Conical scanning angle measurement tracking method, device and system based on spherical phased-array antenna

Abstract

The invention discloses a conical scanning angle measurement tracking method, device and system based on a spherical phased array antenna, and belongs to the technical field of antennae, and the method comprises the steps: firstly, building a conical scanning geometric model based on a spherical phased array, determining the scanning frequency, the scanning deflection angle and the scanning discrete point number, and determining a target direction; secondly, calculating a modulation coefficient, calculating a scanning point according to a target direction, and determining a phased array beam conical scanning process; then, transverse and longitudinal errors are calculated by determining the power of a phased array receiving signal and are further used for estimating the real direction of a target; and finally, estimating, predicting and tracking the real direction of the target through loop filtering. According to the invention, high-precision angle measurement tracking is realized by using high gain of the phased-array antenna and conical scanning, the array arrangement mode of the phased-array antenna is not strictly constrained, the expansion is flexible, the realization is simple, and the cost is low.

Description

Technical Field

[0001] The present invention relates to the technical field of antennas, and more specifically, to a conical scanning angle measurement and tracking method, device, and system based on a spherical phased array antenna. Background Art

[0002] As a key device for receiving and transmitting electromagnetic signals, a phased array antenna has stronger flexibility compared to a traditional mechanical parabolic antenna. It can complete beam pointing based on electronic scanning and has a very important position in the fields of measurement and control, radar, navigation, communication, etc. However, in many application scenarios, the asymmetric structure layout of the antenna array surface results in low angle measurement and tracking accuracy of the array.

[0003] To complete the angle measurement and tracking task based on a phased array antenna, conventional methods include sum-difference ratio phase, sum-difference ratio amplitude, and conical scanning angle measurement methods. Among them, both sum-difference ratio phase and sum-difference ratio amplitude require angle measurement and tracking to be completed under four beam conditions. In particular, the sum-difference ratio phase method requires that the array corresponding to the four beams is completely symmetrically divided. However, for a small spherical cylindrical array, due to the relatively sparse arrangement of array elements, it is difficult to divide the active area into four completely symmetric areas, thus affecting the effects of the sum-difference ratio phase and sum-difference ratio amplitude methods and resulting in a decrease in angle measurement and tracking accuracy. Therefore, finding an easy-to-implement, low-cost, and high-precision angle measurement and tracking method suitable for small spherical phased array antennas is crucial for practical engineering applications. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a conical scanning angle measurement and tracking method, device, and system based on a spherical phased array antenna, which solves the problem that the existing small spherical cylindrical array is difficult to meet the requirements of the sum-difference ratio phase and sum-difference ratio amplitude methods for symmetric division of the active area, resulting in a decrease in angle measurement and tracking accuracy, and has the advantages of simple implementation, low cost, flexible expansion, and high precision.

[0005] The purpose of the present invention is achieved through the following solutions:

[0006] A conical scanning angle measurement and tracking method based on a spherical phased array antenna includes the following steps:

[0007] Step 1: Establish a conical scanning geometric model based on the spherical phased array, and determine the scanning frequency, scanning deflection angle, scanning discrete points, and the assumed target direction;

[0008] Step 2: Calculate the modulation coefficient and scanning trace according to the preset scanning frequency, scanning deflection angle, scanning discrete points, and the assumed target direction, and determine the conical scanning process of the phased array beam;

[0009] Step 3: Calculate the transverse and longitudinal errors by determining the power of the phased array received signal, and estimate the true direction of the target using the transverse and longitudinal errors;

[0010] Step 4: Estimate and predict the target's true direction through loop filtering to track the change of the target direction.

[0011] Further, in Step 1, establishing the conical scanning geometric model based on the spherical phased array specifically includes the following sub-steps:

[0012] Step 1-1: The phased array beam is deflected by an angle ε from the central axis OO', and rotates around the axis at a constant speed. OS' is the beam axis, B is the trajectory of the antenna's circular motion, and T is the target direction; when the beam is not pointing correctly, within a scanning period, the magnitude of the angle β between the beam direction and the target's true direction and the received satellite signal strength are constantly changing. Determine the satellite's location based on the changes in β and the satellite signal strength, and adjust the beam direction; when the beam points at the target, the axis OT and the axis OO' coincide, at this time β no longer changes and the satellite signal strength is the strongest;

[0013] Step 1-2: Determine the scanning frequency f s , the scanning deflection angle α, the number of scanning discrete points N, and the assumed target direction. β represents the angle between the beam direction and the target's true direction, ε represents the angle between the true target direction and the assumed target direction, and φ0 represents the angle of the true target in the x′O′y′ coordinate system.

