On-orbit Calibration Method for Navigation Cameras Based on Single-Star Observations and Singular Value Decomposition

Abstract

This invention discloses an on-orbit calibration method for a navigation camera based on single-star observation and singular value decomposition (SVD). The detector maneuvers its attitude to the target imaging posture, with a single high-brightness target star located within the navigation camera's field of view and near its edge. The navigation camera images the target star, and after image processing, identifies the unit direction vector of the target star in the navigation camera's measurement frame. Simultaneously, a star sensor images the night sky, predicting the unit direction vector of the target star in the detector's own frame. The unit direction vector of the target star in the navigation camera's measurement frame is multiplied by its transpose in the detector's own frame, and then accumulated into a measurement information accumulation matrix. After multiple measurements in the same imaging posture, the detector rotates around the navigation camera's optical axis to the next imaging posture to continue imaging. After all measurements are completed, the measurement information accumulation matrix is ​​processed by a singular value decomposition algorithm to provide an optimal estimate of the navigation camera's installation. The entire process is completed autonomously in orbit.

Description

Technical Field

[0001] This application relates to the technical field of autonomous navigation for spacecraft, and in particular to an on-orbit calibration method for navigation cameras based on single-star observation and singular value decomposition. Background Technology

[0002] Future lunar and Mars orbiters or landers will increasingly be equipped with optical navigation cameras, or simply navigation cameras. These cameras capture images of the target celestial body to achieve autonomous navigation during the orbiting or landing phases. After launch and into orbit, the probe's structure deforms due to mechanical impacts and environmental changes, altering the navigation camera's mounting attitude. To ensure navigation accuracy, especially for planetary landing missions, precise on-orbit calibration of the navigation camera is necessary. Currently, there are two main on-orbit calibration methods for camera-type sensors: one used for optical remote sensing cameras, and the other for star sensors. The on-orbit calibration method for optical remote sensing cameras is well-established and can be adopted by navigation cameras. After capturing planetary images during the approach or orbit phase, the installation is calibrated by matching them with accurate planetary maps. This method is feasible, but its calibration results are affected by orbit determination errors and errors in the 3D map information of the planetary surface. Furthermore, this method is computationally complex, requiring the download of measurement images and attitude data to the ground for subsequent calibration, making the entire process time-consuming and thus not an autonomous calibration method. Traditional star sensor on-orbit mutual calibration methods are autonomous calibration methods with very high accuracy, but they are unsuitable for navigation cameras. This is because these methods require the navigation camera to observe and identify multiple stars in a single image. However, navigation cameras are designed to image planar targets such as planetary surfaces, and their dynamic range of brightness is greater than that of star sensors. Therefore, they cannot successfully image and identify the vast majority of stars simultaneously. Navigation cameras can successfully image and identify a small number of high-brightness stars, such as Sirius. Sirius is the brightest star in the sky besides the Sun, with a magnitude of approximately -1.46. Magnitude is a common parameter for measuring the brightness of celestial objects; the higher the value, the lower the brightness. Each magnitude difference corresponds to approximately a 2.5-fold difference in brightness. Due to the limited number of imageable stars and their dispersed distribution across the celestial sphere, it is impossible to guarantee that multiple imageable stars will appear simultaneously in the navigation camera's field of view.

[0003] The navigation camera installation and calibration process is essentially an attitude determination process, that is, determining the attitude of the navigation camera's measurement system relative to the detector's own system. In the field of autonomous navigation, the two-vector attitude determination algorithm is a basic and common method that can be used for installation and calibration. Theoretically, observing two inertial space vectors in different directions can obtain the camera's attitude relative to inertial space, thereby calculating the navigation camera's installation. However, in order to suppress the influence of measurement noise and improve attitude determination accuracy, the more observation data obtained in practical applications, the better. In this case, the multi-vector attitude determination algorithm can provide more accurate estimation results than the two-vector attitude determination algorithm.

[0004] The method of providing optimal multi-vector attitude estimation by finding pseudo-inverses has two drawbacks that are unsuitable for on-board implementation: 1. It requires storing all measurement information, resulting in excessive data storage; 2. It requires inverting high-order matrices, leading to excessive computation and the need to write reliable inversion functions. The method of providing optimal multi-vector attitude estimation by singular value decomposition accumulates and stores measurement information in real-time into a third-order matrix, resulting in smaller data storage. Furthermore, the estimation and solution process does not involve inverting high-order matrices, leading to relatively lower computational complexity. Therefore, it is suitable for on-board implementation and is recommended as a method for camera on-orbit calibration.

