Radar monopulse angle evaluation curve fitting method based on cost sensitivity weighting

Abstract

The application discloses a radar single-pulse angle discrimination curve fitting method based on cost sensitivity weighting, which comprises the following steps: 1, measuring sum-difference beam patterns of multiple wave positions in a microwave darkroom or an ideal field environment, and extracting original measurement values of angle discrimination curves in an angle range of interest; 2, constructing a measurement value combination for joint fitting of the angle discrimination function of multiple wave positions; 3, constructing a polynomial fitting optimization problem based on a least square criterion; 4, designing a cost sensitivity function and related parameters according to actual application requirements, and further correcting the cost function; 5, calculating intermediate variables and solving fitting coefficients; and 6, in a radar actual working project, on-line single-pulse angle measurement is completed based on the angle discrimination function obtained through fitting. Through simple parameter setting, the fitting accuracy of targets near the beam pointing direction and targets far away from the beam pointing direction can be flexibly adjusted according to actual application requirements.

Description

A Radar Single-Pulse Angle-Discrimination Curve Fitting Method Based on Cost Sensitivity Weighting Technical Field

[0001] This invention relates to the field of radar monopulse angle measurement technology, and in particular to a radar monopulse angle discrimination curve fitting method based on cost sensitivity weighting. Background Technology

[0002] Monopulse angle measurement is a widely used online angle estimation method in phased array radars. It is simple to implement, reliable, and highly favored in engineering applications. The angle sensitivity curve (also known as the S-curve or angle-sensitive curve) is the basis for monopulse angle measurement and is generally obtained during indoor antenna testing in environments such as microwave anechoic chambers. Its accuracy is crucial to the performance of monopulse angle measurement.

[0003] There are two common applications of angle identification curves: one is to directly store the angle identification curves and perform angle measurement by looking up a table during radar operation; the other is to fit the angle identification curves to a specific function, so that only a small number of coefficients need to be stored in the device, and online angle estimation can be completed by formula calculation.

[0004] The advantage of the former method is that it saves computing resources, but since the angle identification curves of different operating frequencies and different wave positions are different, the required storage is relatively large. Although some systems now divide the angle in the sine space and store the corresponding angle identification curves, so that angle identification curves of different wave positions or even different operating frequencies can be obtained through simple mapping, even if only one angle identification curve needs to be stored, a certain amount of storage space is still required to ensure its accuracy.

[0005] While the latter method saves storage resources, since single-pulse angle measurement needs to be completed online, the angle identification curve fitting function cannot be too complex to avoid consuming too many computational resources. However, although the angle identification curve near the beam pointing is approximately linear, in practical applications (especially for search radar, etc.), it is usually desirable for the fitted angle identification function to be applicable to a wider angle range. In this case, taking the most common third-order polynomial fitting as an example, the cost of expanding the applicable range is to reduce the fitting accuracy near the beam pointing to a certain extent, which is often unacceptable for most radar systems.

[0006] In summary, existing angle-finding curve fitting methods struggle to achieve a good balance between low complexity of the fitting function (which determines the complexity of online angle measurement), high accuracy near the beam pointing direction, and accuracy preservation at edge angles. Consequently, they cannot meet diverse application scenarios and increasingly demanding performance requirements. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of traditional angle detection curve fitting methods for monopulse angle measurement radar, which cannot balance the fitting accuracy near and at the edge of the beam pointing, as well as the computational complexity of the angle measurement process. This invention provides a cost-sensitivity-weighted method for fitting radar monopulse angle detection curves. This method designs and introduces a cost-sensitivity function as the weight of the fitting error cost function at different deflection angles. Based on the idea of ​​weighted least squares, it achieves polynomial fitting of the angle detection curve. This allows for flexible optimization of the fitting accuracy in different deflection angle regions by adjusting the relevant parameters of the cost-sensitivity function, avoiding the loss of angle measurement performance within the main beam range. Furthermore, it can further improve the fitting accuracy and reliability through multi-position measurement and joint fitting. In addition, based on the shape characteristics of the angle detection curve, some fitting terms can be flexibly discarded, improving fitting performance while maintaining a relatively low computational load. The proposed method features simple and efficient offline curve fitting and online angle estimation steps, saving computational and storage resources, and is compatible with one-dimensional linear arrays and two-dimensional planar arrays.