[0014] Further, y′ can be selected in the horizontal direction within the plane perpendicular to O′O, and x′ is selected to be perpendicular to both OO′ and y′.

[0015] Further, in Step 2, calculating the modulation coefficient and the scanning trace specifically includes the following sub-steps: According to the preset scanning frequency f s , the scanning deflection angle α, the number of scanning discrete points N, and the assumed target direction, calculate the modulation coefficient and the scanning trace to determine the conical scanning process of the phased array beam;

[0016] Step 2-1: The beam normalized voltage pattern function F(θ) is approximated using a Gaussian function, and its expression is:

[0017] F(θ) = exp(-0.5wθ 2 )

[0018] where θ 3dB represents the 3dB beam width of the array;

[0019] Step 2-2: Calculate the derivative of F(θ) as:

[0020] F′(θ) = -wθ exp(-0.5wθ 2 ) = -wθ F(θ);

[0021] Substitute the scanning declination angle α into F(θ) and F′(θ), and the modulation coefficient m is calculated as follows:

[0022]

[0023] Step 2-3: Scanning point track calculation: Assuming the number of scanning points in one period is N, and the target direction and the true target direction are respectively and With the scanning angular width being α and assuming the target direction is in the zenith direction (0, 90), the direction of the scanning point is calculated as:

[0024]

[0025] Step 2-4: According to the assumed target direction Rotate to the actual scanning position, and the actual scanning direction is obtained as Express the directions before and after rotation in the Cartesian coordinate system as d cn and d sn , and their expressions are:

[0026]

[0027]

[0028] Step 2-5: Calculate the desired scanning point direction and perform two rotation processes: First, rotate d cn counterclockwise around the y-axis by Then rotate counterclockwise around the z-axis by θ0, and the corresponding total rotation matrix is:

[0029]

[0030] Then, d cn after passing through the rotation matrix Γ, d sn is obtained, and its expression is:

[0031] d sn = Γd cn ;

[0032] Step 2-6: According to the solution result d sn , obtain the corresponding scanning point direction

[0033] Furthermore, in Step 2-1, F 2 (0.5θ 3dB ) = 0.5.

[0034] Further, in step 3, the horizontal and vertical errors are calculated by determining the power of the phased array received signal, and the true direction of the target is estimated using the horizontal and vertical errors, which specifically includes the following sub-steps:

[0035] Step 3-1: Calculate the power of the signal at each discrete scan point as:

[0036]

[0037] where K represents the proportionality coefficient, U0 = KF 2 (α), and U0 is estimated by U0 = E(U(t));

[0038] Step 3-2: Calculate the intermediate variables U I0 and U Q0 , and their specific expressions are:

[0039] U I0 = E(U(t)cos(2πf s t)) = 0.5mU0εcosφ0;

[0040] U Q0 = E(U(t)sin(2πf s t)) = 0.5mU0εsinφ0;

[0041] Step 3-4:: Calculate the horizontal and vertical errors respectively as:

[0042]

[0043]

[0044] where G = 0.5mU0;

[0045] Step 3-5: Use the horizontal and vertical errors ε x and ε y to directly obtain:

[0046]

[0047] φ0 = atan2(ε y , ε x );

[0048] According to the scanning point track calculation process, the target direction estimation is:

[0049] θ tc = φ0,

[0050] Step 3-6: The target direction estimation vector d tc is:

[0051]

[0052] According to the dot trace scanning rotation matrix Γ, perform corresponding rotation on d tc to obtain the estimated target direction vector d sn :

[0053] d ts = Γd tc ;

[0054] According to the solution result d ts , obtain the target direction

[0055] Furthermore, in step 4, the estimation and prediction of the true target direction are achieved through loop filtering to track the change of the target direction, which specifically includes the following sub-steps:

[0056] Step 4-1: The azimuth angle of the target tracked and predicted by the loop filter at the k-th moment is θ ts (k), and its expression is:

[0057] δ θ (k) = δ θ (k - 1) + b0x θ (n) + b1x θ (n - 1);

[0058] θ ts (k) = θ ts (k - 1) + T s δ θ (k);

[0059] where B L represents the noise bandwidth, T s is the update period of the loop filter; x θ (k), δ θ (k), θ ts (k) represent the azimuth angle estimation error, the loop filter output result, and the target azimuth angle prediction result at time k respectively;

[0060] Step 4-2: The elevation angle of the target tracked by the loop filter at the k-th moment is and its expression is:

[0061]

[0062] where represent the elevation angle estimation error, the loop filter output result, and the target elevation angle prediction result at time k respectively.