[0005] In summary, how to install a high-precision calibration and navigation camera autonomously in orbit is a technical problem faced in the field of autonomous spacecraft navigation. Summary of the Invention

[0006] This application provides an on-orbit calibration method for navigation cameras based on single-star observation and singular value decomposition, enabling high-precision on-orbit autonomous calibration of navigation camera installation, thereby significantly improving the autonomous navigation accuracy of planetary orbiting or landing probes.

[0007] Firstly, a method for on-orbit calibration of navigation cameras based on single-star observations and singular value decomposition is provided, including:

[0008] When the detector is in the first target imaging attitude, perform one or more of the following steps: control the navigation camera to image the target star, and obtain the unit direction vector V of the target star in the navigation camera's measurement frame. c1,i And predict the unit direction vector V of the target star in the detector body using a star sensor. b1,i , where i in italics represents the current number of measurements under the first target imaging posture, at which point the target star is located at the first designated imaging position in the field of view of the navigation camera;

[0009] When the detector is in the second target imaging attitude, perform one or more of the following steps: control the navigation camera to image the target star, and obtain the unit direction vector V of the target star in the navigation camera's measurement frame. c2,j And predict the unit direction vector V of the target star in the detector body using a star sensor. b2,j, in italics j, indicates the current number of measurements under the second target imaging posture, at which point the target star is located at the second designated imaging position in the field of view of the navigation camera;

[0010] According to the unit direction vector V c1,i Unit direction vector V b1,i Unit direction vector V c2,j Unit direction vector V b2,j The measurement information accumulation matrix is ​​calculated and solved to obtain the installation matrix of the navigation camera.

[0011] In conjunction with the first aspect, in some implementations of the first aspect, the detector rotates around the optical axis of the navigation camera by a preset angle, thereby changing the detector from the imaging posture of the first target to the imaging posture of the second target, wherein the preset angle is 60 to 120°.

[0012] In conjunction with the first aspect, in some implementations of the first aspect, the measurement information accumulation matrix A satisfies: A0 is zero; here, the italicized subscript i represents the number of frames recursively calculated across all target imaging poses, V c V represents the unit direction vector of the target star in the navigation camera's measurement frame at the current number of shots. b This represents the unit direction vector of the target star within the detector body at the current number of frames.

[0013] In conjunction with the first aspect, in some implementations of the first aspect, the unit direction vector V of the target star in the navigation camera measurement frame is obtained. c The value is calculated using the gray-scale centroid method, including:

[0014] Calculate the gray-scale centroid of the target star:

[0015] and The pixel coordinates of the center of the star image spot; n is the total number of pixels in the pixel group; x p,i and y p,i h represents the pixel coordinates of the i-th pixel. i h is the grayscale value of the i-th pixel; m This is the sum of gray levels for the pixel group;

[0016] Convert the pixel coordinates of the center of the stellar image spot into the target star's unit direction vector in the navigation camera's measurement frame:

[0017] k x and k y x is the transformation coefficient from pixel coordinates to unit vector components; po and y po The pixel coordinates of the center of the navigation camera system are measured.

[0018] In conjunction with the first aspect, in some implementations of the first aspect, the target stellar image is obtained by the following method:

[0019] In the navigation camera image, the image is cropped with the predicted target star imaging position as the center and the range is expanded according to a preset threshold; pixels with gray levels lower than the preset threshold in the cropped image are removed; the remaining continuous effective pixels are grouped; the pixel gray levels are accumulated within the group, and the group with the largest accumulated gray level is compared and identified as the target star image spot.

[0020] In conjunction with the first aspect, in some implementations of the first aspect, continuous effective pixel clusters include:

[0021] Create a group label matrix with the same number of rows and columns as the pixel matrix of the cropped image, and initialize the elements in the group label matrix to 0;

[0022] Starting from the first pixel in the pixel matrix, repeat the following steps until all pixels have been traversed:

[0023] If the grayscale of the current pixel is zero, then jump to the next pixel;

[0024] If the gray level of the current pixel is non-zero and it is adjacent to the target group, then the elements in the same row and column of the group labeling matrix are labeled as the group number of the target group.

[0025] If the gray level of the current pixel is non-zero and it is not adjacent to any existing group, then the elements in the same row and column of the group label matrix are labeled as the sum of the number of existing groups and 1.