[0008] To achieve the aforementioned objectives of the invention, the technical solution adopted to solve its technical problems is as follows:

[0009] A cost-sensitivity-weighted method for fitting radar single-pulse angle discrimination curves, the specific steps of which are as follows:

[0010] Step 1: Measure the sum and difference beam patterns of multiple wave positions in a microwave anechoic chamber or an ideal outdoor environment, and extract the original measured values ​​of the angle discrimination curve within the range of the angle of interest.

[0011] Step 2: Construct a combination of measurements for multi-wavelength joint fitting of the angle function;

[0012] Step 3: Construct a polynomial fitting optimization problem based on the least squares criterion;

[0013] Step 4: Design the cost sensitivity function and related parameters according to actual application requirements, and further modify the cost function;

[0014] Step 5: Calculate the intermediate variables and solve for the fitting coefficients;

[0015] Step 6: In actual radar operation, single-pulse angle measurement is performed online based on the angle discrimination function obtained by fitting.

[0016] Furthermore, step 1 includes the following:

[0017] In a microwave anechoic chamber or a relatively ideal outdoor environment, measure the sum and difference beam patterns of M positions at a specified operating frequency. Construct an angle discrimination curve using the difference and sum ratio measurements near the beam pointing direction. Let φ be the pointing angle of the m-th (m = 1, 2, ..., M) position. m(Note: φ=0 corresponds to the array normal), the angle discrimination curve at this wavelength contains N values ​​within the angle range of interest (e.g., the 3dB beamwidth at this wavelength or between the two main peaks of the difference beam). m Group of valid measurements {φ mn ,r mn}, where φ mn and r mn Corresponding to the nth (n=1,2,...,N) m ( ) Measurement angles and their corresponding differences and ratios.

[0018] Furthermore, step 2 includes the following:

[0019] To ensure that the angle discrimination curves under different measurement wave positions can be approximately fitted using the same set of coefficients, the beam direction φ of the measured wave position is used. m The cosine value of the difference and ratio r mn Scaling (i.e.) ), and use it with the deviation angle Δφ mn =φ mn -φ m To form a new combination of measurement values If fitting is chosen to be performed in sinusoidal space, then the following should be used: Δφ mn =sinφ mn -sinφ m Construct new combinations of measurement values.

[0020] Furthermore, step 3 includes the following:

[0021] To facilitate fitting and reduce the complexity of single-pulse angle measurement, an L-order polynomial function is used. A unified fitting is performed on the angle identification curves of the above multi-position, and the optimization problem corresponding to the curve fitting under the least squares criterion is:

[0022] Furthermore, step 4 includes the following:

[0023] Considering that tracking radar requires higher angle measurement accuracy near the beam pointing direction, a cost sensitivity function g(c) (-1≤c≤1) and a normalized deflection value are defined. Based on its constructed weight w mn =g(c mn And the cost function h of the above optimization problem is modified as follows: The general design criteria for g(c) are: 0 ≤ g(c) ≤ 1, g(c) = g(-c), g(c) ∝ 1 / |c|, g(0) = 1 and g′(0) = 0. In the above description, This represents all valid measurements Δφ of wave position m. mnThe maximum value in the equation is given by the symbol “∝”, which means “proportional to”. g′(c0) represents the derivative of the function g(c) at c = c0.

[0024] Specifically, two typical examples of g(c) are given here: g(c) = 1 - (1 - t)·e a-a / |c| Or g(c) = 1 - (1 - t)·|c| a The parameter a (a>0) determines the rate at which the weight w decreases as the absolute value of the normalized deflection angle |c| increases, and the parameter t (0≤t≤1) corresponds to the minimum allowable value of the weight w.