[0063] A conical scanning angle measurement and tracking device based on a spherical phased array antenna, comprising:

[0064] A model construction module for establishing a conical scanning geometric model based on a spherical phased array, determining the scanning frequency, scanning deflection angle, number of scanning discrete points, and the assumed target direction;

[0065] A calculation module for calculating the modulation coefficient and scanning trace according to the preset scanning frequency, scanning deflection angle, number of scanning discrete points, and the assumed target direction, and determining the conical scanning process of the phased array beam;

[0066] A target true direction estimation module for calculating the transverse and longitudinal errors by determining the power of the phased array received signal, and estimating the target true direction using the transverse and longitudinal errors;

[0067] A target true direction tracking and prediction module for estimating and predicting the target true direction through loop filtering and tracking the change of the target direction.

[0068] A conical scanning angle measurement and tracking system based on a spherical phased array antenna, comprising the conical scanning angle measurement and tracking device based on a spherical phased array antenna as described above.

[0069] The beneficial effects of the present invention include:

[0070] (1) The method provided by the present invention is applicable to the conical scanning angle measurement and tracking of a small spherical phased array antenna. The conical scanning is performed in the air by digital beam pointing, and the beamforming process improves the antenna receiving synthetic signal-to-noise ratio gain, thereby improving the angle measurement and tracking accuracy of the target.

[0071] (2) A scanning trace calculation method. Since the phased array antenna uses digital beams for conical scanning angle measurement and tracking, it is necessary to calculate the traces within the conical scanning period for estimating the true position of the target, and the number of scanning traces is flexibly configurable.

[0072] (3) Flexible expansion, simple implementation, low cost, and high angle measurement accuracy. The conical scanning angle measurement and tracking method based on a spherical phased array antenna provided by the present invention has no special requirements for the antenna array and can be extended to angle measurement and tracking systems with any array configuration. This method can not only simplify the design of the phased array antenna, reduce the cost, but also achieve high signal-to-noise ratio synthetic gain and high-precision angle measurement and tracking. Description of the Drawings

[0073] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0074] Figure 1a It is a schematic diagram of the conical scanning geometric model based on a spherical phased array antenna;

[0075] Figure 1b The calculation flow chart of conical scanning angle measurement and tracking;

[0076] Figure 2 It is a schematic diagram of the geometric position of a small spherical phased array antenna in three-dimensional space;

[0077] Figure 3 It is the change of the target motion trajectory, angular velocity and angular acceleration;

[0078] Figure 4 It is the result of the loop filter predicting and tracking the azimuth angle and elevation angle of the target;

[0079] Figure 5 It is the result of the loop filter predicting and tracking the azimuth angle, elevation angle of the target, and the error between the true target direction and the assumed target direction;

[0080] Figure 6 It is the root mean square error of azimuth angle and elevation angle estimation when the signal-to-noise ratio increases from -5 dB to 25 dB. Specific embodiments

[0081] All the features disclosed in all the embodiments in this specification, or all the steps in the methods or processes implicitly disclosed, except for mutually exclusive features and / or steps, can be combined and / or extended and replaced in any way.

[0082] The specific implementation process of the present invention is as follows:

[0083] As the first aspect of the present invention, a conical scanning angle measurement and tracking method based on a spherical phased array antenna is specifically provided. As shown in Figure 1a and Figure 1b shown, it includes the following steps:

[0084] Step 1: Establish a conical scanning geometric model based on a spherical phased array. As shown in Figure 1, the phased array beam is deflected from the central axis OO' by a small angle ε and rotates around the axis at a constant speed. OS' is the beam axis, B is the trajectory of the antenna's circular motion, and T is the target direction. When the beam is not pointed correctly, within a scanning period, the magnitude of the angle δ between the beam direction and the true target direction and the received satellite signal strength are constantly changing. The position of the satellite is determined based on the changes in β and the satellite signal strength, and the beam direction is adjusted. When the beam points accurately at the target, the axis OT and the axis OO' coincide, at which time β no longer changes and the satellite signal strength is the strongest;