[0026] In conjunction with the first aspect, in some implementations of the first aspect, the unit direction vector V is predicted. b When considering the difference Δt between the imaging time of the navigation camera and the imaging time of the star sensor, where, C ω To align the star-aware pose determination results to the direction cosine array at the time of the navigation camera's imaging, ω is the angular velocity of the detector body relative to inertial space, measured by the gyroscope, and f R () is a function that calculates the direction cosine matrix corresponding to the axis and angle of rotation of the Euler rotation; C bi The attitude array of the detector system relative to the inertial frame, measured by the star sensor; The unit direction vector in inertial space after taking into account the aberration of light for the target star.

[0027] In conjunction with the first aspect, in certain implementations of the first aspect, the measurement information accumulation matrix is ​​solved to obtain the navigation camera installation matrix, including:

[0028] Calculate the symmetric matrix B = AT A, and transform the symmetric matrix B into the Cardan equation, calculate the coefficients p, q and auxiliary angle θ of the Cardan equation, and use the following formula:

[0029]

[0030]

[0031] Calculate the three real roots of the characteristic equation of the symmetric matrix B:

[0032]

[0033] Calculate the orthogonal matrix of singular value decomposition. Where v1 is v t1 v t2 and v t3 The eigenvector with the largest modulus value is the eigenvector corresponding to the eigenvalue λ1. I is a 3x3 identity matrix; v2 is v t4 v t5 and v t6 The eigenvector with the largest modulus value is the eigenvector corresponding to the eigenvalue λ2. v3 is the eigenvector corresponding to the eigenvalue λ3, v3 = v1 × v2;

[0034] The installation matrix of the navigation cameras is calculated using the following formula:

[0035] Λ=diag([λ1λ2λ3]), where diag() is a diagonal matrix function.

[0036] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes:

[0037] When the detector is in the third target imaging attitude, perform one or more of the following steps: control the navigation camera to image the target star, and obtain the unit direction vector V of the target star in the navigation camera's measurement frame. c3,s And predict the unit direction vector V of the target star in the detector body using a star sensor. b3,s The italicized 's' indicates the current measurement number under the third target imaging posture, at which point the target star is located at the third designated imaging position in the navigation camera's field of view;

[0038] When the detector is in the fourth target imaging attitude, perform one or more of the following steps: control the navigation camera to image the target star, and obtain the unit direction vector V of the target star in the navigation camera's measurement frame. c4,t And predict the unit direction vector V of the target star in the detector body using a star sensor. b4,tThe italicized t indicates the current measurement number under the fourth target imaging posture, at which point the target star is located at the fourth designated imaging position in the field of view of the navigation camera;

[0039] Among them, the measurement information accumulation matrix is ​​passed through the unit direction vector V. c1,i Unit direction vector V b1,i Unit direction vector V c2,j Unit direction vector V b2,j Unit direction vector V c3,s Unit direction vector V b3,s Unit direction vector V c4,t Unit direction vector V b4,t The calculations show that the first, second, third, and fourth designated imaging positions are located at the four corners of the navigation camera's field of view.

[0040] In conjunction with the first aspect, in some implementations of the first aspect, the measurement information accumulation matrix A = A 1,i +A 2,j +A 3,s +A 4,t Measurement information accumulation matrix A 1,i satisfy: Measurement information accumulation matrix A 2,j satisfy: Measurement information accumulation matrix A 3,s satisfy: Measurement information accumulation matrix A 4,t satisfy:

[0041] In a second aspect, an on-orbit vehicle is provided, which is used to autonomously execute the on-orbit calibration method for a navigation camera based on single-star observation and singular value decomposition as described in any of the implementations of the first aspect above.

[0042] Compared with the prior art, the solution provided in this application has at least the following beneficial technical effects:

[0043] (1) The present invention proposes an on-orbit calibration method for navigation cameras based on single-star observation and singular value decomposition. This method requires only the observation of one star during calibration, making the observation object singular. The orientation of a star in inertial space is fixed and precisely known, providing the highest precision attitude reference in the field of spacecraft autonomous navigation. The observation images obtained using this method are easy to acquire, and the accuracy of the calibration algorithm is guaranteed from the attitude reference source.

[0044] (2) The present invention proposes an on-orbit calibration method for navigation cameras based on single-star observation and singular value decomposition. The method of providing the optimal multi-vector attitude estimation through singular value decomposition accumulates and saves the measurement information into a third-order matrix in real time, avoiding the storage of a large amount of original measurement information, occupying a small amount of data storage, and the estimation and solution process does not involve the inversion of high-order matrices, thus occupying relatively few computing resources. It can run quickly under the existing on-board computer hardware conditions, so this method is suitable for on-orbit application.

