Satellite-borne SAR attitude control method based on optimal azimuth resolution

Abstract

The invention discloses a satellite-borne SAR attitude control method based on optimal azimuth resolution. According to the attitude control method, the velocity of a satellite and the initial direction of an antenna beam can be combined, the beam target direction can be determined according to the actual observation scene and the constraint condition of the optimal azimuth resolution, the yaw angle, the rolling angle and the pitch angle needing to be adjusted of the satellite attitude are calculated in sequence, finally, the wave foot can accurately cover the target observation scene, and the target observation scene is more accurate. Meanwhile, the wave foot direction is parallel to the satellite motion direction, and the optimal azimuth resolution is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of synthetic aperture radar, and particularly relates to a spaceborne SAR attitude control method based on optimal azimuth resolution. Background Technique

[0002] Spaceborne synthetic aperture radar (SAR) is a means of earth observation with a satellite spacecraft as the moving platform. It uses microwave signals to image the earth's surface with high resolution, has the capabilities of all-day and all-weather and large-area observation, and can be widely applied to multiple fields such as remote sensing mapping, geological disaster monitoring, battlefield reconnaissance and surveillance.

[0003] Spaceborne SAR attitude control refers to accurately controlling the attitude of the satellite so that the beam of the SAR antenna carried by it can accurately point to the target area, in order to achieve the goal of earth observation in accordance with the predetermined direction and angle, and meet the requirements of the imaging task. Spaceborne SAR attitude control is one of the key technologies to ensure that the satellite can complete the earth observation task with high quality, and is of great significance for improving the SAR imaging quality.

[0004] Attitude control based on the zero-Doppler criterion is a common technical method, that is, adjusting the beam direction so that the beam can irradiate the target observation scene, and at the same time making the Doppler center frequency of the radar echo signal zero, thereby reducing the imaging processing difficulty and improving the imaging accuracy. The disadvantage is that when the beam direction satisfies the zero-Doppler criterion, but the wave-foot direction is not parallel to the satellite motion direction, the edge position of the irradiation area cannot reach the longest observation time, that is, the synthetic aperture time is shortened, resulting in low imaging azimuth resolution.

[0005] In order to achieve the optimal resolution, it is necessary to further adjust the satellite attitude so that the wave-foot direction is parallel to the satellite motion direction to achieve the optimal azimuth resolution. Summary of the Invention

[0006] The present invention provides a spaceborne SAR attitude control method based on optimal azimuth resolution. This attitude control method can combine the speed of the satellite and the initial pointing of the antenna beam, and determine the beam target pointing according to the actual observation scene and the constraint conditions of the optimal azimuth resolution, and calculate the yaw angle, roll angle and pitch angle of the satellite attitude adjustment in sequence. Finally, the wave-foot can accurately cover the target observation scene, and at the same time the wave-foot direction is parallel to the satellite motion direction to achieve the optimal azimuth resolution.

[0007] The technical solution of the present invention is as follows:

[0008] A spaceborne SAR attitude control method based on optimal azimuth resolution, comprising:

[0009] S1: Obtain parameters and initialize variables. Obtain the velocity v of the satellite in the earth-fixed coordinate system ECF, original beam pointing under ground-fixed system And determine the beam target direction according to the target observation scene and satellite position Get the original antenna direction Initialize the satellite body coordinate system OX o Y o Z o Three-axis vector in With v ECF Same direction, Pointing to the center of the earth, Determined by the right-hand rule, Initialize the number of iterations n = 1, let The attitude angle adjustment step length η = 1 / 2.

[0010] S2: Perform yaw operation, that is, the satellite rotates the yaw angle ψ around the Z axis. The specific steps include:

[0011] S21: Target the beam Project to the XOY plane and construct the reference coordinates in the XOY plane

[0012]

[0013] in Indicates It is the projection matrix of the normal vector. Its physical meaning is the projection matrix onto the XOY plane.