[0085] Step 2: Calculate the modulation coefficient and the scanning trace. According to the pre-set scanning frequency f s 、scanning deflection angle α, number of scanning discrete points N, and the assumed target direction, calculate the modulation coefficient and the scanning trace to determine the conical scanning process of the phased array beam;

[0086] Step 3: Estimate the true target direction. Calculate the transverse and longitudinal errors by determining the power of the phased array received signal, and further estimate the true target direction using the transverse and longitudinal errors;

[0087] Step 4: Real-time track and predict the true target direction. Estimate and predict the true target direction through loop filtering to track the changes in the target direction during long-term variations in real time.

[0088] In a further optional implementation manner, establishing the conical scanning geometric model based on a spherical phased array in Step 1 specifically includes the following steps:

[0089] Step 1-1: As shown in Figure 1, the phased array beam is deflected from the central axis OO' by a small angle ε and rotates around the axis at a constant speed. OS' is the beam axis, B is the trajectory of the antenna's circular motion, and T is the target direction. When the beam is not pointed correctly, within a scanning period, the magnitude of the angle β between the beam direction and the true target direction and the received satellite signal strength are constantly changing. The position of the satellite is determined based on the changes in β and the satellite signal strength, and the beam direction is adjusted. When the beam points accurately at the target, the axis OT and the axis OO' coincide, at which time β no longer changes and the satellite signal strength is the strongest.

[0090] Step 1-2: Determine the scanning frequency f s 、scanning deflection angle α, number of scanning discrete points N, and the assumed target direction. β represents the angle between the beam direction and the true target direction, ε represents the angle between the true target direction and the assumed target direction, and φ0 represents the angle of the true target in the x′O′y′ coordinate system. Without loss of generality, y′ can be selected in the horizontal direction in the plane perpendicular to O′O, and x′ is selected to be perpendicular to both OO′ and y′.

[0091] More specifically, referring to Figures 2 - 3 , the spherical phased array consists of 32 antennas, with a beam width of 20°. The azimuth angle and elevation angle of the target vary within the ranges of 180° and 30° respectively within 12 seconds, the maximum angular velocity is 14° / s, and the maximum angular acceleration is 8° / s². Set the scanning frequency f s = 40 MHz, the scanning deviation angle α = 6°, and the number of scanning discrete points N = 4. In the simulation experiment, the amplitude error and phase error of the received signal are considered to be 0.5 dB and 10° respectively, and they follow a uniform distribution.

[0092] In a further optional implementation manner, for calculating the modulation coefficient and the scanning trace in step 2, it specifically includes the following steps:

[0093] Step 2-1: The beam normalized voltage pattern function F(θ) can be approximately processed using a Gaussian function, and its expression is:

[0094] F(θ) = exp(-0.5wθ 2 ),

[0095] where θ 3dB represents the 3dB beam width of the array. It is easy to verify that F 2 (0.5θ 3dB ) = 0.5.

[0096] Step 2-2: Calculate the derivative of F(θ) as:

[0097] F′(θ) = -wθ exp(-0.5wθ 2 ) = -wθF(θ);

[0098] Substitute the scanning deviation angle α into F(θ) and F′(θ), and the modulation coefficient m can be calculated as:

[0099]

[0100] More specifically, in this embodiment, the calculated modulation coefficient m is:

[0101]

[0102] Step 2-3: Scanning trace calculation. According to the number of scanning points in one period being N, it is considered that the target direction and the true target direction are respectively and The scanning angular extent is α, and it is considered that the target direction is in the zenith direction (0, 90). Calculate the direction of the scanning point as:

[0103]

[0104] More specifically, assuming that the number of scanning points in one period is N = 4, the target direction and the true target direction are respectively and The scanning angle is α = 6°. Assuming that the target direction is at the zenith direction (0, 90), the direction of the scanning point is calculated as follows:

[0105]

[0106] Step 2-4: According to the assumed target direction Rotate to the actual scanning position, and the actual scanning direction is obtained as The directions before and after rotation are respectively represented in the Cartesian coordinate system as d cn and d sn , and their expressions are:

