GNSS-based all-zero Doppler guidance method considering SAR installation deviation

Abstract

This invention presents a GNSS-based all-zero Doppler guidance method considering SAR installation deviations. First, it obtains the satellite's position and trajectory velocity components in the WGS84 coordinate system from the GNSS system and calculates the satellite's inertial velocity component in the WGS84 coordinate system. Then, it calculates the satellite's trajectory velocity component in the orbital coordinate system. Based on the imaging target's downward viewing angle, and ideally the satellite's range and azimuth installation angles in the spaceborne SAR beam, it calculates the ideal yaw, pitch, and roll guidance angles. Subsequently, based on the on-orbit calibrated installation deviations of the spaceborne SAR, it corrects the roll, yaw, and pitch guidance angles, and guides the satellite's attitude according to the corrected results. This invention enables real-time calculation of the satellite's roll, yaw, and pitch guidance angles even with installation deviations in the spaceborne SAR, thereby correcting the SAR beam center Doppler frequency to near zero Hertz.

Description

Technical Field

[0001] This invention belongs to the field of satellite attitude control technology, specifically relating to a satellite attitude guidance method for spaceborne synthetic aperture radar (SAR). Background Technology

[0002] For spaceborne synthetic aperture radar (SAR), Doppler characteristics are the primary factor determining the radar's azimuth performance. It directly affects the radar's azimuth resolution, the choice of pulse repetition frequency (PRF), azimuth ambiguity, and the final image processing accuracy. Inaccurate Doppler center frequency reduces the signal-to-noise ratio, increases azimuth ambiguity, causes positional shifts in the output image, and affects image positioning.

[0003] Because satellites travel at high speeds, the Doppler center typically reaches kHz, necessitating the use of a large pulse repetition frequency (PRF). This makes the trade-off between azimuth and range ambiguity particularly prominent. Furthermore, the Earth's rotation and satellite attitude errors further complicate the Doppler echo characteristics, meaning that incorrect estimations of the Doppler center frequency and modulation slope will affect the accuracy of the final image processing. The significant spatial variation of the Doppler frequency adds to the difficulty of imaging processing, thus requiring attitude guidance technology. Implementing attitude guidance on-board can reduce the burden on ground-based imaging processing and improve image quality.

[0004] Yaw guidance technology is based on this idea. Yaw guidance involves pre-positioning the satellite by a yaw angle through attitude control to compensate for the Doppler center shift caused by the Earth's rotation, thus bringing the Doppler center of the echo closer to zero. Building upon yaw guidance, two-dimensional guidance technology, adding an elevation dimension, has been proposed internationally in recent years to further reduce the Doppler center frequency. However, two-dimensional guidance cannot completely eliminate the Doppler frequency shift at the beam center. The elevation-compensated two-dimensional guidance method, after introducing orbital elements, introduces errors due to approximate simplification and cannot completely eliminate the Doppler frequency shift at the beam center. In engineering applications, spaceborne SAR antennas inevitably have installation deviations. It is necessary to calibrate the spaceborne SAR installation deviations in orbit and correct the roll angle, yaw guidance angle, and elevation guidance angle of the satellite attitude control based on the calibrated installation deviations to achieve the desired guidance effect. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a zero-Doppler guidance method based on a GNSS system that takes into account the installation deviation of spaceborne SAR, which can basically eliminate the Doppler frequency shift of the beam center when there is a deviation in the installation of spaceborne SAR.

[0006] The technical solution of this invention is: a GNSS-based all-zero Doppler guidance method considering SAR installation deviation, comprising the following steps:

[0007] (1) Obtain the position components of the satellite in the WGS84 coordinate system from the GNSS system (R s ) ecf and the trajectory velocity component (V) sp ) ecf Furthermore, the inertial velocity components (V) of the satellite in the WGS84 coordinate system were obtained. s ) ecf ;

[0008] (2) Based on the (V) obtained in step (1) s ) ecf and (R) s ) ecf Calculate the satellite's trajectory velocity components (V) in the orbital coordinate system. sp ) o ;

[0009] (3) Based on the (V) obtained in step (2) sp ) o Calculate the yaw guidance angle ψ and pitch guidance angle θ of the satellite from the orbital coordinate system to the spaceborne SAR beam installation coordinate system under ideal conditions, and obtain the yaw guidance angle ψ from the orbital coordinate system to the satellite's own system under ideal conditions through coordinate system transformation. s Pitch guidance angle θ s Roll angle φ s ;

[0010] (4) Based on the installation deviation of the spaceborne SAR obtained from the on-orbit calibration, the roll angle, yaw guidance angle and pitch guidance angle calculated in step (3) are corrected.