[0014] S22: Direct the beam before adjustment Project to the XOY plane and calculate the yaw angle ψ using the reference coordinates

[0015]

[0016] S23: Update beam pointing, antenna azimuth, and satellite three-axis, i.e. vector Around Vector around Rotation angle ψ=ηψ

[0017]

[0018] The rotation matrix is expressed as

[0019]

[0020] The matrix N z By the rotation axis Decide

[0021]

[0022] And order

[0023] S3: Perform a rolling operation, i.e., the satellite rotates around the X-axis by a roll angle The specific steps include:

[0024] S31: Point the target beam Project it onto the YOZ plane and construct a reference coordinate in the YOZ plane

[0025]

[0026] Where represents the projection matrix with as the normal vector, and its physical meaning is the projection matrix projected onto the YOZ plane

[0027] S32: Project the beam direction before adjustment onto the YOZ plane and calculate the roll angle using the reference coordinate

[0028]

[0029] S33: Update the beam direction, antenna azimuth, and satellite three axes, i.e., the vector Rotate around the vector by

[0030]

[0031] The rotation matrix is expressed as

[0032]

[0033] Where the matrix N x is determined by the rotation axis and let

[0034]

[0035] S4: Perform a pitching operation, i.e., the satellite rotates around the Y-axis by a pitch angle θ. The specific steps include:

[0036] S41: Calculate the projection v of the satellite velocity on the ground

[0037] S41: Calculate the projection v of the satellite velocity on the ground g

[0038] v g = P z v ECF (11)

[0039] S42: Point the target beam Project to the XOZ plane and construct the reference coordinates in the XOZ plane

[0040]

[0041] in Indicates It is the projection matrix of the normal vector, and its physical meaning is the projection matrix projected onto the XOZ plane.

[0042] S43: Calculate antenna orientation The direction after rotation. The direction of the wave foot should be the same as v g Parallel, so the antenna azimuth should be rotated to v g and In the plane of Zhang Cheng, that is Perpendicular to the plane normal n, n can be expressed as

[0043]

[0044] Antenna azimuth With the rotation axis The angle between can be expressed as

[0045]

[0046] The vector projected onto the plane represented by n can be expressed as

[0047]

[0048] and The angle between them can be expressed as

[0049]

[0050] After rotation, it is recorded as and The angle between

[0051]

[0052] There are two situations

[0053]

[0054] in In the plane perpendicular to The sign depends on which case makes and The absolute value of the inner product is larger.

[0055] S44: Calculate the elevation angle θ. and Projection into the XOZ plane

[0056]

[0057] Construct a unit vector in the plane

[0058]

[0059] judge and If the inner product of is less than 0 (indicating an obtuse angle between the two), let

[0060] Calculate the angle between the two and get the pitch angle θ

[0061]

[0062] S45: Update beam pointing, antenna azimuth, and satellite three-axis, i.e. vector Around Vector Rotation θ = ηθ

[0063]

[0064] The rotation matrix is expressed as

[0065]

[0066] The matrix N y By the rotation axis Decide

[0067]

[0068] And order

[0069] S5: After the above steps, the beam pointing will have deviations, so it is necessary to iterate S2-S4 so that the error is within the threshold range. The error includes the angle error E1 between the projection of the antenna azimuth on the ground and the satellite ground speed, and the angle error E2 between the adjusted beam and the target beam direction, which are expressed as

[0070]

[0071] in is the projection of the antenna azimuth on the ground, In the antenna direction With beam In the plane of the span, it is also connected to the ground normal vector n gVertical, so it can be expressed as

[0072]

[0073] S6: Calculate the final yaw angle, roll angle, and pitch angle. Assume the initial state coordinate system OX o Y o Z o Rotates to OX n Y n Z n , then the three attitude angles of the satellite can be expressed as

[0074]

[0075] Beneficial effects:

[0076] 1. Achieve precise coverage of the target scenario: According to the target observation scenario, the present invention combines the satellite speed and the initial state of the antenna, and accurately calculates the satellite attitude adjustment angle, so that the beam precisely covers the target area;

[0077] 2. Achieve the optimal azimuth resolution of the beam coverage range: In traditional attitude control methods, the wave foot direction may deviate from the satellite motion direction, resulting in a decrease in the resolution of the edge area. The present invention takes the wave foot direction parallel to the satellite speed direction as one of the constraint conditions, and achieves the optimal azimuth resolution while satisfying the beam pointing to the target scenario;

