Method for station-target distance inversion based on track bending feature of single station image

Abstract

The present application belongs to the technical field of photoelectric measurement, and particularly relates to a station-target distance inversion method based on single-station image trajectory bending characteristics. The method comprises the following steps: S1: taking a single photoelectric theodolite as a measuring station, and obtaining a set of relative miss distance corresponding to a first group of target image sequences through an image processing method; S2: calculating a set of slopes corresponding to the first group of target image sequences based on an image trajectory bending feature extraction method; S3: calculating a set of first-order difference of slopes based on the set of slopes and a set of dimensionless distances, and obtaining intercepts corresponding to the first group of target image sequences; S4: obtaining intercepts corresponding to a second group of target image sequences and a third group of target image sequences respectively; and S5: selecting a corresponding branch of a Lambert W function to calculate the distance between the measuring station and a high-speed target based on the change rule of the intercepts corresponding to the three groups of target image sequences. The present application effectively solves the difficult problem of obtaining the station-target distance under single-station measurement, and has high algorithm sensitivity and low single-station measurement cost.

Description

Technical Field

[0001] This invention belongs to the field of photoelectric measurement technology, and in particular relates to a method for inverting station-to-target distance based on the curvature characteristics of a single-station image trajectory. Background Technology

[0002] Traditional optical measurement equipment, such as photoelectric theodolites, can measure the trajectory of high-speed targets, primarily based on bi-station intersection measurement or single-station angle measurement combined with laser ranging. However, both methods are costly in terms of equipment and measurement. Ideally, single-station measurement should be the primary method. With only a single station, in tracking measurement mode, azimuth and elevation angles can be accurately measured, but the lack of station-to-target distance information makes it difficult to directly determine the target's three-dimensional position. In staring measurement mode, the mapping of a straight trajectory onto the image plane is a non-linear process, and the station-to-target distance information is indirectly reflected in the curvature of the image trajectory. Therefore, effectively extracting the distance information implicit in the curved trajectory of the image is crucial for achieving single-station measurement of the three-dimensional trajectory of high-speed targets.

[0003] The trajectory of a high-speed target is approximately a straight line, and its projected trajectory in an image typically presents as a curve with a limited number of sampling points and relatively small curvature. There are two major challenges in single-station trajectory measurement of high-speed targets: first, the lack of a theoretical model for retrieving the station-target distance from a single-station measurement necessitates the establishment of a mathematical model of the image trajectory curvature characteristics and the station-target distance using projection principles; second, the single-station tracking measurement mode cannot directly measure distance information, requiring a switch to a staring measurement mode to obtain the curved trajectory of the image. The selection of mathematical features must simultaneously consider computability and high sensitivity, directly impacting the complexity of solving the station-target distance retrieval model. Summary of the Invention

[0004] In view of this, the present invention aims to provide a station-to-target distance inversion method based on the curvature characteristics of a single-station image trajectory, in order to solve the problems of high measurement cost of traditional optical measurement equipment, lack of station-to-target distance information in single-station tracking measurement, and lack of theoretical models and effective methods for converting the curvature characteristics of image trajectory into distance information in gaze measurement, making it difficult to achieve accurate measurement of high-speed target trajectories. The present invention provides a station-to-target distance inversion method under single-station gaze measurement, which is used to extract the station-to-target distance information implied in the curvature trajectory of the image, and combine the azimuth and elevation angles of the measurement station to achieve three-dimensional position measurement of high-speed targets by a single station.

[0005] To achieve the above objectives, the technical solution created by this invention is implemented as follows:

[0006] A station-to-target distance inversion method based on the trajectory curvature features of a single-station image, specifically including the following features:

[0007] S1: Track high-speed targets using a single photoelectric theodolite as a station, acquire the first set of target image sequences, and obtain the relative miss distance set corresponding to the first set of target image sequences through image processing methods;

[0008] S2: Based on the image trajectory curvature feature extraction method, calculate the slope set corresponding to the first set of target image sequences;

[0009] S3: Calculate the dimensionless distance set corresponding to the slope set according to the slope analytical expression of the target projection plane inversion model, and calculate the first-order difference set of the slope based on the slope set and the dimensionless distance set to obtain the intercept corresponding to the first set of target image sequences.

[0010] S4: Replace the current group of target image sequences with the next group of target image sequences, and repeat steps S1-S3 until the intercepts corresponding to the second and third groups of target image sequences are obtained.

