An angle calibration method based on radar rotation center point estimation

Abstract

The present application relates to a kind of angle calibration method based on radar rotation center point estimation, it is characterized in that, include the following steps: S1, with the center of prism as coordinate origin establishes radar angle measurement geometry model;S2, determine pitch motion, azimuth motion, azimuth and pitch angle;S3, by total station instrument measurement target in first position and the coordinate of second position, establish radar measurement azimuth formula and theoretical azimuth formula, and radar measurement pitch angle formula and theoretical pitch angle formula, solve rotation center coordinate position;S4, according to the rotation center of solution establishment azimuth estimation and azimuth measurement value The relationship of value, and pitch angle estimation and pitch angle measurement value The relationship of value.The calibration method of the present application is simple, calibration precision is high, can effectively eliminate the angle error caused by rotation center and prism center inconsistency.

Description

Technical Field

[0001] This invention relates to the field of aerospace radar angle calibration, and in particular to an angle calibration method based on radar rotation center point estimation. Background Technology

[0002] Currently, for spaceborne mechanically scanned radars, a two-dimensional drive mechanism is typically used to move the radar antenna to achieve search, tracking, and measurement. The radar is mounted on a satellite platform to provide measurement information to the satellite, and the installation accuracy is ensured by a prism on the radar. The satellite uses the prism coordinate system as a reference to calculate the angle measured by the radar and adjust its attitude accordingly. However, the angle measured by the mechanically scanned radar is obtained using the rotation center of the two-dimensional drive mechanism as the coordinate system. The discrepancy between the actual prism center and the rotation center of the radar leads to angle errors. Therefore, precise calibration of the radar angle is necessary to ensure that the spaceborne mechanical radar provides the satellite with accurate and reliable target measurement information.

[0003] To ensure reliable target measurement information, existing technologies establish a normalized error vector by tracking and measuring far-field cooperative targets. Using the quantitative relationship between optical miss distance and radar dynamic hysteresis, parameters such as radar photoelectric deviation, directional sensitivity, and cross-coupling coefficient are solved iteratively and uniformly. Furthermore, a method using two total stations for forward intersection is employed to measure the spatial coordinates of a reference point on the radar antenna array. This allows for the calculation of the elevation and azimuth angles of the antenna array relative to the aircraft axis. These angles are then used as the calibration basis for the installation error of the airborne fire control radar antenna array. The operational method and calibration accuracy analysis are described. Summary of the Invention

[0004] This invention calculates the radar's rotation center by analyzing the target's position, the radar-measured target angle, and the angle between the target and the prism. Then, based on geometric relationships, it establishes formulas for the rotation center, the radar-measured angle, and the target's true angle. This solves the problem of large radar angle measurement errors caused by the inconsistency between the radar's rotation center and the prism center. This invention proposes an angle calibration method based on radar rotation center point estimation, comprising the following steps:

[0005] S1. Establish a radar angle measurement geometric model with the center of the prism as the origin of the coordinate system. The X-axis is parallel to the radar line of sight, the Z-axis is parallel to the pitch axis of the drive mechanism, and the Y-axis is obtained by the right-hand rectangular coordinate relationship.

[0006] S2. Define the target's rotation around the Y-axis as pitch motion and rotation around the Z-axis as azimuth motion. The line connecting the radar and the target is the radar's line of sight direction. The angle between the projection of the radar's line of sight onto the XOY plane and the X-axis direction is the azimuth angle α. The angle between the projection of the radar's line of sight onto the XOZ plane and the prism's X-axis direction is the elevation angle β. Define the azimuth angle towards the positive Y-axis direction as positive and the elevation angle towards the positive Z-axis direction as positive.

[0007] S3. Measure the coordinates of the target at the first and second positions using a total station. Establish the radar measurement azimuth formula and theoretical azimuth formula, as well as the radar measurement elevation formula and theoretical elevation formula, based on geometric relationships. Solve the coordinate position of the rotation center by combining the formulas.

[0008] S4. Based on the obtained rotation center, establish the relationship between the estimated azimuth angle and the measured azimuth angle, as well as the relationship between the estimated pitch angle and the measured pitch angle.