[0025] Furthermore, step 5 includes the following:

[0026] Based on the modified optimization problem in step 4, solve for the angle identification curve fitting coefficient k. l (l=0,1,...,L), the closed-form expression of the coefficient vector is [k0k1…k L-1 k L ] T =U -1 v, where: the superscript "T" indicates the matrix transpose operation, and the superscript "-1" indicates the matrix inversion operation (given that U is a symmetric matrix, the computational efficiency of matrix inversion can be improved based on LDLT decomposition, and the relevant calculation methods will not be elaborated here). The relevant variables are specifically represented as follows:

[0027]

[0028]

[0029]

[0030] Specifically, the principle behind the above equation is that by setting the derivative of the cost function with respect to each coefficient to zero, we have:

[0031]

[0032] After sorting, we get:

[0033]

[0034] The corresponding matrix form is U·[k0k1…k] L-1 k L ] T =v, and thus we can obtain the closed-form expression for the coefficient vector as described above.

[0035] Furthermore, based on the shape characteristics of the curve to be fitted, if it is necessary to discard the l-th order term in f(r) (for example, for an odd function, the even-power terms can be discarded), the (l+1)th row and (l+1)th column of the matrix U, and the (l+1)th element of the vector v can be directly deleted. Generally speaking, the angle detection curve is approximately an odd function, the coefficients of the even-order terms are extremely small, and the coefficients of the odd-order terms have an approximately linear relationship with the operating frequency. Therefore, in the indoor field, only the radiation pattern and angle detection curve of some frequencies need to be measured, while the coefficients of the angle detection curve of the unmeasured frequencies can be obtained through interpolation or further function fitting.

[0036] Furthermore, step 6 includes the following:

[0037] Based on the fitting coefficients obtained in steps 1 to 5, the approximate function of the angle-adjustment curve is: Where Δφ = φ - φ0 is the deviation between the target angle φ and the beam pointing angle φ0. The difference and ratio are after scaling. The above steps can be completed offline based on measurement data obtained in a microwave anechoic chamber or under relatively ideal external conditions. Accordingly, the online angle measurement process of the tracking radar in actual operation is as follows: 1) For the range cell of interest, extract and output the beam e. Sum Difference beam output e Diff (This is typically done after pulse compression and target detection), and the difference and ratio r = RorI(e) are calculated. Diff / e Sum ), where the operator RorI() represents taking the real or imaginary part of the complex number (the specific choice should be made according to the weighting method of the antenna array); 2) Combined with the known beam direction φ0, the difference and ratio are scaled, i.e. 3) Obtain the target's angle estimate based on the angle identification function. Right now It should be noted that if fitting is performed in sinusoidal space, then in this step, Δφ = φ - φ0. They need to be modified to Δφ=sinφ-sinφ0,

[0038] By employing the above technical solutions, this invention has the following advantages and positive effects compared with the prior art:

[0039] (1) The proposed method designs and introduces a cost sensitivity function to correct the optimization problem of the angle detection curve fitting. Users can flexibly adjust the fitting accuracy of the beam pointing to nearby targets and targets far away from the beam pointing according to actual application needs through simple parameter settings.

[0040] (2) The proposed method uses the multi-wavelength sum difference beam pattern and angle detection curve measurement results to comprehensively fit the angle detection function, which can further reduce the fitting error and improve the radar single pulse angle measurement accuracy.

[0041] (3) The proposed method for angle estimation is simple and efficient, and does not require storing the angle identification curves of each wave position, saving computational and storage resources and facilitating engineering applications.

[0042] (4) The proposed method is applicable to both arbitrarily arranged one-dimensional linear arrays and regularly arranged two-dimensional planar arrays. Attached Figure Description

[0043] Figure 1 is a flowchart of the method proposed in this invention;

[0044] Figure 2 is a schematic diagram of Example 1 of the cost sensitivity function designed in this invention under different parameter settings;

[0045] Figure 3 is a schematic diagram of Example 2 of the cost sensitivity function designed in this invention under different parameter settings;

[0046] Figure 4 shows a comparison of the angle identification curve fitting results under different cost sensitivity functions;

[0047] Figure 5 shows a comparison of the fitting errors of the angle discrimination curve under different cost sensitivity functions;