[0011] S5: Based on the Gaussian-type function fitting theory intercept-projection distance function, and based on the intercept variation law corresponding to the three sets of target image sequences, the corresponding branch of the Lambert W function is selected to calculate the distance between the station and the high-speed target.

[0012] Furthermore, in step S1, a single photoelectric theodolite is used as a station, and the direction finding of the photoelectric theodolite is directed towards the high-speed target. When the center point of the high-speed target is located at the geometric center of a single frame target image, the station enters the staring measurement mode and acquires the first set of target image sequences.

[0013] Furthermore, the specific steps for obtaining the relative off-target quantity set corresponding to the first set of target image sequences through image processing methods are as follows:

[0014] S11: For the single-frame target images contained in the first set of target image sequences, establish an image coordinate system with the lower left corner of the single-frame target image as the origin, the horizontal direction of the single-frame target image as the horizontal axis, and the vertical direction of the single-frame target image as the vertical axis, and extract the coordinate values ​​of the center point of the high-speed target in the corresponding image coordinate system frame by frame.

[0015] S12: Using the coordinates of the center point of the high-speed target in the second frame of the current target image sequence as the reference point, calculate the difference between the coordinates of the center point of the high-speed target in the corresponding image coordinate system and the reference point frame by frame to obtain the relative miss distance set corresponding to the current frame target image sequence.

[0016] Furthermore, step S2 specifically includes the following steps:

[0017] S21: Based on the first and second frame target images of the first set of target image sequences, and combined with the initial pitch angle, calculate the slope of the straight-line trajectory of the high-speed target on the target projection plane:

[0018] ;

[0019] Where K is the slope of the straight-line trajectory of the high-speed target on the target projection plane. The initial pitch angle, The initial slope is calculated based on the first and second frame target images of the first set of target image sequences;

[0020] S22: Obtain the slope set based on the relative miss distance set corresponding to the current target image sequence. i starts from 3, where:

[0021] ;

[0022] in, Let y be the relative miss distance of the target image in the i-th frame. Let x be the relative miss distance on the x-axis corresponding to the target image in the i-th frame. Let be the slope corresponding to the target image in the i-th frame.

[0023] Furthermore, step S3 specifically includes the following steps:

[0024] S31: The formula used to calculate the dimensionless distance set corresponding to the slope set based on the slope analytical expression of the target projection plane inversion model is as follows:

[0025] ;

[0026] in, slope The corresponding dimensionless distance;

[0027] S32: Calculate the first-order difference set of slopes based on the slope set and the dimensionless distance set, and fit the first-order difference of slopes using a linear function to obtain the intercept corresponding to the first set of target image sequences:

[0028] ;

[0029] in, Let be the slope corresponding to the target image in the (i+1)th frame. slope The corresponding dimensionless distance, The parameter values ​​of a first-order quantity of a linear function. This is the intercept corresponding to the first set of target image sequences.

[0030] Furthermore, in step S4:

[0031] When the high-speed target moves to the boundary of the single-frame target image, the station switches to tracking measurement mode, adjusts the direction finding of the photoelectric theodolite, so that the center point of the high-speed target is located again at the geometric center of the single-frame target image, and the station re-enters the staring measurement mode to acquire the second set of target image sequences.

[0032] When the high-speed target moves back to the boundary of the single-frame target image, repeat the above operation to obtain the third set of acquired target image sequences.

[0033] Furthermore, in step S5, the theoretical intercept-projected distance function is:

[0034] ;

[0035] in, Theoretical intercept, This is the theoretical projected distance value. , , and All are fitted parameters. It is a natural constant;

[0036] The analytical solution of the theoretical intercept-projected distance function is:

[0037] ;

[0038] in, The analytical solution for the projected distance of the increasing function segment. The analytical solution for the projected distance of the decreasing function segment. This is the 0th branch of the Lambert W function. For Lambert's W function 1 branch;

[0039] If the intercept values ​​of the first, second, and third target image sequences increase sequentially, then the analytical solution of the projected distance of the increasing function segment is taken as the final analytical solution. If the intercept values ​​of the first, second, and third target image sequences decrease sequentially, then the analytical solution of the projected distance of the decreasing function segment is taken as the final analytical solution. ;

[0040] Substituting the final analytical solution into the following formula, the distance between the high-speed target and the station is calculated:

[0041] ;

[0042] in, The distance between the high-speed target and the measuring station, ( , () represents the miss distance of the target image to be calculated. This refers to the pixel size of the detector in an optoelectronic theodolite. The focal length of the photoelectric theodolite This is the initial pitch angle.