[0045] (3) The on-orbit calibration method for navigation cameras based on single-star observation and singular value decomposition proposed in this invention is an autonomous on-orbit calibration method. After receiving the calibration task, the probe autonomously executes the calibration process until the final calibration result is given. No ground intervention is required during the calibration process. Traditional on-orbit calibration of surface cameras is not autonomous, requiring the transmission of captured images and attitude determination results to the ground for subsequent calibration work. Compared with non-autonomous calibration, autonomous calibration does not rely on planetary 3D map data and ground resources, significantly improving the speed and efficiency of calibration and reducing the cost of the calibration task.

[0046] (4) The present invention proposes a navigation camera on-orbit calibration method based on single star observation and singular value decomposition. It utilizes a multi-vector attitude determination algorithm based on the least squares principle. Compared with dual-vector attitude determination, the more attitude determination vectors there are, the smaller the impact of observation noise, and the higher the calibration accuracy. This method also makes the spacecraft's attitude jitter at the imaging time somewhat tolerant. Attached Figure Description

[0047] Figure 1 This is a schematic diagram illustrating the principle of an on-orbit calibration method for a navigation camera based on single-star observation and singular value decomposition.

[0048] Figure 2 A flowchart illustrating the implementation of an on-orbit calibration method for navigation cameras based on single-star observations and singular value decomposition.

[0049] Figure 3 This is a schematic diagram illustrating the principle of optical aberration.

[0050] Figure 4 This is a schematic diagram illustrating an example of continuous effective pixel grouping.

[0051] Figure 5 This is a schematic diagram showing the imaging positions of the four recommended target stars within the field of view of the navigation camera. Detailed Implementation

[0052] The present application will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0053] The principle of the on-orbit calibration method for a navigation camera based on single-star observation and singular value decomposition proposed in this invention is as follows: Figure 1 The planetary probe is equipped with a navigation camera, a star sensor, and an autonomous calibration algorithm. After calibration begins, the probe maneuvers its attitude to the target imaging posture. At this point, a single, high-brightness target star is located within the navigation camera's field of view and near its edge. The navigation camera images the target star. Simultaneously, the star sensor images the night sky and acquires the probe's attitude matrix relative to inertial space at the time of imaging. The target star image is transmitted to the autonomous calibration algorithm, which, after image processing, identifies and extracts the target star's unit direction vector in the navigation camera's measurement frame. Based on the probe's attitude relative to the inertial frame determined by the star sensor, the target star's unit direction vector in the inertial frame is transformed to the probe's own frame. The unit direction vector of the target star in the navigation camera's measurement frame is multiplied by its transpose in the probe's own frame, and then accumulated into the measurement information accumulation matrix. After acquiring sufficient effective measurements in the same imaging posture, the probe rotates around the navigation camera's optical axis to the next imaging posture to continue imaging. After all measurements are completed, the measurement information accumulation matrix is ​​processed by a singular value decomposition algorithm to provide an optimal estimate of the navigation camera's installation.

[0054] The implementation process of the navigation camera on-orbit calibration method based on single-star observation and singular value decomposition proposed in this invention is as follows: Figure 2 The specific implementation steps are as follows.

[0055] (1) Determine the target star and initial imaging attitude.

[0056] First, select the first star in the candidate target star list, i.e., the brightest star. Then, search to confirm whether there is a usable imaging posture for this star that is unaffected by stray light from the Sun and nearby large celestial bodies. If so, designate this star as the target star and set its usable imaging posture as the initial imaging posture. If no usable posture is found, perform a usable imaging posture search analysis on the next star in the candidate target star list until a usable imaging posture is found for a star.

[0057] illustrate:

[0058] a) The top 5 brightest stars in the sky, excluding the Sun, are shown in Table 1 and will be used as candidate target stars for calibration. In practical applications, this table can be further expanded to ensure that stars with usable imaging attitudes can be found.

[0059] Table 1. List of candidate target stars

[0060] 1. Sirius -1.45 2. α of the ship's base -0.72 3. South Gate 2 -0.27 4. Arcturus -0.05 5. Vega 0.03

[0061] (b) For lunar probes, nearby large celestial bodies refer to the Moon and Earth. For Mars probes, nearby large celestial bodies refer to Mars, Phobos, and Deimos. If the Sun and nearby large celestial bodies enter the field of view of the navigation camera and star sensor, their high brightness will interfere with the effective operation of the navigation camera and star sensor.

[0062] c) The target star is located within the navigation camera's field of view and close to the edge of the field of view. The angle between the target star and the edge of the field of view should be greater than the detector's attitude control accuracy to ensure that the target star remains within the navigation camera's field of view even with attitude control errors. Positioning the target star close to the edge of the navigation camera's field of view improves the observability of the calibration algorithm.