[0048] Figure 6 shows the verification results of the method of the present invention based on measured data from a large phased array microwave anechoic chamber. Detailed Implementation

[0049] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] Referring to the flowchart in Figure 1, this embodiment discloses a radar monopulse angle discrimination curve fitting method based on cost sensitivity weighting, including the following steps:

[0051] Step 1: Measure the sum and difference beam patterns of multiple wave positions in a microwave anechoic chamber or an ideal outdoor environment, and extract the original measured values ​​of the angle discrimination curve within the range of the angle of interest;

[0052] Step 2: Construct a combination of measurements for multi-wavelength joint fitting of the angle identification function;

[0053] Step 3: Construct a polynomial fitting optimization problem based on the least squares criterion;

[0054] Step 4: Design the cost sensitivity function and related parameters according to actual application requirements, and further refine the cost function;

[0055] Step 5: Calculate the intermediate variables and solve for the fitting coefficients;

[0056] Step 6: In actual radar operation, single-pulse angle measurement is performed online based on the angle discrimination function obtained by fitting.

[0057] The specific explanations for each of the above steps are as follows:

[0058] Furthermore, step 1 includes the following:

[0059] In a microwave anechoic chamber or a relatively ideal outdoor environment, measure a specified operating frequency and a total of M wave positions (pointing angle φ). m The sum and difference beam patterns (where m = 1, 2, ..., M; φ = 0 corresponds to the array normal) are taken, and the beam pointing to the nearest N is selected. m An angle-determining curve is constructed using the differences and ratios of the measured values. The combination of all valid measured values ​​is denoted as {φ}. mn ,r mn}, φ mn and r mn Corresponding to the nth (n=1,2,...,N) m ( ) Measurement angles and their corresponding differences and ratios.

[0060] Specifically: 1) The pointing angle φ of each wave position to be measured m The scanning range required by the coverage radar can be used, and the interval can be arbitrarily chosen. Taking ±60° scanning as an example, {φ} can be selected. m} is 0°, ±10°, ±20°, ±30°, ±40°, ±50°, ±60°; 2) When extracting the effective measurement value of the angle discrimination curve, the selected angle range can be within 3dB beamwidth (for tracking radar, the angle measurement performance within this segment is of more concern) or larger (for example, the angle between the two main peaks of the difference beam generally corresponds to ±0.7 to 0.8 times the beamwidth).

[0061] Furthermore, step 2 includes the following:

[0062] To ensure that the angle discrimination curves under different measurement wave positions can be approximately fitted using the same set of coefficients, the beam direction φ of the measured wave position is used. m The cosine value of the difference and ratio r mn Scaling (i.e.) ), and use it with the deviation angle Δφ mn =φ mn -φ m To form a new combination of measurement values If fitting is chosen to be performed in sinusoidal space, then the following should be used: Δφ mn =sinφ mn -sinφ m Construct new combinations of measurement values.

[0063] Furthermore, step 3 includes the following:

[0064] To facilitate fitting and reduce the complexity of single-pulse angle measurement, an L-order polynomial function is used. A unified fitting is performed on the angle identification curves of the above multi-position, and the optimization problem corresponding to the curve fitting under the least squares criterion is:

[0065] Specifically, the polynomial order L can be selected based on the desired fitting effect and the allocation of computational resources for angle measurement; typically, L = 3 is chosen. Furthermore, since the angle measurement curve is generally approximated as an odd function, the coefficients of even-order polynomials can be directly set to zero.

[0066] Furthermore, step 4 includes the following:

[0067] Considering that tracking radar has higher requirements for angle measurement accuracy near the beam pointing (especially within the 3dB beamwidth range), a cost sensitivity function g(c) (-1≤c≤1) and a normalized deflection value are defined. Based on its constructed weight w mn =g(c mn The cost function h for the above curve fitting optimization problem is then modified as follows: The general design criteria for g(c) are: 0 ≤ g(c) ≤ 1, g(c) = g(-c), g(c) ∝ 1 / |c|, g(0) = 1 and g′(0) = 0. In the above description, This represents all valid measurements Δφ of wave position m. mn The maximum value in the equation is given by the symbol “∝”, which means “proportional to”. g′(c0) represents the derivative of the function g(c) at c = c0.