[0043] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0044] This invention presents a method for retrieving station-to-target distance based on the curvature characteristics of a single-station image trajectory. By combining the projection law of a spatial straight line to the camera's field of view and rigorously solving the target projection plane inversion model, it can effectively retrieve the target projection plane corresponding to the distance of the curved trajectory of the image and accurately extract the station-to-target distance information measured by a single station. This invention effectively solves the problem of difficulty in obtaining station-to-target distance under single-station measurement. The algorithm has high sensitivity and low cost for single-station measurement, and has certain engineering application value. Attached Figure Description

[0045] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0046] Figure 1 A schematic flowchart illustrating the station-to-target distance inversion method based on the curvature features of a single-station image, as an embodiment of the present invention;

[0047] Figure 2 A schematic diagram illustrating the gaze measurement principle of an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of the projection trajectory of a spatial straight line trajectory in a target image according to an embodiment of the present invention;

[0049] Figure 4 A graph showing the function relationship between the slope of the image trajectory and the dimensionless distance in an embodiment of the present invention;

[0050] Figure 5 A fitting curve between the projection distance and the intercept in an embodiment of the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0052] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0053] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0054] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0055] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0056] like Figure 1 As shown, this invention provides a method for inverting station-to-target distance based on the curvature features of a single-station image trajectory, specifically including the following features:

[0057] S1: Track high-speed targets using a single photoelectric theodolite as a station, acquire the first set of target image sequences, and obtain the relative miss distance set corresponding to the first set of target image sequences through image processing methods;

[0058] S2: Based on the image trajectory curvature feature extraction method, calculate the slope set corresponding to the first set of target image sequences;

[0059] S3: Calculate the dimensionless distance set corresponding to the slope set according to the slope analytical expression of the target projection plane inversion model, and calculate the first-order difference set of the slope based on the slope set and the dimensionless distance set to obtain the intercept corresponding to the first set of target image sequences.

[0060] S4: Replace the current group of target image sequences with the next group of target image sequences, and repeat steps S1-S3 until the intercepts corresponding to the second and third groups of target image sequences are obtained.

[0061] S5: Based on the Gaussian-type function fitting theory intercept-projection distance function, and based on the intercept variation law corresponding to the three sets of target image sequences, the corresponding branch of the Lambert W function is selected to calculate the distance between the station and the high-speed target.

[0062] It should be noted that this invention is based on the projection principle of a straight line in space onto the camera's field of view. It inverts the curvature slope of the image trajectory measured by staring into the target projection plane at the corresponding distance, and uses the first-order difference of the image trajectory slope to solve the station-to-target distance. This effectively extracts the station-to-target distance information implied in the curved trajectory of the image, thus solving the problem of difficulty in obtaining the station-to-target distance under single-station measurement. It provides a valid basis for subsequent three-dimensional trajectory positioning, velocity and attitude measurement, and guiding other stations to capture targets.

[0063] In some embodiments, in step S1, a single photoelectric theodolite is used as a station, and the direction finding of the photoelectric theodolite is directed towards the high-speed target. When the center point of the high-speed target is located at the geometric center of a single frame target image, the station enters the staring measurement mode and acquires the first set of target image sequences.

[0064] In some embodiments, the specific steps for obtaining the relative off-target quantity set corresponding to the first set of target image sequences through image processing methods are as follows:

[0065] S11: For the single-frame target images contained in the first set of target image sequences, establish an image coordinate system with the lower left corner of the single-frame target image as the origin, the horizontal direction of the single-frame target image as the horizontal axis, and the vertical direction of the single-frame target image as the vertical axis, and extract the coordinate values ​​of the center point of the high-speed target in the corresponding image coordinate system frame by frame.

[0066] S12: Using the coordinates of the center point of the high-speed target in the second frame of the current target image sequence as the reference point, calculate the difference between the coordinates of the center point of the high-speed target in the corresponding image coordinate system and the reference point frame by frame to obtain the relative miss distance set corresponding to the current frame target image sequence.

[0067] Using a single photoelectric theodolite as a station, the direction is pointed towards the high-speed target. Once the high-speed target is near the center of the target image, the staring measurement mode is entered to acquire the first set of target image sequences.