[0009] Further, in step S1, the center coordinates of the prism are defined as O = (0,0,0); the coordinates of the radar rotation center are defined as C = (x... c ,y c ,z c The center point coordinates of the target are M = (x m ,y m ,z m ).

[0010] Furthermore, according to the definition in step S2, the directional coordinates between the radar rotation center and the target center are obtained from the geometric relationship as Equation (1):

[0011] M C =(x m -x c ,y m -y c ,z m -z c (1)

[0012] The directional coordinates between the prism center and the target center are given by equation (2):

[0013] M Z =(x m ,y m ,z m (2).

[0014] Furthermore, step S3 includes the following solution process:

[0015] The directional coordinates of the radar rotation center and the target center projected onto the XOY plane are given by equation (3):

[0016] M CZ =(x m -x c ,y m -y c ,0)(3);

[0017] The azimuth angle measured by radar is obtained from geometric relationships as shown in equation (4):

[0018]

[0019] The directional coordinates of the prism center and the target center projected onto the XOY plane are given by equation (5):

[0020] M Z =(x m ,y m ,0)(5);

[0021] The theoretical value of the azimuth angle is obtained from geometric relationships, as shown in equation (6):

[0022]

[0023] And in the dark room, the target is moved to the first position and the second position. The coordinates (x1, y1, z1) of the target at the first position are measured by a total station. The azimuth angle α1′ of the target is obtained by radar measurement, and the azimuth angle α1 between the target and the prism is calculated. The coordinates (x2, y2, z2) of the target at the second position are measured by a total station. The azimuth angle α2′ of the target is obtained by radar measurement, and the azimuth angle α2 between the target and the prism is calculated. At the same time, equation (7) is obtained from equations (4) and (6):

[0024]

[0025] The position x of the radar rotation center is obtained by solving the problem. c and y c The coordinate position is given by equation (8):

[0026]

[0027] The projection of the radar and target's directional coordinates onto the XOZ plane is given by equation (9).

[0028] M CY =(x m -x c ,0,z m -z c (9)

[0029] The elevation angle measured by radar is obtained from geometric relationships as shown in equation (10):

[0030]

[0031] The projection of the target's orientation coordinates onto the XOZ plane is given by equation (11):

[0032] M Y =(x m ,0,z m (11)

[0033] The theoretical azimuth angle between the prism and the target is obtained as equation (12):

[0034]

[0035] And in the dark room, the target is moved to the first position and the second position. The coordinates (x1, y1, z1) of the target at the first position are measured by a total station. The elevation angle of the target is obtained by radar measurement as β1′, and the elevation angle β1 between the target and the prism is calculated. When the target is moved to the second position, the coordinates (x2, y2, z2) of the target are measured by a total station. The elevation angle of the target is obtained by radar measurement as β2′, and the elevation angle β2 between the target and the prism is calculated. At the same time, equation (13) is obtained from equations (10) and (12):

[0036]

[0037] The position x of the radar rotation center is obtained by solving the problem. c and z c The coordinate position is obtained from equation (14):

[0038]

[0039] Furthermore, step S4 includes the following solution process:

[0040] The relationship between the true and measured azimuth values ​​is obtained from equations (4) and (6):

[0041]

[0042] From equations (10) and (12), the relationship between the true and measured pitch angles is further obtained:

[0043]

[0044] Distance measured by radar:

[0045] R 2 =(x m -x c ) 2 +(y m -y c ) 2 +(z m -z c ) 2 (17)

[0046] From equations (4), (10), and (17), we obtain:

[0047] x m =Rcos(β′)+x c (18)

[0048] Substituting equation (18) into equation (15) yields the relationship between the estimated azimuth and the radar-measured azimuth:

[0049]

[0050] Substituting equation (18) into equation (16) yields the relationship between the estimated elevation angle and the radar-measured elevation angle:

[0051]

[0052] Furthermore, the angle calibration method also includes a step S6 for angle estimation accuracy, including azimuth angle estimation accuracy and pitch angle estimation accuracy, the solution process of which is as follows:

[0053] Azimuth estimation accuracy:

[0054] From equation (19), let:

[0055]

[0056] The estimated azimuth angle is then obtained as equation (22):

[0057]

