Navigation method based on shadow edge of small celestial body detector

Abstract

The invention relates to a navigation method based on a shadow edge of a small celestial body detector, which belongs to the field of autonomous navigation of deep space exploration, and comprises the following steps: firstly, establishing a navigation camera coordinate system and an attitude reference coordinate system, extracting the shadow edge of a solar panel of the detector, performing convex hull extraction on the contour of the shadow edge, and fitting the convex hull boundary by using a polygon; then, the attitude angle and height of the detector are calculated according to the geometrical relationship between the detector and the shadow, and the inter-frame attitude and zoom coefficient of adjacent moments are calculated; and finally, performing rotation scaling correction on the image at the previous moment, performing bicubic interpolation on the correction result, and calculating the horizontal component of the detector by using template matching. Autonomous navigation is carried out by utilizing the geometrical relationship between the shadow shape of the solar panel and the attitude and height of the detector, the observed quantity can be increased, and the navigation precision is improved.

Description

Technical Field

[0001] The present invention belongs to the field of autonomous navigation for deep space exploration, and is applicable to a navigation method for a descent stage of a small celestial body probe in deep space, and specifically relates to a navigation method based on the shadow edge of a small celestial body probe. Background Art

[0002] At present, most of the visual autonomous navigation for small celestial body detection uses terrain relative navigation, which is a method of autonomous navigation by identifying landmark information on the surface of a celestial body and matching it with known landmarks. The landmarks for terrain relative navigation include natural features such as rocks and craters, image features such as scale-invariant features, and artificial landmarks.

[0003] Natural features such as rocks and craters are unevenly distributed on the surface of the target celestial body, and some areas lack obvious identifiable features, which affects navigation accuracy. Autonomous navigation methods based on image features are also affected by lighting conditions. In the case of insufficient lighting or complex lighting conditions, the image quality decreases, and feature extraction and matching are difficult. Autonomous navigation methods based on artificial landmarks are sensitive to changes in ambient lighting. The visibility of artificial landmarks will be affected by the lighting conditions on the surface of the target celestial body, such as shadows, lighting angles, etc. When artificial landmarks are covered by shadows, sensors cannot accurately detect or identify the landmarks, affecting navigation accuracy.

[0004] When sent to the surface of a small dusty celestial body, the probe needs a navigation method that does not rely on natural features for navigation. Using the shadow of the probe's solar sail is a potential option. Since the shape and size of the probe's solar sail itself are known, the size, position, and shape of the shadow are directly related to its own position and attitude. Autonomous navigation using the geometric relationship between the solar sail shadow shape and the probe's attitude and altitude can increase the amount of observation and improve navigation accuracy. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a navigation method based on the shadow edge of a small celestial body detector, and the technical solution is as follows:

[0006] The navigation method based on the shadow edge of a small celestial body probe includes:

[0007] Step 1: Establish relevant coordinate system;

[0008] Establish navigation camera coordinate system Σ C :O C -X C Y C Z C Describe the position and direction of movement of the small celestial body in the camera coordinate system, and define the optical center of the camera as the origin O C , with the right horizontal direction and the vertical upward direction of the image plane as XC Axis and Y C Axis direction, with the optical axis direction as Z C Axis direction, defining the navigation camera coordinate system Σ C and the detector body coordinate system Σ B Overlap; establish attitude reference coordinate system Σ L :O L -X L Y L Z L Describes the probe attitude, with the origin on the surface of the small celestial body, Z L The axis is parallel to the surface normal direction, X L The axis is parallel to the direction in which the sun casts shadows, O L X L , O L Y L and O L Z L The three axes satisfy the right-hand rule.

[0009] Step 2: detector shadow edge extraction and fitting;

[0010] Step 3: Calculate the attitude angle and height of the detector using the geometric relationship between the detector itself and the shadow;

[0011] Step 4: Calculate the inter-frame pose and scaling coefficient at adjacent moments;

[0012] Step 5: Perform rotation and scaling correction on the image at the previous moment, perform bicubic interpolation on the correction result, and use template matching to calculate the horizontal component of the detector.