[0068] Specifically, two typical examples of g(c) are given here: g(c) = 1 - (1 - t)·e a-a / |c| Or g(c) = 1 - (1 - t)·|c| a In this context, parameter a (a > 0) determines the rate at which the weight w decreases as the absolute value of the normalized deflection angle |c| increases, and parameter t (0 ≤ t ≤ 1) corresponds to the minimum allowable value of the weight w. Generally, the values ​​of parameters a and t should be chosen to ensure that the weight is as close to 1 as possible within the 3dB beamwidth range.

[0069] Furthermore, step 5 includes the following:

[0070] Based on the modified optimization problem in step 4, solve for the angle identification curve fitting coefficient k.l (l=0,1,...,L), the closed-form expression of the coefficient vector is [k0k1…k L-1 k L ] T =U -1 v, where the superscript "T" indicates the matrix transpose operation, the superscript "-1" indicates the matrix inversion operation, and the relevant variables are specifically represented as follows:

[0071]

[0072]

[0073]

[0074] Specifically, given that U is a symmetric matrix, the computational efficiency of matrix inversion can be improved based on LDLT decomposition; the relevant calculation methods will not be elaborated here. Furthermore, based on the shape characteristics of the curve to be fitted, if it is necessary to discard the l-th order terms in f(r) (for example, for odd functions, even-power terms can be discarded), the (l+1)th row and (l+1)th column of the matrix U, and the (l+1)th element of the vector v, can be directly deleted. Taking L=3 as an example, the expression for calculating the coefficient vector is:

[0075]

[0076] If we ignore its second-order terms, the expression for calculating the coefficient vector simplifies to:

[0077]

[0078] If we further ignore its zeroth-order terms, the expression for calculating the coefficient vector simplifies to:

[0079]

[0080] Furthermore, step 6 includes the following:

[0081] Based on the fitting coefficients obtained in steps 1 to 5, the approximate function of the angle-adjustment curve is: Where Δφ = φ - φ0 is the deviation between the target angle φ and the beam pointing angle φ0. The difference and ratio are after scaling. The above steps can be completed offline based on measurement data obtained in a microwave anechoic chamber or under relatively ideal external conditions. Accordingly, the online angle measurement process of the tracking radar in actual operation is as follows: 1) For the range cell of interest, extract and output the beam e. SumDifference beam output e Diff (This is typically done after pulse compression and target detection), and the difference and ratio r = RorI(e) are calculated. Diff / e Sum ), where the operator RorI() represents taking the real or imaginary part of the complex number (the specific choice should be made according to the weighting method of the antenna array); 2) Combined with the known beam direction φ0, the difference and ratio are scaled, i.e. 3) Obtain the target's angle estimate based on the angle identification function. Right now It should be noted that if fitting is performed in sinusoidal space, then in this step, Δφ = φ - φ0. They need to be modified to Δφ=sinφ-sinφ0,

[0082] Specifically, after completing the angle identification curve fitting, the consistency of the angle identification curves for each measured wave position can be verified by comparing the fitted values ​​with the measured values, and the fitting accuracy under different angular deviations (i.e., the level of angle measurement error caused by curve fitting) can be analyzed. Furthermore, since the angle identification curve is approximately an odd function with extremely small coefficients for even-order terms, and the coefficients for odd-order terms have an approximately linear relationship with the operating frequency, only the radiation patterns and angle identification curves for some frequencies need to be measured in the indoor field. The coefficients of the angle identification curves for frequencies not measured can be obtained through interpolation or further function fitting.

[0083] In summary, the cost-sensitivity-weighted radar monopulse angle discrimination curve fitting method proposed in this invention is suitable for analyzing indoor measurement data of phased array radars under the sum-difference beam monopulse angle measurement system. It can flexibly adjust the fitting accuracy for areas near and far from the beam pointing direction according to actual application requirements, and can effectively reduce the angle measurement error caused by angle discrimination curve fitting through comprehensive processing of multi-position measurement results. This method is simple and efficient, saves computational and storage resources, is easy to apply in engineering, and is compatible with arbitrarily arranged one-dimensional linear arrays and regularly arranged two-dimensional planar arrays.