[0058] Taking the partial derivative of equation (22) with respect to the radar measurement range R, we obtain equation (23):

[0059]

[0060] Find x in equation (22) above. c The partial derivative yields equation (24):

[0061]

[0062] Find y in equation (22) above. c The partial derivative yields equation (25):

[0063]

[0064] Let the measurement error of distance R be ε R x c The measurement error is ε xc y c The measurement error is ε yc Then the accuracy of the azimuth angle is obtained as shown in equation (26):

[0065]

[0066] Pitch angle estimation accuracy:

[0067] From equation (20), let:

[0068]

[0069] The estimated pitch angle is then obtained as equation (28):

[0070]

[0071] Taking the partial derivative of the distance R with respect to equation (28) yields equation (29):

[0072]

[0073] Find x in equation (28) c The partial derivative yields equation (30):

[0074]

[0075] Find z for equation (28) c The partial derivative yields equation (31):

[0076]

[0077] Let the error of distance R be ε R x c The error is ε xc , z c The error is ε zc Then the accuracy of the pitch angle is obtained as shown in equation (32):

[0078]

[0079] In summary, the present invention has the following beneficial effects:

[0080] 1. The calibration method is simple and the calibration accuracy is high;

[0081] 2. It can calculate the coordinates of the radar rotation center point;

[0082] 3. Able to establish the relationship between the target's true angle, the radar measurement angle, and the radar rotation center;

[0083] 4. It can effectively eliminate angular errors caused by the misalignment between the rotation center and the prism center. Attached Figure Description

[0084] Figure 1 This is a schematic diagram of the radar structure;

[0085] Figure 2 This is a diagram showing the geometric relationship of radar angle measurement.

[0086] Figure 3 Define the radar angle polarity diagram;

[0087] Figure 4 Diagram of radar angle measurement accuracy calibration system;

[0088] Figure 5 The azimuth simulation results are shown in the graph.

[0089] Figure 6 A diagram showing the azimuth error values;

[0090] Figure 7 The result is a graph showing the simulation results of the pitch angle.

[0091] Figure 8 This is a graph showing the pitch angle error values. Detailed Implementation

[0092] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a further detailed explanation of the angle calibration method based on radar rotation center point estimation proposed in this invention.

[0093] The angle calibration method provided by this invention is based on a radar angle measurement system, such as... Figure 1 As shown, the radar angle measurement system includes a radar antenna 1, a drive mechanism 2 for moving the radar antenna 1, and a prism 3 mounted on the base of the drive mechanism. The rotation center C of the radar is the intersection of the azimuth axis and the elevation axis of the drive mechanism 2. The angle calibration method provided by this invention includes the following steps:

[0094] S1. Establish a radar angle measurement geometric model with the center of prism 3 as the origin, where the X-axis is parallel to the radar line of sight, the Z-axis is parallel to the pitch axis of the drive mechanism, and the Y-axis is obtained from the right-hand rectangular coordinate system; (e.g.) Figure 2 As shown, the center coordinates of prism 3 are defined as O = (0,0,0); the coordinates of the radar rotation center are defined as C = (x... c ,y c ,z c The center point coordinates of the target are M = (x m ,y m ,z m ).

[0095] S2. Define the target's rotation around the Y-axis as pitch motion and rotation around the Z-axis as azimuth motion. The line connecting the radar and the target is the radar's line of sight direction. The prism's X-axis direction is L = (1,0,0). The angle between the radar's projection onto the XOY plane and the X-axis direction is the azimuth angle α, and the angle between its projection onto the XOZ plane and the prism's X-axis direction is the elevation angle β. Define the azimuth angle towards the positive Y-axis as positive, and the elevation angle towards the positive Z-axis as positive. like Figure 3 As shown, α+ represents a positive azimuth angle, α- represents a negative azimuth angle, β+ represents a positive elevation angle, and β- represents a negative elevation angle.

[0096] The directional coordinates between the radar rotation center and the target center are obtained from geometric relationships as shown in equation (1):

[0097] M C =(x m -xc ,y m -y c ,z m -z c (1)

[0098] The directional coordinates between the prism center and the target center are given by equation (2):

[0099] M Z =(x m ,y m ,z m (2).