[0068] Once the high-speed target moves to the boundary of the target image (specifically, the boundary is defined as follows: assuming (u0, v0) is the center coordinate of the target image, then the upper boundary is (u0, v0 + 40% × H), where H is the vertical pixel width of the target image; the lower boundary is (u0, v0 - 40% × H); the left boundary is (u0 + 40% × H, v0); and the right boundary is (u0 - 40% × H, v0)), the station switches to tracking measurement mode. After the photoelectric theodolite rotates until the high-speed target is again near the center of the target image, it re-enters staring measurement mode and acquires the second set of target image sequences. The third set of target image sequences is acquired using the same method. The image miss distance of the center point of the high-speed target is obtained through image processing.

[0069] Furthermore, in automatic tracking mode, the station points at the target, trying to center the target in the image. Then, the station enters a staring measurement mode, such as... Figure 2 As shown, P0 is the initial position of the target, P is the real-time position of the target's movement, and the azimuth angle at this moment is recorded. and pitch angle As the initial azimuth and initial elevation angles, O1 is the spatial coordinate of the station, and P is the initial azimuth and initial elevation angles. n These are the projected coordinates of target location P on the OXY plane; acquire target image sequences, and obtain the miss distance set of the target center through image processing. , This refers to the miss distance of a high-speed target relative to the center of the target image where it is located. The projection effect of a spatial straight-line trajectory onto the target image can be referenced. Figure 3 ;

[0070] Input a set of off-target measurements corresponding to a sequence of target images from gaze measurements. , In a new image coordinate system with the second sampling point (specifically, the center point of the high-speed target in the second frame image) as the image origin, the relative miss distance set is: ,in Depend on get, .

[0071] In some embodiments, step S2 specifically includes the following steps:

[0072] S21: Based on the first and second frame target images of the first set of target image sequences, and combined with the initial pitch angle, calculate the slope of the straight-line trajectory of the high-speed target on the target projection plane (defined as the geometric plane perpendicular to the initial direction-finding axis of the station and passing through the initial position of the target when the station enters the staring measurement mode).

[0073] ;

[0074] Where K is the slope of the straight-line trajectory of the high-speed target on the target projection plane. The initial pitch angle, The initial slope is calculated based on the first and second frame target images of the first set of target image sequences;

[0075] S22: Obtain the slope set based on the relative miss distance set corresponding to the current target image sequence. i starts from 3, where:

[0076] ;

[0077] in, Let y be the relative miss distance of the target image in the i-th frame. Let x be the relative miss distance on the x-axis corresponding to the target image in the i-th frame. Let be the slope corresponding to the target image in the i-th frame.

[0078] It should be noted that the initial slope is calculated from the first two sampling points of the gaze measurement (using the miss distance data point corresponding to the first frame of the target image as the first sampling point, the miss distance data point corresponding to the second frame of the target image as the second sampling point, and so on). and using the initial pitch angle Calculate the slope of the straight line trajectory on the target projection plane. ;

[0079]

[0080] The slope set of the image trajectory points relative to the image origin is calculated starting from the third sampling point of the gaze measurement (i.e., the miss distance data point corresponding to the third frame of the target image is the third sampling point). ,in ;

[0081] In some embodiments, step S3 specifically includes the following steps:

[0082] S31: The formula used to calculate the dimensionless distance set corresponding to the slope set based on the slope analytical expression of the target projection plane inversion model is as follows:

[0083] ;

[0084] in, slope The corresponding dimensionless distance;

[0085] S32: Calculate the first-order difference set of slopes based on the slope set and the dimensionless distance set, and fit the first-order difference of slopes using a linear function to obtain the intercept corresponding to the first set of target image sequences:

[0086] ;

[0087] in, Let be the slope corresponding to the target image in the (i+1)th frame. slope The corresponding dimensionless distance, The parameter values ​​of a first-order quantity of a linear function. This is the intercept corresponding to the first set of target image sequences.

[0088] It should be noted that the dimensionless distance set of the corresponding sampling points is calculated based on the slope analytical expression of the target projection plane inversion model. Then calculate the first-order difference set of the slope. The slope is approximated by a first-order difference function, which is then fitted to determine the intercept. ;

[0089] After outputting the intercept, the mathematical features of the curved trajectory of the image are extracted. The station-to-target distance information implied in the curved trajectory of the image is contained in the intercept.