[0107]

[0108]

[0109] Step 2-5: To calculate the desired scanning point direction, only two rotation processes are required: First, rotate d cn counterclockwise around the y-axis by Then rotate counterclockwise around the z-axis by θ0, and the corresponding total rotation matrix is:

[0110]

[0111] Then, d cn after passing through the rotation matrix Γ, d sn is obtained, and its expression is:

[0112] d sn = Γd cn ;

[0113] Step 2-6: According to the solution result d sn , the corresponding scanning point direction

[0114] In a further optional implementation manner, the estimation of the target true direction in step 3 specifically includes the following steps:

[0115] Step 3-1: Calculate the power of the signal at each discrete scanning point as:

[0116]

[0117] where K represents the proportionality coefficient, U0 = KF 2 (α), and U0 can be estimated by U0 = E(U(t)).

[0118] More specifically, in this embodiment, N = 4.

[0119] Step 3-2: Calculate the intermediate variables U I0 and U Q0 respectively. Their specific expressions are:

[0120] U I0 = E(U(t)cos(2πf s t)) = 0.5mU0εcosφ0;

[0121] U Q0 = E(U(t)sin(2πf s t)) = 0.5mU0εsinφ0;

[0122] Step 3-4: Calculate the horizontal and vertical errors respectively as:

[0123]

[0124] where G = 0.5mU0.

[0125] Step 3-5: Using the horizontal and vertical errors ε x and ε y can be directly obtained:

[0126]

[0127] φ0 = atan2(ε y , ε x );

[0128] According to the scanning point track calculation process, it can be known that the target direction estimation should be:

[0129] θ tc = φ0,

[0130] Step 3-6: The target direction estimation vector d tc is:

[0131]

[0132] According to the point track scanning rotation matrix Γ, perform the corresponding rotation on d tc , and the estimated target direction vector d sn can be obtained:

[0133] d ts = Γd tc ;

[0134] According to the solution result d ts , the target direction

[0135] In a further optional embodiment, the real-time tracking and predicting of the true direction of the target in step 4 specifically includes the following steps:

[0136] Step 4-1: The azimuth angle of the target tracked and predicted by the loop filter at the k-th moment is θ ts (k), and its expression is:

[0137] δ θ (k) = δ θ (k - 1) + b0x θ (n) + b1x θ (n - 1);

[0138] θ ts (k) = θ ts (k - 1) + T S δ θ (k);

[0139] Wherein, B L represents the noise bandwidth, and T s is the update period of the loop filter; x θ (k), δ θ (k), θ ts (k) respectively represent the azimuth angle estimation error, the loop filter output result, and the target azimuth angle prediction result at time k.

[0140] Step 4-2: The loop filter tracks the target elevation angle at the k-th moment as and its expression is:

[0141]

[0142] Wherein, respectively represent the elevation angle estimation error, the loop filter output result, and the target elevation angle prediction result at time k.

[0143] More specifically, in this embodiment, the loop filter bandwidth is 2 Hz and the update period is 10 ms. Referring to Figures 4 - 5 , the loop filter prediction tracking results of the target azimuth angle, elevation angle, and the included angle between the true target direction and the assumed target direction are given. At the starting moment of the target movement, since the loop filter is in the tracking and acquisition stage, the target azimuth estimation result error is relatively large. As time increases, the estimation errors of the azimuth angle and elevation angle are less than 0.1°. Therefore, within a certain angular dynamic range, the loop filter can predict and track the azimuth angle and elevation angle of the target in real time, and the angle measurement and tracking accuracy are relatively high.

[0144] Referring to Figure 6, the tracking errors of the target azimuth and elevation angles at different signal-to-noise ratios are given. It can be seen that when the signal-to-noise ratio is lower than 0 dB, the estimation errors of the azimuth and elevation angles are greater than 1°, and the included angle error is greater than 0.5°; when the signal-to-noise ratio is higher than 5 dB, the target angle estimation errors are all less than 0.5°, meeting the requirements of actual engineering.