[0013] Furthermore, in step 2, the detector shadow edge extraction and fitting are specifically performed in the following manner:

[0014] (1) Threshold segmentation: Assume that the small celestial body image I(x, y) has L grayscale levels, namely [1, 2, …, L], m i represents the number of pixels at level i (i∈[1,L]), and M represents the total number of pixels, then:

[0015]

[0016] If p i represents the pixel distribution probability of gray level i, then:

[0017]

[0018] According to the grayscale characteristics of the image, the image pixels are divided into two categories by the threshold t (t∈[1,L]): the foreground image contains pixels with grayscale levels from 0 to t; the background image contains pixels with grayscale levels from t+1 to L. Let T represent the optimal threshold, then:

[0019]

[0020] If σ 2 (t) is the largest, indicating that the difference between the foreground image and the background image is the largest. At this time, t is the optimal threshold T. When there are multiple t such that σ 2 When the value of (t) is the largest, the average value of t is taken as the optimal threshold T, and the image is segmented using the optimal threshold T;

[0021] (2) Edge extraction: Calculate the gradient value of each pixel in the image:

[0022]

[0023] Among them G x (x,y) and G y (x, y) represents the gradient size of the pixel in the horizontal and vertical directions respectively, G(x, y) and A(x, y) represent the gradient size and direction of the pixel respectively; the pixel point with the largest gradient value in the four neighborhoods is taken as the principal point, and then the principal points with similar gradient directions are connected into line segments, and the invalid connecting line segments are eliminated using the Helmholtz principle to generate an edge image;

[0024] (3) Edge fitting: The shadow of the solar sail panel of the small celestial probe is approximated as a polygon. The convex hull of the shadow edge contour is extracted, and the convex hull boundary is fitted using a polygon.

[0025] Furthermore, in step 3, the attitude angle and height of the detector are calculated in the following manner:

[0026] Assume that the direction of sunlight is consistent with the reference coordinate system Σ L The angle between the z-axis and t is known, represented by γ, t = (x c ,y c ,z c ) T Indicated in Σ L The position of the navigation camera, let [x L ,y L ,z L ] T Indicates that the solar sail panel vertex is at Σ L The coordinates in [x B ,y B ,z B ] T Indicates that the solar sail panel vertex is at Σ C The coordinates in , then:

[0027] [x L ,y L ,z L ]T =R[x B ,y B ,z B ] T +t

[0028] =[x r ,y r ,z r ] T +t

[0029] =[x r +x c ,y r +y c ,z r +z c ] T

[0030] Where R represents the C Convert to Σ L The rotation matrix of

[0031] If S represents the shadow of the solar panel vertex in Σ L In the position, then:

[0032] S=[x L -z L tanγ,y L ,0] T

[0033] =[x r +x c -z L tanγ,y r +y c ,0] T

[0034] The position of the shadow at the vertex of the solar sail relative to the navigation camera can be expressed as:

[0035] St=[x r -z L tanγ,y r ,-z c ] T

[0036] The shadow of the solar panel vertex can be expressed in the pixel homogeneous coordinate system as:

[0037]

[0038] Where (x p ,y p ) represents the coordinates of the shadow of the solar panel vertex in the pixel coordinate system after perspective projection;

[0039] Applied to the case where there are i shadows on the solar sail panel vertices, where i = 1, ... N, N represents the total number of solar sail panel vertices, then:

[0040]

[0041] in and Represents the coordinates of the solar sail panel vertex shadow in the pixel coordinate system;

[0042] Let g(a x ,a y ,a z ,z c ) indicates that it contains unknown parameters a x ,a y ,a z and z c The column vector of the expression, so the projection error function e(a x ,a y ,a z ,z c ) can be expressed as:

[0043]

[0044] in and Indicates the coordinates of the actually extracted solar panel vertex shadow in the pixel coordinate system;

[0045] Define the cost function f as:

[0046]

[0047] where e j represents the j-th row element in e, and finally uses the least squares method to find the parameter a that minimizes the function f x , a y , a z and z c , thereby estimating the attitude and height of the detector.