[0063] (2) Establish the initial imaging pose

[0064] The probe is maneuvered to the target imaging attitude using thrusters or angular momentum exchange devices. Once maneuvered into position, the probe's attitude is maintained stable relative to inertial space. In other words, the probe is maneuvered so that the target star appears at the designated imaging location within the navigation camera's field of view. Figure 5 As shown, this method recommends four imaging positions for target stars within the navigation camera's field of view. These four recommended positions are located at the four corners of the navigation camera's field of view.

[0065] (3) Obtain the unit direction vector of the target star in inertial space after considering axial aberration.

[0066] First, the axis of rotation for attitude rotation is calculated by the cross product of the target star's unit direction vector in inertial space and the probe's velocity vector relative to the Sun in inertial space, as shown in the following formula:

[0067]

[0068] In the formula, V i is the unit direction vector of the target star in inertial space; u is the velocity vector of the probe relative to the Sun in inertial space; |||| is the vector modulus operator; the solid subscript i indicates the inertial frame, the same below.

[0069] Then, calculate the angle between the target star's unit direction vector in inertial space and the probe's velocity vector relative to the Sun in inertial space, using the following formula:

[0070]

[0071] In the formula, arccos is the inverse cosine function; T is the transpose sign.

[0072] Then, calculate the aberration angle, which is the angle between the apparent direction and the true direction of the star, using the following formula:

[0073]

[0074] In the formula, the unit of the skewing angle α is rad; c is the speed of light in vacuum; and sin is the sine function.

[0075] Then, calculate the direction cosine matrix that takes into account the effect of axial aberration.

[0076] C L =f R (e,α) (4)

[0077] In the formula, C L A directional cosine matrix to account for the effects of axial aberration; f R () is a function for calculating the direction cosine matrix corresponding to the axis and angle of rotation of the Euler rotation. The calculation method is well-known in the art and will not be described in detail here. The concept of the direction cosine matrix is ​​also well-known in the art and will not be described in detail here.

[0078] Finally, the unit direction vector of the target star in inertial space, considering axial aberration, is calculated using the following formula:

[0079]

[0080] In the formula, C L A directional cosine matrix to account for the effects of axial aberration; V i The unit direction vector of the target star in inertial space; The unit direction vector in inertial space after taking into account the aberration of light for the target star.

[0081] illustrate:

[0082] a) Aberration refers to the difference between the apparent direction of a star as observed by a moving observer and the true direction of a star as observed by a stationary observer at the same instant. (The principle is explained in the diagram.) Figure 3 This is a professional concept known to those skilled in the art.

[0083] b) During the calibration period of the navigation camera, it can be assumed that the velocity vector of the detector relative to the sun in inertial space remains unchanged. Therefore, it is only necessary to calculate the unit direction vector of the target star in inertial space after considering the aberration of light, i.e. the line of sight, once.

[0084] (4) Navigation camera imaging

[0085] The navigation camera images the target star according to the specified exposure time. The image of the target star is then transmitted to the autonomous calibration algorithm within the detector's computer.

[0086] illustrate:

[0087] a) The imaging exposure times for different stars in the calibrated candidate target star list are pre-calculated on the ground and stored in the list.

[0088] b) The determination of the imaging exposure time is related to the structural design and parameters of the navigation camera, and is not within the scope of this invention.

[0089] (5) Identify and extract the direction of the target star

[0090] In the navigation camera image, the image is cropped with the predicted target star imaging position as the center and the range expanded by a pre-set threshold. Pixels with gray levels lower than the pre-set threshold in the cropped image are removed. The remaining continuous effective pixels are grouped, and the gray levels of the pixels in each group are accumulated. The group with the largest sum of gray levels is found by comparison. The pixel coordinates of the center of the star image are found using the gray centroid method. The pixel coordinates of the center of the star image are converted into the target star unit direction vector in the navigation camera measurement system.

[0091] The method for grouping consecutive effective pixels is as follows: 1. Establish a group label matrix with the same number of rows and columns as the pixel matrix of the cropped image, initially set to 0; 2. Starting from the first pixel in the pixel matrix, if its gray level is non-zero, mark the same row and column element in the group label matrix as 1, indicating that it belongs to group 1; continue to traverse the remaining pixels. If its gray level is non-zero and it is adjacent to an existing group, mark the same row and column element in the group label matrix with that group number. If it is not adjacent to an existing group, mark the same row and column element in the group label matrix as the sum of the existing group number and 1. See the example of consecutive effective pixel grouping. Figure 4 The left grid in the image represents the grayscale value of the pixels. The right grid marks pixels with a grayscale value greater than the threshold that belong to the same continuous valid pixel group with group numbers. There are two groups marked: group 1 and group 2.