[0145] As a second aspect of the present invention, based on the above method, a conical scanning angle measurement and tracking device based on a spherical phased array antenna is provided, including:

[0146] A model construction module, used to establish a conical scanning geometric model based on the spherical phased array, and determine the scanning frequency, scanning deflection angle, scanning discrete points, and the assumed target direction;

[0147] A calculation module, used to calculate the modulation coefficient and scanning trace according to the pre-set scanning frequency, scanning deflection angle, scanning discrete points, and the assumed target direction, and determine the conical scanning process of the phased array beam;

[0148] A target true direction estimation module, used to calculate the transverse and longitudinal errors by determining the power of the phased array received signal, and estimate the target true direction using the transverse and longitudinal errors;

[0149] A target true direction tracking and prediction module, used to estimate and predict the target true direction through loop filtering, and track the change of the target direction.

[0150] As a third aspect of the present invention, based on the above device, a conical scanning angle measurement and tracking system based on a spherical phased array antenna is provided.

[0151] In summary, the technical solution of the embodiment of the present invention is applicable to the angle measurement and tracking technology of small phased array antennas. Through this technology, high-precision and low-cost angle measurement and tracking of spherical phased array antennas can be achieved.

[0152] The specific implementation manners of the present invention are not limited to the above manners. The above are only the preferred embodiments of the present invention and the applied technical principles. Those skilled in the art can understand that the present invention is not limited to the specific embodiments described herein. Various obvious changes, adjustments, and substitutions can be made by those skilled in the art without departing from the protection scope of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments. Without departing from the principles and concepts of the present invention, more other equivalent embodiments can be included, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A conical scanning angle measurement and tracking method based on a spherical phased array antenna, characterized in that, Including the following steps: Step 1: Establish a conical scanning geometric model based on a spherical phased array, and determine the scanning frequency, scanning deflection angle, number of scanning discrete points, and assumed target direction; Step 2: Calculate the modulation coefficient and scanning trace according to the pre-set scanning frequency, scanning deflection angle, number of scanning discrete points, and assumed target direction, and determine the conical scanning process of the phased array beam; Step 3: Calculate the transverse and longitudinal errors by determining the power of the phased array received signal, and estimate the true target direction using the transverse and longitudinal errors; Step 4: Estimate and predict the true target direction through loop filtering, and track the change of the target direction.

2. The conical scanning angle measurement and tracking method based on a spherical phased array antenna according to claim 1, wherein In Step 1, the establishment of the conical scanning geometric model based on a spherical phased array specifically includes the following sub-steps: Step 1-1: The phased array beam is deflected from the central axis OO' by an angle ε and rotates around the axis at a constant speed. OS' is the beam axis, B is the trajectory of the antenna's circular motion, and T is the target direction. When the beam is not pointing correctly, within a scanning period, the magnitude of the angle β between the beam direction and the true target direction and the received satellite signal strength are constantly changing. Determine the position of the satellite according to the changes of β and the satellite signal strength, and adjust the beam direction. When the beam points to the target, the axis OT and the axis OO' coincide, at which time β no longer changes and the satellite signal strength is the strongest; Step 1-2: Determine the scanning frequency f s , the scanning declination α, the number of discrete scanning points N, and the assumed target direction. β represents the angle between the beam pointing and the true target direction, ε represents the angle between the true target direction and the assumed target direction, and φ0 represents the angle of the true target in the ′ O′y ′ coordinate system of x 3. The conical scanning angle measurement and tracking method based on a spherical phased array antenna according to claim 2, characterized in that, y ′ It is possible to select the horizontal direction within the plane perpendicular to O ′ O, and x ′ Select the direction perpendicular to both OO′ and y′ simultaneously.

4. The conical scanning angle measurement and tracking method based on a spherical phased array antenna according to claim 2, characterized in that, In step 2, the calculation of the modulation coefficient and the scanning trace specifically includes the following sub-steps: According to the preset scanning frequency f s , scanning deflection angle α, number of scanning discrete points N, and the considered target direction, calculate the modulation coefficient and the scanning trace to determine the phased array beam conical scanning process; Step 2-1: The beam normalized voltage pattern function F(θ) is approximated using a Gaussian function, and its expression is: where θ 3dB represents the 3dB beamwidth of the array; Step 2-2: Calculate the derivative of F(θ) as: F′(θ) = -wθ exp(-0.5wθ 2 ) = -wθF(θ); Substitute the scanning deflection angle α into F(θ) and F ′ (θ), and the modulation coefficient m is calculated as follows: Step 2-3: Scanning point calculation: Given that the number of scanning points in one period is N, assume that the target direction and the true target direction are respectively and The scanning angular width is α. Assume that the target direction is in the zenith direction (0, 90), and calculate the direction of the scanning point as: Step 2-4: According to the considered target direction Rotate to the actual scanning position, and obtain the actual scanning direction as Express the directions before and after rotation in the Cartesian coordinate system as d cn and d sn , and their expressions are as follows: Step 2-5: Calculate the desired scanning point direction and perform two rotation processes: First, rotate d cn counterclockwise about the y-axis by and then rotate counterclockwise about the z-axis by θ0. The corresponding total rotation matrix is: Then, d cn After passing through the rotation matrix Γ, we get d sn , and its expression is: d sn = Γd cn ; Step 2-6: According to the solution result d sn , obtain the corresponding scanning point direction 5. The conical scanning angle measurement and tracking method based on a spherical phased array antenna according to claim 4, wherein In step 2-1, F 2 (0.5θ 3dB ) = 0.