[0084] The effectiveness of the present invention has been verified through the following embodiments, simulation experiments, and measured data.

[0085] Figures 2 and 3 show the curve shapes of the cost sensitivity function in step 4 under different parameter settings, for Examples 1 and 2, respectively. It can be seen that the larger the parameter a, the larger the flat range of the cost sensitivity near c = 0, and the faster the rate of decrease near |c| = 1; the smaller the parameter t, the larger the minimum value of the cost sensitivity (when |c| = 1), meaning that the importance of fitting accuracy at the edges of the angle curve is lower.

[0086] Figure 4 compares the measured and fitted values ​​of the azimuth angle discrimination curve of a phased array radar. The azimuth of this radar is 10°, and the measured values ​​are given by digital simulation. The conventional polynomial fitting method uses third-order least squares fitting, while the proposed method uses the cost sensitivity function Example 1, with parameter t set to 0.1 and parameter a set to 0.2 and 8 respectively. It can be seen that the proposed method has a higher degree of fit near the beam pointing (the deviation angle is close to 0), thus reducing the impact of fitting error on the angle measurement accuracy near the beam pointing (within ±0.5 times the beamwidth in the figure). Although the proposed method has a slightly worse fitting effect at the very edge of the angle discrimination curve when the fitting order is the same, the proposed method can easily add a fifth-order fitting term and discard the fourth-order and second-order fitting terms, thereby further improving the fitting accuracy while maintaining a comparable amount of computation (see the "Proposed Method - Fifth Order" curve in the figure; the corresponding fitting coefficient expression in step 5 can be written in the following form).

[0087]

[0088] Figure 5 shows the fitting error comparison corresponding to Figure 4. It can be seen that the proposed method's fitting accuracy near the beam pointing direction is significantly better than the conventional polynomial fitting method. When parameter t is 0.1 and parameter a is 0.2, the proposed method achieves a fitting accuracy better than 1% of the beamwidth within a range of ±0.5 times the beamwidth; when parameter t is 0.1 and parameter a is 8, the proposed method achieves a fitting accuracy better than 1.35% of the beamwidth within a range of ±0.8 times the beamwidth; if a 5th-order fitting is used (and the 4th and 2nd-order terms are discarded), the proposed method achieves a fitting accuracy better than 0.5% of the beamwidth within a range of ±0.8 times the beamwidth.

[0089] Figure 6 further presents the angle discrimination curve fitting results of the proposed method based on measured data from a microwave anechoic chamber of a large phased array radar. Eleven beam positions were tested at the operating frequency, corresponding to beam pointing angles of 0°, ±10°, ±20°, ±30°, ±45°, and ±60°. The proposed method uses a 5th-order fitting. To maintain the same number of coefficients as the conventional 3rd-order polynomial fitting and avoid increasing the computational load required for angle estimation, the 4th-order and 2nd-order terms were discarded. It can be seen that the proposed method outperforms the conventional polynomial fitting method across the entire angle range.

[0090] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for fitting radar single-pulse angle discrimination curves based on cost sensitivity weighting, characterized in that, include: Step 1: Measure the sum and difference beam patterns of multiple wavefronts in a microwave anechoic chamber or ideal outdoor environment, and extract the original measured values ​​of the angle discrimination curve within the range of angles of interest; Step 2: Construct a combination of measured values ​​for multi-wavefront joint fitting of the angle discrimination function; Step 3: Construct a polynomial fitting optimization problem based on the least squares criterion; Step 4: Design the cost sensitivity function and related parameters according to actual application requirements, and further modify the cost function; Step 5: Calculate the intermediate variables and solve for the fitting coefficients; Step 6: In actual radar operation, complete single-pulse angle measurement online based on the angle discrimination function obtained by fitting.