[0048] Furthermore, in step 4, the inter-frame posture and scaling coefficient at adjacent moments are calculated, specifically in the following manner:

[0049] Use the method in step 3 to obtain the height and attitude angle of the previous moment and the current moment, and calculate the attitude change between frames at adjacent moments: Where R1 represents the rotation matrix of the previous moment, and R2 represents the rotation matrix of the current moment. The rotation matrix representing the relative change from the previous moment to the current moment, the height change of the detector in adjacent frames △z c And the scaling factor λ is:

[0050]

[0051] Furthermore, in step 5, bicubic interpolation is performed on the correction result, specifically in the following manner:

[0052] The image at the previous moment is rotated and scaled using the inter-frame posture and scaling coefficient obtained in step 4. After the image is rotated and scaled, the position and order of the pixels in the original image will be changed, and there will be gaps or overlaps between the pixels, causing image deformation and distortion. The image needs to be interpolated. Assume that h1 represents the interpolation result image, (u+△i,v+△j) represents the pixel coordinates of the interpolation point, u and v are positive integers, △i and △j are decimals greater than 0 and less than 1, and the BiCubic function is used to calculate the weights of the 16 pixels. The grayscale value of the interpolation point is equal to the weighted superposition of the 16 pixels. The grayscale value of the interpolation point is:

[0053] h1(u,v)=h1(u+△i,v+△j)=M v M h M u

[0054] M v =[s(1+△j)s(△j)s(1-△j)s(2-△j)]

[0055]

[0056] M u =[s(1+△i)s(△i)s(1-△i)s(2-△i)] T

[0057] Where s(·) represents the weight, M u represents the horizontal coordinate weight matrix, M v represents the longitudinal coordinate weight matrix, M h Represents the grayscale value matrix of 16 pixels adjacent to the interpolation point.

[0058] Furthermore, in step 5, the horizontal component of the detector is calculated by using template matching, specifically in the following manner:

[0059] Assume that h1(u,v) represents the template image, h2(u,v) represents the image to be matched, and the pixel value of the navigation image taken by the small celestial body detector at the current position at (u,v) is:

[0060] h2(u,v)=h1(u-△u,v-△v)

[0061] Where (△u,△v) represents the horizontal component of the small body detector translation in the pixel coordinate system;

[0062] Perform Fourier transform on h2(u,v), then:

[0063] F2(ξ,η)=e -2πj(ξ△u+η△v) F1(ξ,η)

[0064] Where F1(ξ,η) represents the spectrum of h1(u,v), and F2(ξ,η) represents the spectrum of h2(u,v), so the cross-power spectrum of the two is:

[0065]

[0066] in is the complex conjugate of F2(ξ,η);

[0067] The cross power spectrum function CPS(ξ,η) is inversely transformed by Fourier to obtain the impulse function δ(u-△u,v-△v), which reaches its maximum value at (△u,△v). Therefore, the small celestial body detector is in Σ L The horizontal component of the translation (△x c ,△y c )for:

[0068]

[0069] where p x and p y Indicates the resolution of the image, l x and l y Indicates the physical size of the image.

[0070] The beneficial effects of the present invention specifically include:

[0071] (1) Obtain the edge feature information of the detector's solar panel shadow, calculate the relative attitude and height based on the geometric relationship between the solar panel and the shadow, and calculate the horizontal component of the detector's position using template matching to achieve the detector's posture estimation;

[0072] (2) In the process of image-based navigation, the shadow of the probe has always been considered an adverse factor. However, the shadow of the solar panel has a clear geometric relationship with its position and posture. Using the geometric relationship between the shadow of the solar panel and the position and posture of the probe during the landing process for navigation can increase the amount of observation and improve navigation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a basic flow chart of the invention;

[0074] Figure 2 is the original image at a certain height;

[0075] Figure 3 This is the result of fitting the shadow edge contour of the solar sail panel;

[0076] Figure 4 It is a schematic diagram of the angle between the reference coordinate system and the direction of sunlight;

[0077] Figure 5 It is a simulation platform diagram;

[0078] Figure 6 is the trajectory diagram of the detector;

[0079] Figure 7 is the cross-power spectrum;

[0080] Figure 8 is the matching result graph;

[0081] Fig. 9 It is the relationship diagram between the detector height and the detector posture error. DETAILED DESCRIPTION

[0082] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is clearly and completely described below in conjunction with the accompanying drawings of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in the field without making creative work should fall within the scope of protection of the present invention.

[0083] Navigation methods based on the edge of the shadow of a small celestial body probe, such as Figure 1 As shown, the specific steps are:

[0084] Step 1: Establish relevant coordinate system;

[0085] Step 2: detector shadow edge extraction and fitting;

[0086] Step 3: Calculate the attitude angle and height of the detector using the geometric relationship between the detector itself and the shadow;

[0087] Step 4: Calculate the inter-frame pose and scaling coefficient at adjacent moments;

[0088] Step 5: Perform rotation and scaling correction on the image at the previous moment, perform bicubic interpolation on the correction result, and use template matching to calculate the horizontal component of the detector.