[0090] The specific principle of the target projection plane inversion model is as follows:

[0091] For a straight trajectory in space, the initial azimuth and initial elevation angles of the station relative to the target are respectively... and The measurement scenario is as follows: In the station coordinate system, assuming that at the initial moment, the station points to the high-speed target, the plane perpendicular to the initial direction-finding axis of the station and passing through the initial position of the high-speed target is defined as the target projection plane.

[0092] In a spatial rectangular coordinate system Now, consider a simplified scenario where a high-speed target is in A plane undergoes uniform linear motion; its trajectory equation is:

[0093] ;

[0094] in,( , , (Target point) 3D coordinates;

[0095] Let the initial position of the high-speed target be... The location of the measuring station is High-speed target at The projection point on the axis is According to geometric relationships, the azimuth A and elevation E at subsequent moments are respectively:

[0096]

[0097] In the new image coordinate system, the horizontal and vertical coordinates of the image are represented by the miss distance:

[0098]

[0099] Among them, by have , This refers to the pixel size of the detector in an optoelectronic theodolite. y is the focal length of the photoelectric theodolite, and (x,y) is the miss distance of the target image to be measured.

[0100] In the new image coordinate system, initially, the high-speed target is imaged at the image origin. Therefore, the slope of the high-speed target's trajectory in the image is:

[0101] ;

[0102] The above formula is equivalent to It can be proven that the slope is usually non-constant, which means that the spatial straight line trajectory is usually a curved trajectory after being projected onto the target image.

[0103] Considering that the camera's field of view is usually small, and the spatial distance between the high-speed target and the station is much greater than the spatial distance between the high-speed target and the center point of the target's projection plane, the above formula can be expressed as:

[0104] ;

[0105] make To represent dimensionless distance, the above formula can be rewritten as:

[0106] ;

[0107] The expression for this function is quite complex, and its monotonicity is not immediately apparent after direct differentiation. To directly prove its monotonicity is equivalent to analyzing the monotonicity of the following function:

[0108]

[0109] because Therefore, the molecules follow The growth is slower than the denominator, which means... Monotonically decreasing, thus proving Monotonically decreasing, The introduction of functions is to simplify the mathematical proof. The monotonically decreasing property, It has no physical meaning.

[0110] Numerical calculation results also prove this. The function value varies As the value increases, it gradually decreases, so the slope of the spatial straight line trajectory gradually decreases in the target image, appearing as a downward curve. This function value is... When it approaches 0, it tends to Therefore, the slope of the tangent line to the trajectory curve at the origin of the image is used. and initial pitch angle The slope of a straight line trajectory in space on the target projection plane can be calculated. ;

[0111] ;

[0112] The slope of the tangent line to the trajectory curve at the origin of the image can be calculated from each sampling point of the target image sequence. Then, the dimensionless distance of the corresponding sampling point can be calculated using the slope formula. Then calculate the interval. , Then calculate the first difference of the slope and approximate it using a linear function:

[0113] ;

[0114] The intercept of this trajectory curve changes as the projection distance changes.

[0115] like Figure 4 As shown in the figure, the slope of the target image trajectory as a function of dimensionless distance is represented by the red line. Considering that the slope of the target projection plane inversion model is monotonically decreasing, the bisection method can be used to iteratively solve for the slope. This leads to the dimensionless distance set. Then calculate the first-order difference set of the slope. The first-order difference of the slope can be approximated by a linear function:

[0116] ;

[0117] This determines the intercept. Similarly, the intercept values ​​corresponding to the three sets of target image sequences can be measured through the above steps. ;

[0118] In some embodiments, in step S4:

[0119] When the high-speed target moves to the boundary of the single-frame target image, the station switches to tracking measurement mode, adjusts the direction finding of the photoelectric theodolite, so that the center point of the high-speed target is located again at the geometric center of the single-frame target image, and the station re-enters the staring measurement mode to acquire the second set of target image sequences.

[0120] When the high-speed target moves back to the boundary of the single-frame target image, repeat the above operation to obtain the third set of acquired target image sequences.