2. The radar single-pulse angle discrimination curve fitting method based on cost sensitivity weighting according to claim 1, characterized in that, Step 1 includes: measuring the specified operating frequency and common frequency in a microwave anechoic chamber or a pre-defined ideal outdoor environment. The sum and difference beam patterns of each wave position are used to construct an angle discrimination curve by taking the difference and ratio measurements near the beam direction. The nth beam pattern is denoted as... The pointing angle of each wave position is ， ， Corresponding to the array normal, the angle discrimination curve at this wavelength contains a total of [number] within the angle range of interest. Group of valid measurements ,in, and Corresponding to the first Each measurement angle and its corresponding difference and ratio measurement value, 。 3. The radar single-pulse angle discrimination curve fitting method based on cost sensitivity weighting according to claim 2, characterized in that, Step 2 includes: to ensure that the angle discrimination curves under different measurement wave positions are fitted using the same set of coefficients, the beam pointing at the measured wave position is used. cosine values ​​of difference and ratio To scale down, that is and utilize and deviation angle To form a new combination of measurement values If fitting is chosen to be performed in the sinusoidal space, then the following method is used: 、 Construct new combinations of measurement values.

4. The radar single-pulse angle discrimination curve fitting method based on cost sensitivity weighting according to claim 3, characterized in that, Step 3 includes: To facilitate fitting and reduce the complexity of single-pulse angle measurement, the following steps are taken: polynomial function of order ,in, Representing variables The function, In polynomial functions The coefficient of the order term, A unified fitting is performed on the angle identification curves of multiple wave positions. The optimization problem corresponding to the curve fitting under the least squares criterion is as follows: 。 5. The radar single-pulse angle discrimination curve fitting method based on cost sensitivity weighting according to claim 4, characterized in that, Step 4 includes: considering that some applications, such as tracking radar, have higher requirements for angular measurement accuracy near the beam pointing direction, defining a cost sensitivity function. （ ) and normalized deflection angle value ,based on Construct weights The cost function of the optimization problem Revised to ， The general design principles are: ， ， ， and ,in, Indicates wave position All valid measurements The maximum value in, symbol " "indicates "proportional to", Representation function exist The derivative value at the point; the function Pick or , where the parameters （ The weight is determined. The absolute value of the deflection angle after normalization The speed that increases and decreases, parameter （ Corresponding weights The minimum allowable value.

6. The radar single-pulse angle discrimination curve fitting method based on cost sensitivity weighting according to claim 5, characterized in that, Step 5 includes: solving for the angle fitting coefficients based on the modified optimization problem in Step 4. ， The closed-form expression for the coefficient vector is: In this context, the superscript "T" indicates the matrix transpose operation, and the superscript "-1" indicates the matrix inversion operation. For a symmetric matrix, LDLT decomposition is used to improve the computational efficiency of matrix inversion. The relevant variables are represented as follows: ， , The principle behind the above formula is that by setting the derivative of the cost function with respect to each coefficient to zero, we have: After sorting, we get: The corresponding matrix form is This leads to the closed-form expression for the coefficient vector as described above; depending on the shape characteristics of the curve to be fitted, if it is necessary to discard... In Order terms, directly delete the matrix The first in row and number Columns and vectors The first in The elements are used to measure the radiation pattern and angle discrimination curve at only some frequencies in the indoor field, while the angle discrimination curve coefficients at frequencies not measured are obtained by interpolation or further function fitting.

7. The radar monopulse angle discrimination curve fitting method based on cost sensitivity weighting according to claim 6, characterized in that, Step 6 includes: Based on the fitting coefficients obtained in steps 1 to 5, the approximate function of the angle-adjustment curve is... ,in, From the perspective of the target With beam pointing angle The deviation between them The difference and ratio after scaling; the online single-pulse angle measurement implementation method of the tracking radar in actual operation is as follows: 1) For the range cell of interest, extract and output the beam. Difference beam output And calculate the difference and ratio. , where operators 1) To take the real or imaginary part of a complex number; 2) Combined with the known beam direction Scaling the difference and ratio, i.e. 3) Obtain the target's angle estimate based on the angle identification function. ,Right now Additionally, if fitting is performed in the sinusoidal space, the steps in this process... 、 、 Modify them respectively to 、 、 。

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