5.

6. The conical scanning angle measurement and tracking method based on a spherical phased array antenna according to claim 2, wherein In Step 3, the calculation of the transverse and longitudinal errors by determining the power of the phased array received signal and the estimation of the true target direction using the transverse and longitudinal errors specifically includes the following sub-steps: Step 3-1: Calculate the power of the signal at each discrete scanning point as: where K represents a proportionality coefficient, and U0 = KF 2 (α), and U0 is estimated by U0 = E(U(t)); Step 3-2: Calculate intermediate variables U I0 and U Q0 respectively. Their specific expressions are as follows: U I0 = E(U(t)cos(2πf s t)) = 0.5mU0εcosφ0; U Q0 = E(U(t)sin(2πf s t)) = 0.5mU0εsinφ0; Step 3-4:: Calculate the transverse and longitudinal errors respectively as: where G = 0.5mU0; Step 3-5: Utilize the horizontal and vertical errors ε x and ε y to directly obtain: φ0 = atan2(ε y , ε x ); According to the scanning point track calculation process, the target direction estimation is as follows: Step 3-6: Target direction estimation vector d tc is as follows: According to the dot trace scanning rotation matrix Γ, perform corresponding rotation on d tc to obtain the estimated target direction vector d sn : d ts = Γd tc ; According to the solution result d ts , the target direction is obtained 7. The conical scanning angle measurement and tracking method based on a spherical phased array antenna according to claim 2, wherein In Step 4, the estimation and prediction of the true target direction through loop filtering and the tracking of the change of the target direction specifically includes the following sub-steps: Step 4-1: The target azimuth angle predicted by loop filtering at the k-th moment is θ ts (k), and its expression is: δ θ ψ(k) = δ θ (k - 1)+b0x θ (n)+b1x θ (n - 1); θ ts ψ(k)=θ ts ψ(k - 1)+T s δ θ (K); It should be noted that in the original text, there seems to be some unclear or incorrect notations. The above translation is based on the best understanding of the provided content. If there are specific context or corrections needed, it would be beneficial for a more accurate translation. Among them, B L represents the noise bandwidth, and T s is the update period of the loop filter; x θ (k), δ θ (k), θ ts (k) represent the azimuth estimation error, the loop filter output result, and the target azimuth prediction result at time k, respectively. Step 4-2: At the k-th moment, the loop filter tracks the target pitch angle as Its expression is: wherein, respectively represent the pitch angle estimation error, the loop filter output result, and the target pitch angle prediction result at time k.

8. A conical scanning angle measurement and tracking device based on a spherical phased array antenna, characterized in that, Including: A model construction module for establishing a conical scanning geometric model based on a spherical phased array, and determining the scanning frequency, scanning deflection angle, number of scanning discrete points, and assumed target direction; A calculation module for calculating the modulation coefficient and scanning trace according to the pre-set scanning frequency, scanning deflection angle, number of scanning discrete points, and assumed target direction, and determining the conical scanning process of the phased array beam; A true target direction estimation module for calculating the transverse and longitudinal errors by determining the power of the phased array received signal, and estimating the true target direction using the transverse and longitudinal errors; A true target direction tracking and prediction module for estimating and predicting the true target direction through loop filtering, and tracking the change of the target direction.

9. A conical scanning angle measurement and tracking system based on a spherical phased array antenna, characterized in that, Including the conical scanning angle measurement and tracking device based on a spherical phased array antenna described in claim 8.

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