[0121] In some embodiments, in step S5, the theoretical intercept-projected distance function is:

[0122] ;

[0123] in, Theoretical intercept, This is the theoretical projected distance value. , , and All are fitted parameters. It is a natural constant;

[0124] The analytical solution of the theoretical intercept-projected distance function is:

[0125] ;

[0126] in, The analytical solution for the projected distance of the increasing function segment. The analytical solution for the projected distance of the decreasing function segment. This is the 0th branch of the Lambert W function. For Lambert's W function 1 branch;

[0127] If the intercept values ​​of the first, second, and third target image sequences increase sequentially, then the analytical solution of the projected distance of the increasing function segment is taken as the final analytical solution. If the intercept values ​​of the first, second, and third target image sequences decrease sequentially, then the analytical solution of the projected distance of the decreasing function segment is taken as the final analytical solution. ;

[0128] Substituting the final analytical solution into the following formula, the distance between the high-speed target and the station is calculated:

[0129] ;

[0130] in, The distance between the high-speed target and the measuring station, ( , ) represents the miss distance of the target image to be calculated (the miss distance of the center point of the high-speed target in the target image relative to the center of the target image to be calculated). This refers to the pixel size of the detector in an optoelectronic theodolite. The focal length of the photoelectric theodolite This is the initial pitch angle.

[0131] It should be noted that, using the intercept as the independent variable, this function can be divided into an increasing segment and a decreasing segment. The fitting function can be a quartic polynomial or a Gaussian function. Considering that the quartic polynomial has a simple form but a complex root-finding formula, while Gaussian functions have fewer formal parameters and analytical solutions, the following analysis uses the following Gaussian function for fitting:

[0132] ;

[0133] Its analytical solution is:

[0134] ;

[0135] In the formula, These are the four fitting parameters for Gaussian-type functions. and These are the analytical solutions for the projected distances of the increasing function segment and the decreasing function segment, respectively. and These are the 0 branch and 2 branches of the Lambert W function, respectively. Branch 1: The Lambert W function is a special function that can be called directly from a special function library.

[0136] It is known that the projected distance of the measuring station is minimum at the initial moment when pointing towards the high-speed target, and the projected distances of subsequent measurements increase sequentially. Based on the monotonicity of the intercept changing with the projected distance, the solution can be determined as follows: If the intercept values ​​of the three target image sequences increase sequentially, the increasing function segment is taken, i.e. Conversely, take the segment of the decreasing function, i.e. Substituting the intercept value, the corresponding projected distance value can be calculated.

[0137] Finally, the distance between the station and the target can be calculated based on geometric relationships:

[0138]

[0139] The velocity estimate for a high-speed target is:

[0140] :

[0141] In the formula, For the first The and the first The difference in dimensionless distance between each sampling point For the first The sampling point and the first The time interval between sampling points This is the velocity estimate of the high-speed target corresponding to the i-th sampling point.

[0142] It should be added that if the target's initial velocity vector and the target's projection plane are not coplanar, i.e., the angle between them is not zero (usually very small), the target's initial velocity vector can be orthogonally decomposed into velocity components parallel to the target's projection plane and velocity components perpendicular to the target's projection plane. The parallel velocity component is analyzed in the same way as above; the perpendicular velocity component is usually very small and can be considered as a disturbance error, which will introduce measurement error into the station-target distance calculated by the above analysis method. The specific analysis is as follows:

[0143] Assume the angle between the target's initial velocity vector and the target's projection plane is... The vertical component of velocity is equal to the parallel component of velocity. times, that is:

[0144] ;

[0145] in, For the goal The velocity component in the direction, Let the velocity components of the target be those within the target projection plane. For the goal The velocity component in the direction.

[0146] From the geometric relationship of the camera's field of view, we have:

[0147] ;

[0148] in, The time length corresponding to the target flight distance. This represents the horizontal length of the physical space corresponding to the camera's field of view. This represents the camera's horizontal field of view.

[0149] The projection distance error introduced by the vertical component of velocity is:

[0150] ;

[0151] Therefore, the relative error of the distance between the station and the target is:

[0152] ;

[0153] in, To account for the error in projected distance caused by the vertical component of velocity, This is to account for the error in station-to-eye distance caused by the vertical component of velocity.

[0154] Without loss of generality, we take typical values ​​of measurement conditions for analysis: when the field of view is 5°, the non-coplanar angle is 30°, the initial pitch angle is 50°, and the slope of the spatial straight line is 1, the relative error value of the station-to-eye distance calculated by the above formula is 5.5%, indicating that the vertical component of velocity has little influence on the station-to-eye distance solution of this invention.