[0078] 3. Achieve efficient and high-precision iterative calculation: The present invention adopts a cyclic iterative strategy, optimizes the adjustment step size, significantly improves the convergence speed while ensuring the calculation accuracy, and can effectively avoid the oscillation problem caused by directly adjusting the pointing. Description of the drawings

[0079] Figure 1 is the flowchart of the attitude control method of the present invention;

[0080] Figure 2 is the schematic diagram of the satellite coordinate system;

[0081] Figure 3 is the schematic diagram of the attitude angle;

[0082] Figure 4 is the schematic diagram of the pitch angle adjustment;

[0083] Figure 5 is the diagram of the satellite attitude and beam irradiation in the initial state; (a) 3D view, (b) 2D view;

[0084] Figure 6 is the diagram of the satellite attitude angle adjustment process in each iteration process;

[0085] Figure 7 is the diagram of the angle error in each iteration process;

[0086] Figure 8 It is a diagram of the adjusted satellite attitude and beam irradiation; (a) 3D view, (b) 2D view. Specific implementation mode

[0087] The present invention will be described in detail below with reference to the accompanying drawings. The flowchart of the overall attitude control method of the present invention is as Figure 1 .

[0088] As Figure 2 shown, in the initial state, the beam is not pointed at the target observation area. It is necessary to adjust the beam to point at the target through satellite attitude control. The adjustment sequence is yaw, roll, and pitch. At the same time, the constraint condition of the optimal azimuth resolution must also be satisfied, that is, the wave foot direction is parallel to the satellite movement direction. The X-axis of the satellite orbit coordinate system OX o Y o Z o has the same direction as the velocity v of the satellite in the geocentric fixed coordinate system ECF .

[0089] The processes of yaw, roll, and pitch adjustment are as Figure 3 shown. Assume that the coordinate system S a is rotated around the Z-axis, X-axis, and Y-axis respectively to obtain S b . All three processes will affect the beam pointing. Directly adjusting the corresponding attitude angles may cause oscillation and the result cannot converge. Therefore, the attitude adjustment is carried out in half-step length and the final state is gradually approximated by using multiple iterations. Finally, the orientations of the three axes of the satellite are recorded, and the final yaw angle ψ, roll angle pitch angle θ are obtained by using the changes of the three axes before and after. Specifically, it includes:

[0090] S1: Obtain parameters and initialize variables. Obtain the velocity v of the satellite in the geocentric fixed coordinate system ECF , the original beam pointing in the geocentric fixed coordinate system and determine the beam target pointing according to the target observation scene and the satellite position. Obtain the original antenna pointing Initialize the triaxial vectors of the satellite body coordinate system OX o Y o Z o where is in the same direction as v , ECF points to the center of the earth, is determined by the right-hand rule, initialize the iteration number n = 1, and let the attitude angle adjustment step size η = 1 / 2.

[0091] S2: Perform a yaw operation, i.e., rotate the satellite around the Z-axis by the yaw angle ψ, and the beam direction after rotation should be as close as possible to That is, the following cost is minimized

[0092]

[0093] where R z represents the rotation matrix around the Z-axis. Since and are both unit vectors, so is also a unit vector. Therefore, minimizing (28) is equivalent to maximizing the inner product of and after rotation, that is Considering that R z is the rotation matrix around the Z-axis, this is equivalent to regarding ψ as and the azimuth angle change in the XY plane. The specific steps include:

[0094] S21: Project the beam target direction onto the XOY plane to construct a reference coordinate in the XOY plane

[0095]

[0096] where represents the projection matrix with as the normal vector, and its physical meaning is the projection matrix projected onto the XOY plane.

[0097] S22: Project the beam direction before adjustment onto the XOY plane, and calculate the yaw angle ψ using the reference coordinate

[0098]

[0099] S23: Update the beam direction, antenna azimuth, and satellite three axes, i.e., the vector rotate around the vector by the angle ψ = ηψ

[0100]

[0101] According to the Rodrigues rotation formula, the rotation matrix R z is

[0102]

[0103] where the matrix N z is determined by the rotation axis

[0104] ​

[0105] And let

[0106] S3: Perform a rolling operation, i.e., the satellite rotates around the X-axis by a rolling angle The specific steps include:

[0107] S31: Point the target beam to Project it onto the YOZ plane and construct a reference coordinate in the YOZ plane

[0108]

[0109] Where represents the projection matrix with as the normal vector, and its physical meaning is the projection matrix projected onto the YOZ plane.

