflector, and the angle measuring instrument, respectively S2, on the photosensitive surface of the goniometer A plane coordinate system is established in the same way on the photosensitive surface of the goniometer: taking the optical axis direction as the axis, taking the frame of the photosensitive chip of the goniometer as the axis, ; S3, compute vector after rotation of position A and angle between angle measuring instrument readings determined by the change of pose of position A when position A is rotated, the transformation of vector is decomposed into three rotations, respectively, counterclockwise rotation around the x, y, z negative axis direction of the world coordinate system , using the Rodrigues rotation formula to get vector after rotation of position A , and get angle between angle measuring instrument S4. Assume the reflected ray is measured by the angle measuring instrument. Plane coordinate system The intersection point on the plane is a point. Calculation points The coordinate values, i.e., the included angle measuring instrument reading :according to and Calculation point of included angle to angle measuring instrument Distance from the origin of the plane coordinate system and angle measuring instrument From the origin of the plane coordinate system to the point Direction vector Then calculate the vector Same coordinate axis , The included angle , According to the distance and included angle , The included angle measuring instrument was calculated. reading ; S5, goniometer readings from the change in pose of position B determined, the goniometer readings calculated according to the method of steps S3-S4 readings ; S6, goniometer readings from the change in the poses of positions A, B , determined together, the calculated is subtracted from the goniometer readings ; S7、 To the first approximation, the matrix form is given by where M is a 6x6 matrix, , The known coordinate transformation of the goniometer is The three-axis pointing change of the line of sight is given by is ; , With respectively: 、 、 ； The light axis direction is The frame of the photosensitive chip of the measuring instrument is The frame of the photosensitive chip of the measuring instrument is Specifically as follows: 、 、 ； 、 、 ； 、 、 ； The calculation Vector after rotation by position A And The angle with Specifically as follows: The x, y, z negative axis vectors of the world coordinate system are , and , the vectors are calculated in turn , and after rotation: vector around the vector the rotated vector is represented as: where denotes the dot product of the vectors denotes the cross product of the vectors ; the vector is rotated around afterwards​​​ Vector around after rotation: Finally After rotation by position A, the vector , the vector The angle between is expressed as: ； distance , vector respectively: In the formula, is the focal length of the goniometer; angle between , respectively: ； Goniometer Readings Is: ； goniometer readings goniometer readings goniometer readings Respectively, the following forms: Let , , , 。 2. The angularly laid out on-orbit boresight pointing triaxial measurement method of claim 1, wherein, The matrix M is in particular: 。

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