[0011] (5) Guide the satellite attitude according to the corrected roll angle, yaw guidance angle and pitch guidance angle.

[0012] Furthermore, in step (1), the inertial velocity component (V) of the satellite in the WGS84 coordinate system is further obtained. s ) ecf Specifically:

[0013] Calculate the position components of the satellite in the J2000 coordinate system Where S wj This is the coordinate transformation matrix from the J2000 coordinate system to the WGS84 coordinate system, with the superscript T indicating the transpose of the matrix;

[0014] Calculate the inertial velocity components of the satellite in the WGS84 coordinate system. Where S wj S is the coordinate transformation matrixwj The derivative matrix;

[0015] Furthermore, in step (2), based on the (V) obtained in step (1) s ) ecf and (R) s ) ecf Calculate the satellite's trajectory velocity components (V) in the orbital coordinate system. sp ) o Specifically:

[0016] Calculate the components of each coordinate axis of the orbital coordinate system in the WGS84 coordinate system:

[0017]

[0018]

[0019]

[0020] in, Represents vector (R) s ) ecf The cross product matrix, Represents vector The cross product matrix;

[0021] The origin O of the orbital coordinate system is the satellite's center of mass, OZ o The axis points from the origin to the Earth's center, OY o The axis is aligned with the negative normal direction of the orbital plane, OX o Axis and OY o Axis, OZ o The right-hand axis is orthogonal and points in the direction of the satellite's velocity.

[0022] Determine the coordinate transformation matrix S from the orbital coordinate system to the WGS84 coordinate system. ow :

[0023]

[0024] Calculate the trajectory velocity components (V) of the satellite in the orbital coordinate system. sp ) o :

[0025]

[0026] Furthermore, the (V) obtained based on step (2) sp ) o To calculate the yaw guidance angle ψ and pitch guidance angle θ of the satellite from the orbital coordinate system to the spaceborne SAR beam installation coordinate system under ideal conditions, specifically: using a 3-2-1 conversion sequence, ψ = arctan2(V spoy Vspox ),

[0027] Furthermore, the yaw guidance angle ψ from the orbital coordinate system to the satellite's own coordinate system under ideal conditions is obtained through coordinate system transformation. s Pitch guidance angle θ s Roll angle φ s Specifically:

[0028] Based on the downward viewing angle σ of the imaging target, the ideal range angle α of the spaceborne SAR beam, and the azimuth angle β of the beam, calculate the transformation matrix S from the spaceborne SAR beam installation coordinate system to the satellite body coordinate system. bs Finally, the transformation matrix S from the orbital coordinate system to the satellite body coordinate system is obtained. bo :

[0029] S bs =C x (-α)·C y (-β)

[0030] S so =C x (σ)·C y (θ)C z (ψ)

[0031] S bo =S bs S so

[0032] Where S so C is the transformation matrix from the orbital coordinate system to the spaceborne SAR beam mounting coordinate system. x (-α) represents the elementary transformation matrix that rotates through an angle of -α around the X-axis of the spaceborne SAR beam mounting coordinate system. C y (-β) The elementary transformation matrix that rotates the Y-axis of the spaceborne SAR beam-mounted coordinate system by an angle of -β. C x (σ) represents the primitive transformation matrix of the orbital coordinate system rotating about the X-axis by an angle of σ. C y (θ) is the primitive transformation matrix that rotates about the Y-axis of the orbital coordinate system by an angle of θ. C z (ψ) is the primitive transformation matrix that rotates about the Z-axis of the orbital coordinate system by an angle of ψ.