[0089] Specific:

[0090] Step 1: Establish relevant coordinate system

[0091] Establish navigation camera coordinate system Σ C :O C -X C Y C Z C Describe the position and direction of movement of the small celestial body in the camera coordinate system, and define the optical center of the camera as the origin O C, with the right horizontal direction and the vertical upward direction of the image plane as X C Axis and Y C Axis direction, with the optical axis direction as Z C Axis direction, defining the navigation camera coordinate system Σ C and the detector body coordinate system Σ B Overlap; establish attitude reference coordinate system Σ L :O L -X L Y L Z L Describes the probe attitude, with the origin on the surface of the small celestial body, Z L The axis is parallel to the surface normal direction, X L The axis is parallel to the direction in which the sun casts shadows, O L X L , O L Y L and O L Z L The three axes satisfy the right-hand rule.

[0092] Step 2: Detector shadow edge extraction and fitting

[0093] Assume that the small celestial body image I(x,y) has L gray levels, namely [1,2,…,L], m i represents the number of pixels at level i (i∈[1,L]), and M represents the total number of pixels, then:

[0094]

[0095] If p i represents the pixel distribution probability of gray level i, then:

[0096]

[0097] According to the grayscale characteristics of the image, the image pixels are divided into two categories by the threshold t (t∈[1,L]): the foreground image contains pixels with grayscale levels from 0 to t, and the background image contains pixels with grayscale levels from t+1 to L. Let T represent the optimal threshold, then:

[0098]

[0099] If σ 2 (t) is the largest, indicating that the difference between the foreground image and the background image is the largest. At this time, t is the optimal threshold T. When there are multiple t such that σ 2 When the value of (t) is the largest, the average value of t is taken as the optimal threshold T, and the image is threshold segmented using the optimal threshold T.

[0100] Calculate the gradient value for each pixel in the image:

[0101]

[0102] Among them G x (x,y) and G y (x, y) represents the gradient size of the pixel in the horizontal and vertical directions respectively, G(x, y) and A(x, y) represent the gradient size and direction of the pixel respectively; the pixel point with the largest gradient value in the four neighborhoods is taken as the principal point, and then the principal points with similar gradient directions are connected into line segments, and the Helmholtz principle is used to eliminate invalid connecting line segments to generate an edge image.

[0103] The shadow of the solar sail panel of a small celestial body probe is approximately a polygon. The convex hull of the shadow edge contour is extracted, and the convex hull boundary is fitted using a polygon. For example, a probe with a regular decagonal solar sail panel is used. Figure 2 is the original image taken by the camera at a certain height, Figure 3 This is the fitting result of the shadow edge profile of the probe's solar sail.

[0104] Step 3: Calculate the detector's attitude angle and height using the geometric relationship between the detector and the shadow

[0105] Assume that the direction of sunlight is consistent with the reference coordinate system Σ L The angle between the z-axis direction is known and is represented by γ, such as Figure 4 As shown, t=(x c ,y c ,z c ) T Indicated in Σ L The position of the navigation camera, let [x L ,y L ,z L ] T Indicates that the solar sail panel vertex is at Σ L The coordinates in [x B ,y B ,z B ] T Indicates that the solar sail panel vertex is at Σ C The coordinates in , then:

[0106] [x L ,y L ,z L ] T =R[x B ,y B ,z B ] T +t

[0107] =[x r ,y r ,z r ]T +t

[0108] =[x r +x c ,y r +y c ,z r +z c ] T

[0109] Where R represents the C Convert to Σ L The rotation matrix of .

[0110] If S represents the shadow of the solar panel vertex in Σ L In the position, then:

[0111] S=[x L -z L tanγ,y L ,0] T

[0112] =[x r +x c -z L tanγ,y r +y c ,0] T

[0113] The position of the shadow at the vertex of the solar sail relative to the navigation camera can be expressed as:

[0114] St=[x r -z L tanγ,y r ,-z c ] T

[0115] The shadow of the solar panel vertex can be expressed in the pixel homogeneous coordinate system as:

[0116]

[0117] Where (x p ,y p ) represents the coordinates of the shadow of the solar panel vertex in the pixel coordinate system after perspective projection.