[0100] S3, The total station is positioned between the radar and the target, such as Figure 4 As shown. The coordinates of the target at the first and second positions are obtained by measuring the prism and the target with a total station. Radar measurement azimuth formulas and theoretical azimuth formulas, as well as radar measurement elevation angle formulas and theoretical elevation angle formulas, are established based on geometric relationships. The coordinates of the rotation center are then solved by combining these formulas. The specific solution process is as follows:

[0101] M CZ The projection of the directional coordinates of the radar rotation center and the target center onto the XOY plane is given by equation (3):

[0102] M CZ =(x m -x c ,y m -y c ,0)(3);

[0103] The azimuth angle measured by radar is obtained from geometric relationships as shown in equation (4):

[0104]

[0105] The directional coordinates of the prism center and the target center projected onto the XOY plane are given by equation (5):

[0106] M Z =(x m ,y m ,0)(5);

[0107] The theoretical value of the azimuth angle is obtained from geometric relationships, as shown in equation (6):

[0108]

[0109] And in the dark room, the target is moved to the first position and the second position. The coordinates (x1, y1, z1) of the target at the first position are measured by a total station. The azimuth angle α1′ of the target is obtained by radar measurement, and the azimuth angle α1 between the target and the prism is calculated. The coordinates (x2, y2, z2) of the target at the second position are measured by a total station. The azimuth angle α2′ of the target is obtained by radar measurement, and the azimuth angle α2 between the target and the prism is calculated. At the same time, equation (7) is obtained from equations (4) and (6):

[0110]

[0111] The position x of the radar rotation center is obtained by solving the problem. c and y c The coordinates of the coordinates are shown in equation (8):

[0112]

[0113] The projection of the radar and target directional coordinates onto the XOZ plane is shown in equation (9):

[0114] M CY =(x m -x c ,0,z m -z c (9);

[0115] The elevation angle measured by radar is obtained from geometric relationships as shown in equation (10):

[0116]

[0117] The projection of the target's orientation coordinates onto the XOZ plane is given by equation (11):

[0118] M Y =(x m ,0,z m (11);

[0119] The theoretical azimuth angle between the prism and the target is obtained as equation (12):

[0120]

[0121] And in the dark room, the target is moved to the first position and the second position. The coordinates (x1, y1, z1) of the target at the first position are measured by a total station. The elevation angle of the target is obtained by radar measurement as β1′, and the elevation angle β1 between the target and the prism is calculated. When the target is moved to the second position, the coordinates (x2, y2, z2) of the target are measured by a total station. The elevation angle of the target is obtained by radar measurement as β2′, and the elevation angle β2 between the target and the prism is calculated. At the same time, equation (13) is obtained from equations (10) and (12):

[0122]

[0123] The position x of the radar rotation center is obtained by solving the problem. c and z c The coordinate position is obtained from equation (14):

[0124]

[0125] S4. Based on the obtained rotation center, establish the relationship between the estimated azimuth angle and the measured azimuth angle, as well as the relationship between the estimated pitch angle and the measured pitch angle. The specific solution process is as follows:

[0126] The relationship between the true and measured azimuth values ​​is obtained from equations (4) and (6):

[0127]

[0128] From equations (10) and (12), the relationship between the true and measured pitch angles is further obtained:

[0129]

[0130] Distance measured by radar:

[0131] R 2 =(x m -x c ) 2 +(y m -y c ) 2 +(z m -z c ) 2 (17)

[0132] From equations (4), (10), and (17), we obtain:

[0133] x m =Rcos(β′)+x c (18)

[0134] Substituting equation (18) into equation (15) yields the relationship between the estimated azimuth and the radar-measured azimuth:

[0135]

[0136] Substituting equation (18) into equation (16) yields the relationship between the estimated elevation angle and the radar-measured elevation angle:

[0137]

[0138] The angle calibration method described in this example also includes step S6, which involves estimating the accuracy of the angle estimation, including the accuracy of the heading angle estimation and the accuracy of the pitch angle estimation. The solution process is as follows:

[0139] Azimuth estimation accuracy:

[0140] From equation (19), let:

[0141]

[0142] The estimated azimuth angle is then obtained as equation (22):

[0143]