[0155] Furthermore, for ease of understanding, the above operations will be explained in detail:

[0156] Based on the geometric relationship between the spatial line and the projection of the camera field of view, a target projection plane inversion model is constructed. The intercept value of the first-order difference of the slope of the target image trajectory corresponding to the target projection plane within a given projection distance interval is calculated. For example, given estimated projection distances of 10km, 20km, 40km, 60km, 80km, and 100km, six intercept values ​​are calculated by the inversion model. The intercept-projection distance function is then fitted according to a given functional form.

[0157] In this invention, after processing the three sets of target image sequences, three sets of intercept values ​​are obtained (each set contains one intercept value). If the intercept values ​​increase sequentially, it indicates that the theoretical intercept-projection distance function should take the increasing function segment; otherwise, the decreasing function segment should be taken.

[0158] Substituting the intercept value extracted from the image into the theoretical intercept-projection distance function mentioned above, the projection distance corresponding to the curved trajectory of the image is calculated, and then the distance to the target and the velocity estimate of the high-speed target are calculated from the geometric relationship.

[0159] Specifically, the intercept of the first-order difference curve of the slope varies with the dimensionless distance and the initial pitch angle. The theoretical intercept at different projection distances is given through the target projection plane inversion model. For example, for an aerial target moving at Mach 2.5, the slope of its spatial straight trajectory is 1. Initially, the projected distance between the high-speed target and the station is 31 km, the initial pitch angle of the station pointing at the high-speed target is 50°, the initial azimuth angle is arbitrary, the frame rate is ≥1000Hz, and 20 points are taken at equal intervals within the projection distance range of 5 km to 200 km. The theoretical intercept calculated from these points is shown in the figure. Figure 5 The black cross scatter plot is shown; the theoretical intercept-projected distance data is fitted using the following Gaussian class function:

[0160] ;

[0161] The analytical solution to the above equation is:

[0162] ;

[0163] In the formula, These are the four fitting parameters for Gaussian-type functions. For Lambert's W function Branches, among which, Take 0 and 1 corresponds to the increasing function segment of the analytical solution of the projected distance. and decreasing function segment See Figure 5 The blue and red dashed lines. The monotonicity of the intercept as a function of the projected distance can be used to determine... The value of: if the intercept value Increase sequentially, take Conversely, take ;

[0164] Substituting the measured intercept value under the given measurement conditions into the above formula It can be calculated For example, the four parameters of the fit The values ​​are 61.8, -19.8, 1.64, and 0.288 respectively. If the measured intercept value is 0.67 calculated using the above algorithm, the projected distance can be calculated to be 30.4 km.

[0165] Finally, the distance between the station and the target can be calculated based on geometric relationships:

[0166]

[0167] Average velocity estimation for high-speed targets for:

[0168] ;

[0169] in, For camera frame rate, The first calculated from the relative off-target set 1 dimensionless distance (total) indivual);

[0170] The formula here calculates the average velocity of the target using dimensionless distance values ​​from all frames. The time interval between every two frames is represented by the camera frame rate, so this formula calculates the average velocity of the target across all frames. Furthermore, as mentioned earlier, one characteristic of high-speed targets is that their velocity can be approximated as a fixed value within a finite time interval.

[0171] Furthermore, the relative error in station-to-eye distance introduced by the vertical component of velocity can be calculated as follows:

[0172] .