[0118] Applied to the case where there are i shadows on the solar sail panel vertices, where i = 1, ... N, N represents the total number of solar sail panel vertices, then:

[0119]

[0120] in and Represents the coordinates of the solar panel vertex shadow in the pixel coordinate system.

[0121] Let g(a x ,a y ,a z ,z c ) indicates that it contains unknown parameters a x ,a y ,a z and z c The column vector of the expression, so the projection error function e(a x ,a y ,a z ,z c ) can be expressed as:

[0122]

[0123] in and Indicates the coordinates of the actually extracted solar panel vertex shadow in the pixel coordinate system.

[0124] Define the cost function f as:

[0125]

[0126] where e j represents the j-th row element in e, and finally uses the least squares method to find the parameter a that minimizes the function f x , a y , a z and z c , thereby estimating the attitude and height of the detector.

[0127] Step 4: Calculate the inter-frame pose and scaling factor at adjacent moments

[0128] Use the method in step 3 to obtain the height and attitude angle of the previous moment and the current moment, and calculate the attitude change between frames at adjacent moments: Where R1 represents the rotation matrix of the previous moment, and R2 represents the rotation matrix of the current moment. The rotation matrix representing the relative change from the previous moment to the current moment, the height change of the detector in adjacent frames △z c And the scaling factor λ is:

[0129]

[0130] Step 5: Perform rotation and scaling correction on the image at the previous moment, perform bicubic interpolation on the correction result, and use template matching to calculate the horizontal component of the detector

[0131] The navigation image taken at the last moment is used as the image to be matched, and the navigation image at the current moment is used as the template image. The image to be matched is rotated and corrected. If (u′, v′) represents the coordinates of the pixel in the navigation image at the current moment, and (u, v) represents the coordinates of the pixel in the image after rotation correction, then:

[0132]

[0133] After rotation correction, scaling correction is performed. After rotation and scaling correction of the image, the position and order of the pixels in the original image will be changed, and there will be gaps or overlaps between the pixels, causing image deformation and distortion. Therefore, bicubic interpolation is used to interpolate the image to deduce the pixel value at any position in the corrected image. Assume that h1 represents the interpolation result image, (u+△i,v+△j) represents the pixel coordinates of the interpolation point, u and v are positive integers, △i and △j are decimals greater than 0 and less than 1, and use the BiCubic function to calculate the weights of the 16 pixels. The gray value of the interpolation point is equal to the weighted superposition of the 16 pixels, so the gray value of the interpolation point is:

[0134] h1(u,v)=h1(u+△i,v+△j)=M v M h M u

[0135] M v =[s(1+△j)s(△j)s(1-△j)s(2-△j)]

[0136]

[0137] M u =[s(1+△i)s(△i)s(1-△i)s(2-△i)] T

[0138] Where s(·) represents the weight, M u represents the horizontal coordinate weight matrix, M v represents the longitudinal coordinate weight matrix, M h The gray value matrix of the 16 pixels adjacent to the interpolation point is calculated using the BiCubic function as the weight function. The calculation formula is:

[0139]

[0140] The value of a is generally -0.5, and |x| represents the horizontal distance or vertical distance between the adjacent pixel point and the interpolation point.

[0141] Assume that h1(u,v) represents the template image, h2(u,v) represents the image to be matched, and the pixel value of the navigation image taken by the small celestial body detector at the current position at (u,v) is:

[0142] h2(u,v)=h1(u-△u,v-△v)

[0143] Where (△u,△v) represents the horizontal component of the small body detector translation in the pixel coordinate system. Perform Fourier transform on h2(u,v), then:

[0144] F2(ξ,η)=e -2πj(ξ△u+η△v) F1(ξ,η)

[0145] Where F1(ξ,η) represents the spectrum of h1(u,v), and F2(ξ,η) represents the spectrum of h2(u,v). Therefore, the cross power spectrum of the two is:

[0146]

[0147] in is the conjugate complex number of F2(ξ,η). The inverse Fourier transform of the cross power spectrum function CPS(ξ,η) is performed to obtain the impulse function δ(u-△u,v-△v), which reaches its maximum value at (△u,△v). L The horizontal component of the translation (△x c ,△y c )for:

[0148]

[0149] where p x and p y Indicates the resolution of the image, l x and l y Indicates the physical size of the image.