[0110] S32: Project the beam direction before adjustment onto the YOZ plane and calculate the rolling angle using the reference coordinate

[0111]

[0112] S33: Update the beam direction, antenna azimuth, and satellite three axes, i.e., the vector Rotate around the vector by

[0113]

[0114] The rotation matrix is expressed as

[0115]

[0116] Where the matrix N x is determined by the rotation axis

[0117]

[0118] And let

[0119] S4: After the above two-dimensional guidance, theoretically the beam has pointed to the required direction, but at this time the wave foot may not be the best. Specifically, the azimuth of the wave foot may not be parallel to the movement direction of the wave foot. Therefore, the wave foot needs to be adjusted through a pitching operation. To achieve the optimal azimuth resolution, a direction constraint for the wave foot is added, i.e., one of the directions of the wave foot shape is parallel to the movement direction of the wave foot. The specific steps include:

[0120] ​S41: Calculate the projection \(v\) of the satellite velocity on the ground g

[0121] \(v\) g = \(P\) z \(v\) ECF (39)

[0122] S42: Point the target beam to Project it onto the XOZ plane and construct a reference coordinate in the XOZ plane

[0123]

[0124] where represents the projection matrix with as the normal vector, and its physical meaning is the projection matrix projected onto the XOZ plane.

[0125] S43: Calculate the direction where the antenna azimuth is located after rotation. The wave foot direction should be parallel to \(v\) , so the antenna azimuth needs to be rotated to the plane spanned by \(v\) g and g . As shown in , that is, Figure 4 is perpendicular to the normal \(n\) of this plane, and \(n\) can be expressed as . The angle between the antenna azimuth

[0126]

[0127] and the rotation axis can be expressed as

[0128]

[0129] The vector after projecting onto the plane represented by \(n\) can be expressed as

[0130]

[0131] The angle between and

[0132]

[0133] After rotation, it is denoted as The angle between and

[0134]

[0135] where the calculation principle of \(\gamma\) is as follows, as shownFigure 4 , assume that rotates to the plane and is denoted as the direction where it is located is In the plane, draw a perpendicular line through point B, which intersects at point D, and connect DY o , it can be proved that OD and DY o are perpendicular. According to the known angles and geometric relationships, the following relationships can be obtained

[0136]

[0137] Therefore the included angle between and

[0138]

[0139] Further calculation can obtain formula (45).

[0140] The rotation of Figure 4 has two directions, and in are obtained respectively. Therefore can be expressed as

[0141]

[0142] where is the unit vector perpendicular to in the plane. The plus or minus sign depends on which case makes the absolute value of the inner product of and

[0143] S44: Solve the pitch angle θ. Project the azimuth directions of the antenna before and after rotation and onto the XOZ plane

[0144]

[0145] Construct the unit vector in the plane

[0146]

[0147] Judge the inner product of and

[0148] If it is less than 0 (indicating that the two form an obtuse angle), then let

[0149]

[0150] Calculate the included angle between the two to obtain the pitch angle θS45: Update the beam pointing, antenna azimuth, and satellite's three axes, i.e., the vector Rotate around the vector by θ = ηθ

[0151]

[0152] The rotation matrix is expressed as

[0153]

[0154] where the matrix N y is determined by the rotation axis and

[0155]

[0156] Let

[0157] S5: After the above steps, there will be a deviation in the beam pointing. Therefore, it is necessary to iteratively loop through S2 - S4 to make the error within the threshold range. The error includes the angle error E1 between the projection of the antenna azimuth on the ground and the satellite's ground speed, and the angle error E2 between the adjusted beam and the target beam direction, which are respectively expressed as

[0158]

[0159] The final error takes the larger value, Error = max(E1, E2). is the projection of the antenna azimuth on the ground, in the plane formed by the antenna azimuth and the beam and is also perpendicular to the ground normal vector n g and can be expressed as

[0160]

[0161] S6: Calculate the final yaw angle, roll angle, and pitch angle. Assume that the initial state coordinate system OX o Y o Z o rotates to OX n Y n Z n Then the three attitude angles of the satellite can be expressed as

[0162]