[0092] The formula for calculating the centroid of grayscale is as follows:

[0093]

[0094] In the formula, and The pixel coordinates of the center of the star image spot; n is the total number of pixels in the pixel group; x p,i and y p,i h represents the pixel coordinates of the i-th pixel. i h is the grayscale value of the i-th pixel; m This is the accumulation of grayscale values ​​for a group of pixels.

[0095] The formula for converting the pixel coordinates of the center of a stellar image into the target star's unit direction vector in the navigation camera's measurement frame is as follows:

[0096]

[0097] In the formula, k x and k yx represents the transformation coefficient from pixel coordinates to unit vector components, and x represents an intrinsic parameter of the navigation camera. po and y po Here are the pixel coordinates of the center of the navigation camera's measurement system, and here are the inherent parameters of the navigation camera.

[0098] Note: Navigation camera measurement systems conventionally use the lower right-front definition method, meaning the origin is defined at the center of the navigation camera's focal plane, X... c The axis is parallel to the pixel row direction of the focal plane, Y c The axis is parallel to the pixel column direction of the focal plane, Z c The axis direction follows the right-hand rule, pointing outwards along the optical axis of the navigation camera. Figure 5 .

[0099] (6) Predict the direction of the target star at the imaging time based on the attitude determination results of the star sensor gyroscope.

[0100] First, calculate the difference between the imaging time of the navigation camera and the imaging time of the star sensor, using the following formula:

[0101] Δt=t c -t q (8)

[0102] In the formula, Δt is the difference between the imaging time of the navigation camera and the imaging time of the star sensor; t c The moment the navigation camera captures the image; t q This is the moment when the star sensor is imaging.

[0103] Then, combining the angular velocity estimate given by the gyroscope, the direction cosine matrix that aligns the star-aware attitude determination results to the imaging time of the navigation camera is calculated:

[0104]

[0105] In the formula, ω is the angular velocity of the detector body relative to inertial space, measured by the gyroscope; f R () is a function for calculating the direction cosine matrix corresponding to the axis of rotation and the angle of rotation of the Euler rotation. The calculation method is well known in this field and will not be described in detail here.

[0106]

[0107] In the formula, C ω To align the star-aware attitude determination results to the direction cosine array at the time of the navigation camera's imaging; C bi The attitude matrix of the detector's intrinsic system relative to the inertial frame, measured by the star sensor, is also known as the direction cosine matrix; the solid subscript b denotes the detector's intrinsic system, and the same applies below. If the difference between the imaging time of the navigation camera and the imaging time of the star sensor is not considered, then...

[0108] Then, the unit direction vector of the target star within the detector body at the imaging moment is calculated using the following formula:

[0109]

[0110] (7) Update the measurement information accumulation matrix

[0111] The formula for updating the measurement information accumulation matrix is ​​as follows:

[0112]

[0113] In the formula, A is the measurement information accumulation matrix, with an initial value of zero; the italic subscript i here indicates the number of steps calculated recursively.

[0114] After step (7) is completed, it is necessary to determine whether the number of effective imaging attempts for the current attitude is sufficient. If not, proceed to step (4) (navigation camera imaging) to continue imaging. The number of effective imaging attempts for the current attitude can be greater than or equal to 2, for example, 2 to 5. Multiple measurements in the same attitude are beneficial for offsetting errors introduced by noise. If the number of imaging attempts for the current attitude is sufficient but the number of already imaged attitudes is insufficient, proceed to step (8) (attitude rotation maneuver around the optical axis of the navigation camera). If the number of imaging attempts for the current attitude is sufficient and the number of already imaged attitudes is also sufficient, proceed to step (9) (providing the optimal estimate of navigation camera installation using singular value decomposition).

[0115] Note: The number of imaging poses should be no less than two. Theoretically, at least two different poses are required for the navigation camera to be calibrated. Therefore, the number of target poses should be greater than or equal to two. To improve calibration accuracy, this method recommends four imaging positions of target stars within the navigation camera's field of view, see... Figure 5 These four recommended locations are situated at the four corners of the navigation camera's field of view.

[0116] (8) Perform attitude rotation maneuvers around the optical axis of the navigation camera.