[0033] Based on the transformation matrix S from the orbital coordinate system to the satellite's body coordinate system bo Calculate the yaw guidance angle ψ from the orbital coordinate system to the satellite's own system. s Pitch guidance angle θs Roll angle φ s They are respectively:

[0034]

[0035] θ s = -arcsin(A 13 )=-arcsin(-cos(β)sin(θ)+sin(β)cos(σ)cos(θ)).

[0036]

[0037] Furthermore, in step (4), the roll angle, yaw guidance angle, and pitch guidance angle calculated in step (3) are corrected based on the installation deviation of the onboard SAR obtained from the on-orbit calibration. Specifically, after the satellite is calibrated in orbit, the installation deviation Δα in the range direction and the installation deviation Δβ in the azimuth direction of the onboard SAR beam are obtained. According to the 3-2-1 sequence, the following can be obtained:

[0038]

[0039] θ c = -arcsin(A 13 )=-arcsin(-cos(β+Δβ)sin(θ)+sin(β+Δβ)cos(σ)cos(θ))

[0040]

[0041] The advantages of this invention compared to the prior art are:

[0042] (1) The method of the present invention can effectively solve the problem of Doppler frequency shift of SAR beam center under the condition of installation deviation of spaceborne SAR, and can reduce the Doppler frequency to near 0 Hz.

[0043] (2) The method of the present invention directly utilizes the satellite position information output by the GNSS system to calculate the satellite track speed in real time and then obtain the yaw guidance angle and pitch guidance angle, avoiding the error caused by approximate simplification after introducing orbital elements in the traditional method, and has a better guidance compensation effect.

[0044] (3) The satellite position data used to calculate the roll angle, yaw guidance angle and pitch guidance angle in this invention are derived from GNSS systems, including mainstream navigation systems such as Beidou, GPS, Galileo and GLONASS, which are convenient to use. Attached Figure Description

[0045] Figure 1 This is a flowchart of the method of the present invention;

[0046] Figure 2 This is a schematic diagram illustrating the control principle of the method of the present invention;

[0047] Figure 3 This is a schematic diagram of the installation of the spaceborne SAR of the present invention in the satellite system;

[0048] Figure 4 This is a schematic diagram of the imaging target's perspective in the satellite orbit coordinate system according to the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0050] like Figure 1 The diagram shown is a flowchart of the method of the present invention, and the main steps are as follows:

[0051] (1) Calculate the inertial velocity component (V) of the satellite in the WGS84 coordinate system. s ) ecf The calculation steps are as follows:

[0052] (1a) Obtain the satellite's position components (R) in the WGS84 coordinate system at time t from the GNSS system. s ) ecf , trajectory velocity component (V sp ) ecf ;

[0053] (1b) Calculate the position components (R) of the satellite in the J2000 coordinate system. s ) eci :

[0054]

[0055] Among them, S wj This is the coordinate transformation matrix from the J2000 coordinate system to the WGS84 coordinate system.

[0056] (1c) Calculate the inertial velocity components (V) of the satellite in the WGS84 coordinate system. s ) ecf :

[0057]

[0058] in, S is the coordinate transformation matrix wj The derivative matrix.

[0059] (2) Based on the (V) obtained in step (1) s ) ecf and (R) s ) ecfCalculate the satellite's trajectory velocity components (V) in the orbital coordinate system. sp ) o The calculation steps are as follows:

[0060] (2a) Calculate the components of each axis of the orbital coordinate system in the WGS84 coordinate system:

[0061]

[0062]

[0063]

[0064] in, Represents vector (R) s ) ecf The cross product matrix, Represents vector The cross product matrix.

[0065] The orbital coordinate system has its origin O as the satellite's center of mass, OZ. o The axis points from the origin to the Earth's center, OY o The axis is aligned with the negative normal direction of the orbital plane, OX o Axis and OY o Axis, OZ o The right-hand axis is orthogonal and points in the direction of the satellite's velocity.