[0144] Taking the partial derivative of equation (22) with respect to the radar measurement range R, we obtain equation (23):

[0145]

[0146] Find x in equation (22) above. c The partial derivative yields equation (24):

[0147]

[0148] Find y in equation (22) above. c The partial derivative yields equation (25):

[0149]

[0150] Let the measurement error of distance R be ε R x c The measurement error is ε xc y c The measurement error is ε yc Then the accuracy of the azimuth angle is obtained as shown in equation (26):

[0151]

[0152] Pitch angle estimation accuracy:

[0153] From equation (20), let:

[0154]

[0155] The estimated pitch angle is then obtained as equation (28):

[0156]

[0157] Taking the partial derivative of the distance R with respect to equation (28) yields equation (29):

[0158]

[0159] Find x in equation (28) c The partial derivative yields equation (30):

[0160]

[0161] Find z for equation (28) c The partial derivative yields equation (31):

[0162]

[0163] Let the error of distance R be ε R x c The error is ε xc , z c The error is ε zc Then the accuracy of the pitch angle is obtained as shown in equation (32):

[0164]

[0165] In one embodiment, taking the radar's rotation center as (0.2, -1.3, 1.5) m as an example, the measurement error of the radar's rotation center is 0.001 m. The target's x-axis is set... m The coordinates are 500m, y m The coordinates are (-200~200)m, z m The coordinates are (-200~200)m, and the radar ranging error is 10m.

[0166] The azimuth simulation results are as follows Figure 6 As shown, the "*" line represents the theoretical azimuth, the "O" line represents the measured azimuth, and the "△" line represents the estimated azimuth. Figure 7 The figure shows the error between the measured azimuth angle and the estimated azimuth angle and the theoretical azimuth angle. As can be seen from the figure, the measured azimuth angle error is between 0.12° and 0.16°, while the estimated azimuth angle error is less than 0.02°. The estimated azimuth angle error is relatively small, meaning that the estimated azimuth angle is close to the theoretical azimuth angle.

[0167] The simulation results of pitch angle are as follows Figure 8 As shown, the "*" line represents the theoretical azimuth, the "O" line represents the measured azimuth, and the "△" line represents the estimated azimuth. Figure 8 The figure shows the error between the measured pitch angle and the estimated pitch angle and the theoretical pitch angle. As can be seen from the figure, the measured pitch angle error is between 0.14° and 0.18°, while the estimated azimuth angle error is less than 0.02°. The estimated pitch angle error is relatively small, meaning that the estimated pitch angle is close to the theoretical pitch angle.

[0168] The present invention has the following beneficial effects:

[0169] 1. The calibration method is simple and the calibration accuracy is high;

[0170] 2. It can calculate the coordinates of the radar rotation center point;

[0171] 3. Able to establish the relationship between the target's true angle, the radar measurement angle, and the radar rotation center;

[0172] 4. It can effectively eliminate angular errors caused by the misalignment between the rotation center and the prism center.