[0117] The probe is rotated by a preset angle around the optical axis of the navigation camera using a thruster or angular momentum exchange device, positioning the target star at a designated imaging position within the navigation camera's field of view. This designated imaging position differs from the designated imaging position in the previous orientation. In some embodiments, the preset angle of rotation around the optical axis of the navigation camera is 60–120°, for example, 90°. After maneuvering to the desired position, the probe's attitude is kept stable relative to inertial space. Then, proceed to step 4 (navigation camera imaging).

[0118] (9) Use singular value decomposition to give the optimal estimate of navigation camera installation.

[0119] First, the symmetric matrix B is calculated from the measurement information accumulation matrix, as follows:

[0120] B = AT A (13) Then calculate the coefficients a, b, and c of the characteristic polynomial of the symmetric matrix B, as follows:

[0121]

[0122] In the formula, B ij Let be the element in the i-th row and j-th column of the symmetric matrix B.

[0123] The characteristic equation of the symmetric matrix B is a cubic equation, which can be transformed into the Cardan equation for solution. The coefficients p and q of the Cardan equation are calculated using the following formula.

[0124]

[0125] Next, the auxiliary angle θ for solving Cardan's formula is calculated, as follows:

[0126]

[0127] In the formula, arccos is the inverse cosine function.

[0128] Next, calculate the three real roots, or three eigenvalues, of the characteristic equation of the symmetric matrix B, using the following formula:

[0129]

[0130] remember

[0131]

[0132] In the formula, C is a 3rd order auxiliary square matrix; I is a 3rd order identity matrix; C i (i = 1, 2, 3) represents the i-th row of the auxiliary square matrix C.

[0133] Then calculate vector v t1 v t2 and v t3 The formula is as follows:

[0134]

[0135] In the formula, "×" is the vector cross product operator.

[0136] v t1 v t2 and v t3 The eigenvector v1 corresponding to the eigenvalue λ1 is the one with the largest modulus. The eigenvector v2 corresponding to the eigenvalue λ2 is then calculated using the same method as for v1. The eigenvector v2 corresponding to the eigenvalue λ3 is calculated using the orthogonality property, as shown in the following formula:

[0137] v3 = v1 × v2 (20)

[0138] Then, the orthogonal matrix of the singular value decomposition is calculated using v1, v2, and v3, as shown in the following formula:

[0139]

[0140] Construct the diagonal matrix for singular value decomposition, as shown in the following formula:

[0141] Λ=diag([λ1 λ2 λ3]) (22)

[0142] In the formula, diag() is a diagonal matrix function.

[0143] Finally, the installation matrix of the navigation cameras is calculated using the following formula:

[0144]

[0145] Note: The mounting matrix of the navigation camera is the direction cosine array of the navigation camera's measurement system relative to the detector's main system.

[0146] This concludes the implementation steps of the present invention.

[0147] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0148] The mathematical simulation results of the method described in this invention are shown in Table 2. The simulation used 400 sets of noisy observations for camera installation calibration. Table 2 shows that the calibration results of this method are very close to the true values, thus indicating that the method is effective.

[0149] Table 2. Mathematical simulation results of the method described in this invention.

[0150]

[0151] 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 without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope defined in the claims of the present invention.

Claims

1. A method for on-orbit calibration of a navigation camera based on single-star observation and singular value decomposition, characterized in that, include: When the detector is in the first target imaging attitude, perform one or more of the following steps: control the navigation camera to image the target star, and obtain the unit direction vector of the target star in the navigation camera's measurement frame. And predict the unit direction vector of the target star in the detector body using a star sensor. italics i This indicates the current measurement count under the first target imaging posture, at which point the target star is located at the first designated imaging position in the navigation camera's field of view; When the detector is in the second target imaging attitude, perform one or more of the following steps: control the navigation camera to image the target star, and obtain the unit direction vector of the target star in the navigation camera's measurement frame. And predict the unit direction vector of the target star in the detector body using a star sensor. italics j This indicates the current measurement count under the second target imaging posture, at which point the target star is located at the second designated imaging position in the navigation camera's field of view; According to the unit direction vector Unit direction vector Unit direction vector Unit direction vector The measurement information accumulation matrix is ​​calculated and solved to obtain the installation matrix of the navigation camera; Measurement information accumulation matrix satisfy: , Zero; italicized subscript here This represents the number of frames recursively calculated across all target imaging poses. This represents the unit direction vector of the target star in the navigation camera's measurement frame at the current number of shots. This represents the unit direction vector of the target star within the detector body at the current frame rate; Solving the measurement information accumulation matrix yields the navigation camera installation matrix, including: Calculate a symmetric matrix and the symmetric matrix Convert to Cardan equations and calculate the coefficients of Cardan equations. The calculation formula is as follows: ， ， Calculate a symmetric matrix The characteristic equation has three real roots: ； Calculate the orthogonal matrix of singular value decomposition. ;in, for , and The one with the largest modulus value is an eigenvalue. The corresponding feature vector, , , It is a 3-order identity matrix; for , and The one with the largest modulus value is an eigenvalue. The corresponding feature vector, , ; For eigenvalues The corresponding feature vector, ; The installation matrix of the navigation cameras is calculated using the following formula: , , It is a diagonal matrix function.