[0150] The present invention uses the navigation method of the small celestial body probe based on the shadow edge of the small celestial body probe landing phase as an example analysis, selects two small celestial body probes with regular decagonal solar sail panels as the research object, takes the probe Lucy as an example, loads the probe and the small celestial body surface 3D model into Unity3D, and uses the script to control the small celestial body probe to take images while descending. Figure 5 It is an experimental simulation platform. Figure 6 The curve in represents the motion trajectory of the detector, and the relevant simulation parameters are shown in Table 1.

[0151]

[0152] The navigation image simulated and shot at the current moment is used as the image to be matched, and template matching is performed. In order to display the matching results vividly, some areas are selected for experiments. Figure 7 To calculate the mutual power spectrum of the two images, Figure 8 This is the matching result graph. Fig. 9 (a) and Fig. 9(b) is the relationship diagram between the detector height and the detector posture error. The position error is within 1.4 meters and the angle error is within 0.3°. As the height of the small celestial body detector decreases, the shadow of the solar sail in the navigation image continues to grow, the influence of the same noise will continue to weaken, the accuracy of the shadow edge feature information extraction will become higher and higher, and the position error and attitude error of the detector will continue to decrease.

[0153] The above discussion is only a preferred embodiment of the present invention and does not limit the present invention in other forms. Any technician familiar with the profession may use the above content to change or modify it into an equivalent variation and equivalent embodiment for application in other fields. However, any simple modification, equivalent variation and modification made to the above embodiment based on the technical essence of the present invention without departing from the technical solution content of the present invention still falls within the protection scope of the present invention.

Claims

1. A navigation method based on the shadow edge of a small celestial body detector, characterized in that: The specific steps are: Step 1: Establish relevant coordinate system; Step 2: detector shadow edge extraction and fitting; Step 3: Calculate the attitude angle and height of the detector using the geometric relationship between the detector itself and the shadow; Step 4: Calculate the inter-frame pose and scaling coefficient at adjacent moments; Step 5: Perform rotation and scaling correction on the image at the previous moment, perform bicubic interpolation on the correction result, and use template matching to calculate the horizontal component of the detector.

2. The navigation method based on the shadow edge of a small celestial body probe according to claim 1 is characterized in that: Establish the relevant coordinate system, specifically: Establish navigation camera coordinate system Σ C :O C -X C Y C Z C Describe the position and direction of movement of the small celestial body in the camera coordinate system, and define the optical center of the camera as the origin O C , with the right horizontal direction and the vertical upward direction of the image plane as X C Axis and Y C Axis direction, with the optical axis direction as Z C Axis direction, defining the navigation camera coordinate system Σ C and the detector body coordinate system Σ B Overlap; establish attitude reference coordinate system Σ L :O L -X L Y L Z L Describes the probe attitude, with the origin on the surface of the small celestial body, Z L The axis is parallel to the surface normal direction, X L The axis is parallel to the direction in which the sun casts shadows, O L X L , O L Y L and O L Z L The three axes satisfy the right-hand rule.

3. The navigation method based on the shadow edge of a small celestial body probe according to claim 1 is characterized in that: Detector shadow edge extraction and fitting, specifically: After threshold segmentation of the image, the EDPF algorithm is used to extract the edges of the segmentation results; the shadow of the solar sail panel of the small celestial body probe is approximated as a polygon, the convex hull of the shadow edge contour is extracted, and the convex hull boundary is fitted using a polygon.