[0173] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. An angle calibration method based on radar rotation center point estimation, characterized in that, Includes the following steps: S1. Establish a radar angle measurement geometric model with the center of the prism as the origin of the coordinate system, where... X The axis is parallel to the radar line of sight. Z The axis is parallel to the pitch axis of the drive mechanism. Y The axes are obtained using the right-hand rectangular coordinate system; S2, Define target orbit Y Rotation of the axis is a pitch motion, around Z The rotation of the axial direction represents azimuthal motion; the line connecting the radar and the target represents the radar's line-of-sight direction; and the prism's X-axis direction... Radar line of sight XOY Projection on the surface and X The angle between the axes is the azimuth angle. ,exist XOZ Projection on the surface and prism X The angle between the axes is the pitch angle. Define azimuth direction Y The positive direction of the axis is positive, and the pitch angle is towards... Z The positive direction of the axis is positive; S3. Measure the coordinates of the target at the first and second positions using a total station. Establish the radar measurement azimuth formula and theoretical azimuth formula, as well as the radar measurement elevation formula and theoretical elevation formula, based on geometric relationships. Solve the coordinate position of the rotation center by combining the formulas. S4. Based on the obtained rotation center, establish the relationship between the estimated azimuth angle and the measured azimuth angle, as well as the relationship between the estimated pitch angle and the measured pitch angle. Step S3 includes the following solution process: M CZ The directional coordinates of the radar rotation center and the target center are in XOY The surface projection is given by equation (3): （3）； The azimuth angle measured by radar is obtained from geometric relationships as shown in equation (4): （4）； The directional coordinates of the prism center and the target center are in XOY The surface projection is given by equation (5): （5）； The theoretical value of the azimuth angle is obtained from geometric relationships, as shown in equation (6): （6） And in the darkroom, the target is moved to a first position and a second position, and the coordinates of the target at the first position are measured using a total station. The radar measured the target azimuth angle. And the azimuth angle between the target and the prism is calculated. ; Measure the coordinates of the target at its second position using a total station. The radar measured the target azimuth angle. And the azimuth angle between the target and the prism is calculated. Simultaneously, equation (7) is obtained from equations (4) and (6): （7）； The position of the radar rotation center is obtained by solving the problem. x c and y c The coordinate position is given by equation (8): （8）； The directional coordinates of the radar and the target are at XOZ The surface projection is given by equation (9). （9） The elevation angle measured by radar is obtained from geometric relationships as shown in equation (10): （10） The target's direction coordinates are XOZ The surface projection is given by equation (11): （11） The theoretical azimuth angle between the prism and the target is obtained by equation (12): （12） And in the darkroom, the target is moved to a first position and a second position, and the coordinates of the target at the first position are measured using a total station. The radar measured the target's elevation angle as And calculate the pitch angle between the target and the prism. When the target is moved to the second position, its coordinates are measured using a total station. The radar measured the target's elevation angle as And calculate the pitch angle between the target and the prism. Simultaneously, equation (13) is obtained from equations (10) and (12): （13） The position of the radar rotation center can be obtained by solving the problem. x c and z c The coordinate position is obtained from equation (14): （14）。 2. The angle calibration method based on radar rotation center point estimation as described in claim 1, characterized in that, Step S1 defines the center coordinates of the prism as follows: ; The coordinates of the radar rotation center are The coordinates of the target's center point are: .

3. The angle calibration method based on radar rotation center point estimation as described in claim 2, characterized in that, According to the definition in step S2, the directional coordinates between the radar rotation center and the target center are obtained from the geometric relationship as Equation (1): （1） The directional coordinates between the prism center and the target center are given by equation (2): （2）。 4. The angle calibration method based on radar rotation center point estimation as described in claim 3, characterized in that, Step S4 includes the following solution process: The relationship between the true and measured azimuth values ​​is obtained from equations (4) and (6): （15） From equations (10) and (12), the relationship between the true and measured values ​​of the pitch angle is further obtained: （16） Distance measured by radar: （17） From equations (4), (10), and (17), we obtain: （18） Substituting equation (18) into equation (15) yields the relationship between the estimated azimuth and the radar-measured azimuth: （19） Substituting equation (18) into equation (16), we obtain the relationship between the estimated elevation angle and the radar-measured elevation angle: （20）。 5. The angle calibration method based on radar rotation center point estimation as described in claim 4, characterized in that, The process also includes step S6, which assesses the accuracy of angle estimation, including both the accuracy of the heading angle and the accuracy of the pitch angle. The solution process is as follows: Azimuth estimation accuracy: From equation (19), let: （21） The estimated azimuth angle is then obtained as equation (22): （22） Calculate the radar measurement range using equation (22). R The partial derivative yields equation (23): （23） Find the above equation (22). x c The partial derivative yields equation (24): （24） Find the above equation (22). y c The partial derivative yields equation (25): （25） Let distance The measurement error is , The measurement error is , The measurement error is Then the accuracy of the azimuth angle is obtained as shown in equation (26): （26） Pitch angle estimation accuracy: From equation (20), let: （27） The estimated pitch angle is then obtained as equation (28): （28） Find the distance in equation (28) R The partial derivative yields equation (29): （29） Find the equation (28). x c The partial derivative yields equation (30): （30） Find the equation (28). z c The partial derivative yields equation (31): （31） Let distance The error is , The error is , The error is Then the accuracy of the pitch angle is obtained as shown in equation (32): （32）。

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