2. The method according to claim 1, characterized in that, The detector rotates around the optical axis of the navigation camera by a preset angle, which changes the detector from the first target imaging posture to the second target imaging posture. The preset angle is 60~120°.

3. The method according to claim 1, characterized in that, Obtain the unit direction vector of the target star in the navigation camera's measurement frame. The value is calculated using the gray-scale centroid method, including: Calculate the gray-scale centroid of the target star: , and The pixel coordinates of the center of the star image spot; This represents the total number of pixels within a pixel group. and For the first The pixel coordinates of each pixel; For the first grayscale value of each pixel; This is the sum of gray levels for the pixel group; Convert the pixel coordinates of the center of the stellar image spot into the target star's unit direction vector in the navigation camera's measurement frame: , and The conversion coefficient from pixel coordinates to unit vector components; and The pixel coordinates of the center of the navigation camera system are measured.

4. The method according to claim 1, characterized in that, The target star image was obtained using the following method: In the navigation camera image, the image is cropped with the predicted target star imaging position as the center and the range is expanded according to a preset threshold; pixels with gray levels lower than the preset threshold in the cropped image are removed; the remaining continuous effective pixels are grouped; the pixel gray levels are accumulated within the group, and the group with the largest accumulated gray level is compared and identified as the target star image spot.

5. The method according to claim 4, characterized in that, Continuous effective pixel clusters include: Create a group label matrix with the same number of rows and columns as the pixel matrix of the cropped image, and initialize the elements in the group label matrix to 0; Starting from the first pixel in the pixel matrix, repeat the following steps until all pixels have been traversed: If the grayscale of the current pixel is zero, then jump to the next pixel; If the gray level of the current pixel is non-zero and it is adjacent to the target group, then the elements in the same row and column of the group labeling matrix are labeled as the group number of the target group. If the gray level of the current pixel is non-zero and it is not adjacent to any existing group, then the elements in the same row and column of the group label matrix are labeled as the sum of the number of existing groups and 1.

6. The method according to claim 1, characterized in that, Predicted unit direction vector When considering the difference between the imaging time of the navigation camera and the imaging time of the star sensor ,in, , To align the star-aware pose determination results to the direction cosine array at the time of the navigation camera's imaging, , The angular velocity of the detector body relative to inertial space, as measured by the gyroscope. A function for calculating the direction cosine matrix corresponding to the axis of rotation and the angle of rotation of an Euler rotation; The attitude array of the detector system relative to the inertial frame, measured by the star sensor; The unit direction vector in inertial space after taking into account the aberration of light for the target star.

7. The method according to claim 1, characterized in that, The method further includes: When the detector is in the third target imaging attitude, perform one or more of the following steps: control the navigation camera to image the target star, and obtain the unit direction vector of the target star in the navigation camera's measurement frame. And predict the unit direction vector of the target star in the detector body using a star sensor. italics s This indicates the current measurement count in the third target imaging posture, at which point the target star is located at the third designated imaging position in the navigation camera's field of view; When the detector is in the fourth target imaging attitude, perform one or more of the following steps: control the navigation camera to image the target star, and obtain the unit direction vector of the target star in the navigation camera's measurement frame. And predict the unit direction vector of the target star in the detector body using a star sensor. italics t This indicates the current measurement count in the fourth target imaging posture, at which point the target star is located at the fourth designated imaging position in the navigation camera's field of view; Among them, the measurement information accumulation matrix is ​​passed through the unit direction vector. Unit direction vector Unit direction vector Unit direction vector Unit direction vector Unit direction vector Unit direction vector Unit direction vector The calculations show that the first, second, third, and fourth designated imaging positions are located at the four corners of the navigation camera's field of view.

8. An on-orbit spacecraft, characterized in that, The on-orbit spacecraft is used to autonomously execute the on-orbit calibration method for navigation cameras based on single-star observation and singular value decomposition as described in any one of claims 1 to 7.

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