[0163] The principle of the above formula is as follows. The satellite adjusts its attitude in the order of yaw, roll, and pitch, i.e., the coordinate system OX o Y o Z oRotate around the z, x, and y axes by the yaw angle ψ, roll angle pitch angle θ in sequence, and finally adjust to OX b Y b Z b , expressed as

[0164]

[0165] x o , y o , z o is the unit vector of the original coordinate system OX o Y o Z o The unit vectors of the coordinate axes, x b , y b , z b is the unit vector of the rotated coordinate system OX b Y b Z b The unit vectors of the coordinate axes, and R1, R2, and R3 are the matrices for rotation around the x, y, and z axes respectively

[0166]

[0167] Therefore, the attitude matrix is simplified to

[0168]

[0169] where "c" and "s" are the abbreviated forms of "cos" and "sin" respectively

[0170] The coordinate system OX o Y o Z o and OX b Y b Z b The coordinate axes of are all unit vectors, and there are nine direction cosines between them, which are represented by A xx , A xy ,...

[0171]

[0172] Then the three coordinate axes can be represented by the direction cosines. Taking x b as an example

[0173] x b = A xx x o + A xy y o + A xz z o (62)

[0174] Therefore, the three coordinate axes can be expressed as

[0175]

[0176] where A is the direction cosine matrix

[0177]

[0178] Matrix A completely determines the coordinate system OX b Y b Z b relative to the reference coordinate system OX o Y o Z o The orientation. Combining formulas (60) and (64), the three attitude angles can be obtained

[0179]

[0180] Expressed in terms of the coordinate axis vectors, it is formula (57).

[0181] So far, all steps are completed.

[0182] Next, an example implemented in the STK software is given in combination with specific parameters. In this example, the satellite beam setting parameters are shown in Table 1, the target observation scenario is Jinan, and the initial attitude of the satellite and the beam illumination situation are as Figure 5 , at this time, the satellite beam cannot illuminate the observation scenario. Next, the method of the present invention is used to adjust the satellite attitude to achieve the goal of illuminating Jinan.

[0183] Table 1 Satellite beam angle parameters

[0184] Parameter Value Beam type Rectangle Vertical half angle (deg) 2 Horizontal half angle (deg) 2 Azimuth angle (deg) 90 Downward viewing angle (deg) 30

[0185] Execute S1 to obtain the parameters, that is, the velocity v of the satellite in the geocentric coordinate system ECF , the pointing of the center of the initial state beam illumination The target pointing (the satellite points to Jinan) The azimuth of the antenna The numerical values of each vector are shown in Table 2; Initialize the variable Initialize the iteration number n = 1, and let The attitude angle adjustment step η = 1 / 2.

[0186] Table 2 Initial parameters

[0187]

[0188]

[0189] Execute S2 - S5, calculate the attitude angles that need to be adjusted in the order of yaw, roll, and pitch, and perform iterative calculations to keep the angle error within the threshold, obtaining Figure 6 , 7 which are the adjustment processes and angle errors of the three attitude angles in each iterative process. As the number of iterations increases, the adjustment angles gradually decrease, and the errors also gradually decrease to within the threshold range.

[0190] Execute S6, calculate the final yaw angle, roll angle, and pitch angle that the satellite needs to adjust, as shown in Table 3. Adjust the satellite attitude according to the calculation results. At this time, the satellite attitude and the beam irradiation situation are as Figure 8 . The beam can irradiate the target observation scene, and the wave - foot edge direction is parallel to the moving direction, ensuring the optimal azimuth resolution of the beam - irradiated edge area, thus proving the effectiveness of this method.

[0191] Table 3 Satellite attitude angle adjustment results

[0192] Parameter Value Yaw angle (deg) 1.0309 Roll angle (deg) -31.1423 Pitch angle (deg) -0.9435

[0193] Certainly, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention. However, these corresponding changes and deformations should all fall within the protection scope of the appended claims of the present invention.