[0173] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0174] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for inverting station-to-target distance based on the trajectory curvature features of a single-station image, characterized in that: Specifically, it includes the following features: S1: Track high-speed targets using a single photoelectric theodolite as a station, acquire the first set of target image sequences, and obtain the relative miss distance set corresponding to the first set of target image sequences through image processing methods; S2: Based on the image trajectory curvature feature extraction method, calculate the slope set corresponding to the first set of target image sequences; Step S2 specifically includes the following steps: S21: Based on the first and second frame target images of the first set of target image sequences, and combined with the initial pitch angle, calculate the slope of the straight-line trajectory of the high-speed target on the target projection plane: ； Where K is the slope of the straight-line trajectory of the high-speed target on the target projection plane. The initial pitch angle, The initial slope is calculated based on the first and second frame target images of the first set of target image sequences; S22: Obtain the slope set based on the relative miss distance set corresponding to the current target image sequence. i starts from 3, where: ； in, Let y be the relative miss distance of the target image in the i-th frame. Let x be the relative miss distance on the x-axis corresponding to the target image in the i-th frame. Let be the slope corresponding to the target image in the i-th frame; S3: Calculate the dimensionless distance set corresponding to the slope set according to the slope analytical expression of the target projection plane inversion model, and calculate the first-order difference set of the slope based on the slope set and the dimensionless distance set to obtain the intercept corresponding to the first set of target image sequences. Step S3 specifically includes the following steps: S31: The formula used to calculate the dimensionless distance set corresponding to the slope set based on the slope analytical expression of the target projection plane inversion model is as follows: ； in, slope The corresponding dimensionless distance; S32: Calculate the first-order difference set of slopes based on the slope set and the dimensionless distance set, and fit the first-order difference of slopes using a linear function to obtain the intercept corresponding to the first set of target image sequences: ； in, Let be the slope corresponding to the target image in the (i+1)th frame. slope The corresponding dimensionless distance, The parameter values ​​of a first-order quantity of a linear function. The intercept corresponding to the first group of target image sequences; S4: Replace the current group of target image sequences with the next group of target image sequences, and repeat steps S1-S3 until the intercepts corresponding to the second and third groups of target image sequences are obtained. S5: Based on the Gaussian-type function fitting theory intercept-projection distance function, and based on the intercept variation law corresponding to the three sets of target image sequences, the corresponding branch of the Lambert W function is selected to calculate the distance between the station and the high-speed target.

2. The station-to-target distance inversion method based on the trajectory curvature features of a single-station image according to claim 1, characterized in that: In step S1, a single photoelectric theodolite is used as a station, and the direction finding of the photoelectric theodolite is directed towards the high-speed target. When the center point of the high-speed target is located at the geometric center of a single frame target image, the station enters the staring measurement mode and acquires the first set of target image sequences.

3. The station-to-target distance inversion method based on the trajectory curvature features of a single-station image according to claim 1, characterized in that: The specific steps for obtaining the relative off-target quantity set corresponding to the first set of target image sequences using image processing methods are as follows: S11: For the single-frame target images contained in the first set of target image sequences, establish an image coordinate system with the lower left corner of the single-frame target image as the origin, the horizontal direction of the single-frame target image as the horizontal axis, and the vertical direction of the single-frame target image as the vertical axis, and extract the coordinate values ​​of the center point of the high-speed target in the corresponding image coordinate system frame by frame. S12: Using the coordinates of the center point of the high-speed target in the second frame of the current target image sequence as the reference point, calculate the difference between the coordinates of the center point of the high-speed target in the corresponding image coordinate system and the reference point frame by frame to obtain the relative miss distance set corresponding to the current frame target image sequence.

4. The station-to-target distance inversion method based on the single-station image trajectory curvature features according to claim 2, characterized in that: In step S4: When the high-speed target moves to the boundary of the single-frame target image, the station switches to tracking measurement mode, adjusts the direction finding of the photoelectric theodolite, so that the center point of the high-speed target is located again at the geometric center of the single-frame target image, and the station re-enters the staring measurement mode to acquire the second set of target image sequences. When the high-speed target moves back to the boundary of the single-frame target image, repeat the above operation to obtain the third set of acquired target image sequences.

5. The station-to-target distance inversion method based on the trajectory curvature features of a single-station image according to claim 1, characterized in that: In step S5, the theoretical intercept-projected distance function is: ； in, Theoretical intercept, This is the theoretical projected distance value. , , and All are fitted parameters. It is a natural constant; The analytical solution of the theoretical intercept-projected distance function is: ； in, The analytical solution for the projected distance of the increasing function segment. The analytical solution for the projected distance of the decreasing function segment. This is the 0th branch of the Lambert W function. For Lambert's W function 1 branch; If the intercept values ​​of the first, second, and third target image sequences increase sequentially, then the analytical solution of the projected distance of the increasing function segment is taken as the final analytical solution. If the intercept values ​​of the first, second, and third target image sequences decrease sequentially, then the analytical solution of the projected distance of the decreasing function segment is taken as the final analytical solution. ; Substituting the final analytical solution into the following formula, the distance between the high-speed target and the station is calculated: ； in, The distance between the high-speed target and the measuring station, ( , () represents the miss distance of the target image to be calculated. This refers to the pixel size of the detector in an optoelectronic theodolite. The focal length of the photoelectric theodolite. This is the initial pitch angle.

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