[0066] (2b) Determine the coordinate transformation matrix S from the orbital coordinate system to the WGS84 coordinate system. ow :

[0067]

[0068] (2c) Calculate the satellite's trajectory velocity components (V) in the orbital coordinate system. sp ) o :

[0069]

[0070] (3) Calculate the yaw guidance angle ψ of the satellite under ideal conditions. s Pitch guidance angle θ s Roll angle φ s The calculation steps are as follows:

[0071] (3a) Based on the (V) obtained in step (2) sp ) o Calculate the yaw guidance angle ψ and pitch guidance angle θ from the orbital coordinate system to the spaceborne SAR beam installation system (using a 3-2-1 conversion sequence):

[0072] ψ=arctan2(V spoy Vspox )

[0073]

[0074] (3b) Based on the downward viewing angle σ of the imaging target, the ideal satellite-borne SAR beam range angle α, and the beam azimuth angle β (specifically as follows) Figure 3 As shown, the range-direction installation angle α of the spaceborne SAR beam describes the spaceborne SAR beam relative to the satellite's own system OZ. b The offset angle of the axis, the beam azimuth installation angle β, describes the spaceborne SAR beam relative to the satellite's own system Y. b OZ b (Axis offset angle), calculate the transformation matrix S from the spaceborne SAR beam mounting coordinate system to the satellite body coordinate system. bs Finally, the transformation matrix S from the orbital coordinate system to the satellite body coordinate system is obtained. bo :

[0075] S bs =C x (-α)·C y (-β)

[0076] S so =C x (σ)·C y (θ)C z (ψ)

[0077] S bo =S bs S so

[0078] Among them, S so σ is the transformation matrix from the orbital coordinate system to the spaceborne SAR beam-mounted coordinate system; σ is the downward viewing angle of the imaging target, such as... Figure 4 As shown, the downward angle σ of the imaging target describes the nominal side angle when the satellite passes overhead to image the target, and its positive direction is consistent with the positive direction of the roll angle; C x (-α) represents the elementary transformation matrix that rotates through an angle of -α around the X-axis of the spaceborne SAR beam mounting coordinate system. C y (-β) The elementary transformation matrix that rotates the Y-axis of the spaceborne SAR beam-mounted coordinate system by an angle of -β. C x (σ) represents the primitive transformation matrix of the orbital coordinate system rotating about the X-axis by an angle of σ. C y (θ) is the primitive transformation matrix that rotates about the Y-axis of the orbital coordinate system by an angle of θ. C z (ψ) is the primitive transformation matrix that rotates about the Z-axis of the orbital coordinate system by an angle of ψ. Specifically as follows:

[0079] A 11 =cos(β)*cos(θ)*cos(ψ)+sin(β)*(cos(σ)*sin(θ)*cos(ψ)+sin(σ)*sin(ψ))

[0080] A 12 =cos(β)*cos(θ)*sin(ψ)+sin(β)*(cos(σ)*sin(θ)*sin(ψ)-sin(σ)*cos(ψ))

[0081] A 13 =-cos(β)*sin(θ)+sin(β)*cos(σ)*cos(θ)

[0082] A 21 =sin(α)*sin(β)*cos(θ)*cos(ψ)+cos(α)*(sin(σ)*sin(θ)*cos(ψ)-cos(σ)*sin(ψ))-sin(α)*cos(β)*(cos(σ)*sin(θ)*cos(ψ)+sin(σ)*sin(ψ))

[0083] A 22 =sin(α)*sin(β)*cos(θ)*sin(ψ)+cos(α)*(sin(σ)*sin(θ)*sin(ψ)+cos(σ)*cos(ψ))-sin(α)*cos(β)*(cos(σ)*sin(θ)*sin(ψ)-sin(σ)*cos(ψ))

[0084] A 23 =-sin(α)*sin(β)*sin(θ)+cos(α)*sin(σ)*cos(θ)-sin(α)*cos(β)*cos(σ)*cos(θ)

[0085] A 31 =-cos(α)*sin(β)*cos(θ)*cos(ψ)+sin(α)*(sin(σ)*sin(θ)*cos(ψ)-cos(σ)*sin(ψ))+cos(α)*cos(β)*(cos(σ)*sin(θ)*cos(ψ)+sin(σ)*sin(ψ))