Claims

1. A spaceborne SAR attitude control method based on optimal azimuth resolution, characterized in that, The steps include: S1: Obtain parameters and initialize variables; S2: Perform a yaw operation, i.e., the satellite rotates around the Z-axis by the yaw angle ψ; S3: Perform a rolling operation, i.e., the satellite rotates around the X-axis by a roll angle S4: Perform a pitch operation, i.e., the satellite rotates around the Y-axis by the pitch angle θ; S5: Iteratively loop through S2 - S4 until the error is within the threshold range. The error includes the included angle error E1 between the projection of the antenna azimuth on the ground and the satellite ground speed, and the included angle error E2 between the adjusted beam and the target beam direction; S6: Calculate the final yaw angle, roll angle, and pitch angle.

2. A spaceborne SAR attitude control method based on optimal azimuth resolution - Zhang Yaru as described in claim 1, characterized in that In the initial state, the beam needs to be adjusted to point to the target. The adjustment sequence is yaw, roll, and pitch, and the wave foot direction should be parallel to the satellite motion direction; The attitude adjustment is carried out in a half-step manner, and multiple iterations are used to gradually approach the final state.

3. A spaceborne SAR attitude control method based on optimal azimuth resolution - Zhang Yaru as described in claim 1, characterized in that Step S2 specifically includes: S21: Point the beam target at Project it onto the XOY plane and construct a reference coordinate system in the XOY plane Among them represents the projection matrix with as the normal vector, and its physical meaning is the projection matrix projected onto the XOY plane; S22: Point the beam before adjustment Project it onto the XOY plane and calculate the yaw angle ψ using the reference coordinates S23: Update the beam pointing, antenna azimuth, and satellite three axes, i.e., the vector Around the vector Around The rotation angle ψ = ηψ The rotation matrix is expressed as where the matrix N z is determined by the axis of rotation decide And let 4. A spaceborne SAR attitude control method based on optimal azimuth resolution - Zhang Yaru as described in claim 1, characterized in that, Step S3 specifically includes: S31: Point the target beam at Project it onto the YOZ plane and construct a reference coordinate in the YOZ plane wherein represents a projection matrix with as the normal vector, and its physical meaning is the projection matrix projected onto the YOZ plane; S32: Point the beam before adjustment Project it onto the YOZ plane and calculate the roll angle using the reference coordinates S33: Update the beam pointing, antenna azimuth, and satellite three axes, i.e., the vector Around the vector Rotate The rotation matrix is expressed as where matrix N x is determined by the rotation axis determines And let 5. A spaceborne SAR attitude control method based on optimal azimuth resolution - Zhang Yaru as described in claim 1, characterized in that Step S4 specifically includes: S41: Calculate the projection v of the satellite velocity on the ground g v g = P z v ECF (11) S42: Point the target beam at Project it onto the XOZ plane and construct a reference coordinate in the XOZ plane Among them represents the projection matrix with as the normal vector, and its physical meaning is the projection matrix projected onto the XOZ plane; S43: Calculate the azimuth direction of the antenna The direction after rotation; the wave foot direction should be parallel to v g Therefore, the azimuth direction of the antenna needs to be rotated to the plane spanned by v g and That is, it is perpendicular to the normal vector n of this plane, and n is expressed as ​ Azimuth direction of the antenna and the rotation axis The angle between them is expressed as The vector representation after projection onto the plane represented by n is and The included angle between is expressed as Denoted as after rotation And The included angle between them is There are two possible cases wherein is a unit vector perpendicular to in the plane; The plus or minus sign depends on which case makes and the absolute value of the inner product larger; S44: Solve for the pitch angle θ; project the azimuth directions of the antenna before and after rotation and onto the XOZ plane Construct a unit vector in the plane Judge and Inner product. If it is less than 0 (indicating an obtuse angle between the two), then set Calculate the included angle between the two to obtain the pitch angle θ S45: Update the beam pointing, antenna azimuth, and satellite three axes, i.e., the vector Around the vector Rotate θ = ηθ The rotation matrix is expressed as where the matrix N y is determined by the rotation axis ​ And let 6. A spaceborne SAR attitude control method based on optimal azimuth resolution - Zhang Yaru as described in claim 1, characterized in that In step S5, the error includes the included angle error E1 between the projection of the antenna azimuth on the ground and the satellite ground speed, and the included angle error E2 between the adjusted beam and the target beam direction, which are respectively expressed as wherein is the projection of the antenna azimuth on the ground, in the antenna azimuth and the beam in the plane formed, and is also perpendicular to the ground normal vector n g Therefore, it is expressed as

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