4. The navigation method based on the shadow edge of a small celestial body probe according to claim 1 is characterized in that: The geometric relationship between the detector and the shadow is used to calculate the detector's attitude angle and height, specifically: Assume that the direction of sunlight is consistent with the reference coordinate system Σ L The angle between the z-axis and t is known, represented by γ, t = (x c ,y c ,z c ) T Indicated in Σ L The position of the navigation camera, let [x L ,y L ,z L ] T Indicates that the solar sail panel vertex is at Σ L The coordinates in [x B ,y B ,z B ] T Indicates that the solar sail panel vertex is at Σ C The coordinates in , then: [x L ,y L ,z L ] T =R[x B ,y B ,z B ] T +t =[x r ,y r ,z r ] T +t =[x r +x c ,y r +y c ,z r +z c ] T Where R represents the C Convert to Σ L The rotation matrix of If S represents the shadow of the solar panel vertex in Σ L In the position, then: S=[x L -z L tanγ,y L ,0] T =[x r +x c -z L tanγ,y r +y c ,0] T The position of the shadow at the vertex of the solar sail relative to the navigation camera can be expressed as: S-t=[x r -z L tanγ,y r ,-z c ] T The shadow of the solar panel vertex can be expressed in the pixel homogeneous coordinate system as: Where (x p ,y p ) represents the coordinates of the shadow of the solar panel vertex in the pixel coordinate system after perspective projection; Applied to the case where there are i shadows on the solar sail panel vertices, where i = 1, ... N, N represents the total number of solar sail panel vertices, then: in and Represents the coordinates of the solar sail panel vertex shadow in the pixel coordinate system; Let g(a x ,a y ,a z ,z c ) indicates that it contains unknown parameters a x ,a y ,a z and z c The column vector of the expression, so the projection error function e(a x ,a y ,a z ,z c ) can be expressed as: in and Indicates the coordinates of the actually extracted solar panel vertex shadow in the pixel coordinate system; Define the cost function f as: where e j represents the j-th row element in e, and finally uses the least squares method to find the parameter a that minimizes the function f x , a y , a z and z c , thereby estimating the attitude and height of the detector.

5. The navigation method based on the shadow edge of a small celestial body probe according to claim 1 is characterized in that: Calculate the inter-frame pose and scaling factor at adjacent moments, specifically: Use the method in step 3 to obtain the height and attitude angle of the previous moment and the current moment, and calculate the attitude change between frames at adjacent moments: Where R1 represents the rotation matrix of the previous moment, and R2 represents the rotation matrix of the current moment. The rotation matrix representing the relative change from the previous moment to the current moment, the height change of the detector in adjacent frames △z c And the scaling factor λ is:

6. The navigation method based on the shadow edge of a small celestial body probe according to claim 1, characterized in that: The image at the previous moment is rotated and scaled, and the correction result is bicubic interpolated. The horizontal component of the detector is calculated using template matching, specifically: The image at the previous moment is rotated and scaled using the inter-frame posture and scaling coefficient obtained in step 4. After the image is rotated and scaled, the position and order of the pixels in the original image will be changed, and there will be gaps or overlaps between the pixels, causing image deformation and distortion. The image needs to be interpolated. Assume that h1 represents the interpolation result image, (u+△i,v+△j) represents the pixel coordinates of the interpolation point, u and v are positive integers, △i and △j are decimals greater than 0 and less than 1, and the BiCubic function is used to calculate the weights of the 16 pixels. The grayscale value of the interpolation point is equal to the weighted superposition of the 16 pixels. The grayscale value of the interpolation point is: h1(u,v)=h1(u+△i,v+△j)=M v M h M u M v =[s(1+△j)s(△j)s(1-△j)s(2-△j)] M u =[s(1+△i)s(△i)s(1-△i)s(2-△i)] T Where s(·) represents the weight, M u represents the horizontal coordinate weight matrix, M v represents the longitudinal coordinate weight matrix, M h Represents the gray value matrix of 16 pixels adjacent to the interpolation point; Assume that h1(u,v) represents the template image, h2(u,v) represents the image to be matched, and the pixel value of the navigation image taken by the small celestial body detector at the current position at (u,v) is: h2(u,v)=h1(u-△u,v-△v) Where (△u,△v) represents the horizontal component of the translation of the small body detector in the pixel coordinate system; h2(u,v) is Fourier transformed, then: F2(ξ,η)=e -2πj(ξ△u+η△v) F1(ξ,η) Where F1(ξ,η) represents the spectrum of h1(u,v), and F2(ξ,η) represents the spectrum of h2(u,v), so the cross-power spectrum of the two is: in is the conjugate complex number of F2(ξ,η); the cross power spectrum function CPS(ξ,η) is inversely transformed by Fourier to obtain the impulse function δ(u-△u,v-△v), which reaches its maximum value at (△u,△v), so the small celestial body detector is in Σ L The horizontal component of the translation (△x c ,△y c )for: where p x and p y Indicates the resolution of the image, l x and l y Indicates the physical size of the image.

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