[0086] A 32=-cos(α)*sin(β)*cos(θ)*sin(ψ)+sin(α)*(sin(σ)*sin(θ)*sin(ψ)+cos(σ)*cos(ψ))+cos(α)*cos(β)*(cos(σ)*sin(θ)*sin(ψ)-sin(σ)*cos(ψ))

[0087] A 33 =cos(α)*sin(β)*sin(θ)+sin(α)*sin(σ)*cos(θ)+cos(α)*cos(β)*cos(σ)*cos(θ)

[0088] In the formula, ψ is the yaw guidance angle calculated in step (3a), and θ is the pitch guidance angle calculated in step (3a).

[0089] Satellite body coordinate system: This is the fixed coordinate system of the celestial body. The origin O is a characteristic point within the celestial body (usually the center of mass). The three coordinate axes point in the direction of the characteristic axis of the celestial body. When the attitude deviation between the satellite body coordinate system and the orbital coordinate system is zero, the three coordinate axes of the satellite body coordinate system coincide with the coordinate axes of the orbital coordinate system. OX b The axis is a rolling axis (pointing in the direction of satellite flight), OY b The axis is the pitch axis, OZ b The axis is the yaw axis (pointing towards the Earth's center).

[0090] Spaceborne SAR beam mounting coordinate system: The origin O is the center point of the spaceborne SAR payload, OZ s The axis is aligned with the feed beam direction of the SAR payload, OY s Shaft, OX s The axis is located perpendicular to OZ s In the plane of the axis, OY s The axis points to the satellite's body coordinate system OY. b axial direction, OX s The axis points to the satellite's body coordinate system OX. b Axial direction, OZ s Axis and OX s Axis, OY s The axes form a right-handed orthogonal coordinate system. When the azimuth and range installation angles of the astronautical antenna are zero, this coordinate system coincides with the satellite's body coordinate system.

[0091] (3c) Based on the transformation matrix S from the orbital coordinate system to the satellite local coordinate system in step (3b) bo Calculate the yaw guidance angle ψ from the orbital coordinate system to the satellite's own system. s Pitch guidance angle θ s Roll angle φ s (following the 3-2-1 sequence) are as follows:

[0092]

[0093] θ s = -arcsin(A 13 )=-arcsin(-cos(β)sin(θ)+sin(β)cos(σ)cos(θ))

[0094]

[0095] (4) After the satellite is calibrated in orbit, the installation deviation Δα (consistent with the positive direction of α) of the range direction of the onboard SAR beam and the installation deviation Δβ (consistent with the positive direction of β) of the beam are obtained, and the corrected roll angle φ is calculated based on these deviations. c yaw guidance angle ψ c and pitch guidance angle θ c (Following the 3-2-1 sequence):

[0096]

[0097] θ c = -arcsin(A 13 )=-arcsin(-cos(β+Δβ)sin(θ)+sin(β+Δβ)cos(σ)cos(θ))

[0098]

[0099] The entire control process described above is as follows: Figure 2 As shown.

[0100] 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.

[0101] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A GNSS-based all-zero Doppler guidance method taking into account SAR installation biases, characterized in that The method comprises the following steps: (1) obtaining position components of the satellite in the WGS84 coordinate system from the GNSS system and a track velocity component , and further obtaining an inertial velocity component of the satellite in the WGS84 coordinate system ; (2) calculating the velocity component of the satellite in the orbit coordinate system based on the result of step (1) and ;​ (3) Based on the yaw angle of the orbit coordinate system to the satellite body coordinate system obtained in step (2) , the yaw angle of the orbit coordinate system to the satellite body coordinate system in the ideal case is calculated , the pitch angle , and the yaw angle of the orbit coordinate system to the satellite body coordinate system in the ideal case is obtained through coordinate system conversion , the pitch angle , the roll angle ; (4) According to the satellite-borne SAR installation deviation obtained by on-orbit calibration, the rolling angle, the yaw guide angle and the pitch guide angle calculated in step (3) are corrected; (5) The satellite attitude is guided according to the corrected rolling angle, yaw guide angle and pitch guide angle.

2. The GNSS-based all-zero Doppler guidance method considering SAR installation bias according to claim 1, characterized in that: In the step (1), and further obtain the inertial velocity component of the satellite in the WGS84 coordinate system Specifically, Compute the position components of the satellite in the J2000 coordinate system wherein is the coordinate transformation matrix from the J2000 coordinate system to the WGS84 coordinate system, and the upper index T is the transpose of the matrix. calculating the inertial velocity components of the satellite in the WGS84 coordinate system wherein is a derivative matrix of the coordinate transformation matrix .

3. The GNSS-based all-zero Doppler guidance method considering SAR installation bias according to claim 2, characterized in that: In the step (2), the orbit velocity component of the satellite in the orbit coordinate system is calculated based on the orbit position of the satellite in the orbit coordinate system obtained in the step (1) and , and the orbit position of the satellite in the orbit coordinate system obtained in the step (1) , and the orbit position of the satellite in the orbit coordinate system obtained in the step (1) The components of the coordinate axes of the orbit coordinate system in the WGS84 coordinate system are calculated: wherein denotes the cross product matrix of the vector denotes the cross product matrix of the vector denotes the cross product matrix of the vector​ The origin O of the orbit coordinate system is the satellite center of mass, The axis points from the origin to the center of the earth, The axis is consistent with the negative normal direction of the orbit plane, The axis is consistent with The axis, The axis is right-handed and points to the satellite velocity direction; Determining a coordinate conversion matrix of an orbital coordinate system to a WGS84 coordinate system : Computing a satellite's track velocity component in an orbital coordinate system : 。 4. The GNSS-based all-zero Doppler guidance method considering SAR installation bias according to claim 3, characterized in that: The step (2) obtained , the yaw guide angle of the satellite of the ideal case orbital coordinate system to the satellite-borne SAR beam installation coordinate system , the pitch guide angle , specifically: adopting 3-2-1 rotation sequence, , .

5. The GNSS based all zero Doppler guidance method considering SAR installation bias according to claim 1, characterized in that: The yaw guide angle from the ideal orbit coordinate system to the satellite body coordinate system obtained through coordinate system conversion , the pitch guide angle , the roll angle , and specifically: According to the lower view angle of the imaging target , the ideal satellite-borne SAR beam distance direction installation angle , and the beam azimuth direction installation angle , the conversion matrix of the satellite-borne SAR beam installation coordinate system to the satellite body coordinate system is calculated , and finally the conversion matrix of the orbital coordinate system to the satellite body coordinate system is obtained : wherein is a transformation matrix from the orbital coordinate system to the spaceborne SAR beam mount coordinate system, represents a primitive transformation matrix that rotates about the X-axis of the spaceborne SAR beam mount coordinate system by an angle of φx, ; Elementary transformation matrix representing a rotation of the on-board SAR beam coordinate system around the Y axis through an angle ; ; Elementary transformation matrix representing a rotation of the orbital coordinate system around the X axis through an angle ; ; Elementary transformation matrix representing a rotation of the orbital coordinate system around the Y axis through an angle ; ; Elementary transformation matrix representing a rotation of the orbital coordinate system around the Z axis through an angle ; , ; According to the conversion matrix from the orbital coordinate system to the satellite body coordinate system , the yaw steering angle from the orbital coordinate system to the satellite body coordinate system , the pitch steering angle from the orbital coordinate system to the satellite body coordinate system , and the roll angle from the orbital coordinate system to the satellite body coordinate system are respectively calculated as 。 6. The GNSS-based all-zero Doppler guidance method considering SAR installation bias according to claim 5, characterized in that: In the step (4), the roll angle, the yaw angle and the pitch angle calculated in the step (3) are corrected according to the installation deviation of the space-borne SAR obtained by the in-orbit calibration, specifically, after the satellite is calibrated in orbit, the installation deviation of the space-borne SAR in the range direction and the installation deviation of the space-borne SAR in the azimuth direction are obtained , and the following can be obtained according to the rotation sequence of 3-2-1: is the corrected roll angle; is the corrected yaw steering angle; is the corrected pitch steering angle.

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