Array pointing error correction method based on the relationship between cooperative target and radar position

Abstract

This invention discloses a radar array pointing error correction method based on the relationship between cooperative targets and radar positions. The implementation steps are as follows: the radar measures all cooperative targets to obtain target measurement parameters; the coordinates of each cooperative target after coordinate transformation are interpolated; a normalized direction vector is constructed; a relational equation is constructed using the interpolated coordinates of each cooperative target and the radar measurements of each cooperative target; the normalized direction vector is expanded using a first-order Taylor series at the array pointing error, and then substituted into the relational equation; the equations formed by all radar measurements of all cooperative targets are combined, and a weighted matrix is ​​calculated. The equations are then solved using the weighted least squares method to obtain the array pointing error. The radar array pointing error correction method designed in this invention considers the array pointing error in the normalized direction vector. The array pointing error is simple and clear in its representation, the solution is faster and more convenient, and the application range is wider.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and more specifically relates to a radar array pointing error correction method based on the relationship between the cooperative target and the radar position. This invention can be applied to correct the angular deviation of the array pointing relative to a reference coordinate system. After correcting the pointing error, the radar's target measurement accuracy can be improved, thereby enhancing the radar's target positioning and tracking performance. Background Technology

[0002] Array pointing error refers to the angular deviation of the radar array pointing relative to the reference coordinate system. Its main cause is the difficulty in aligning the array antenna with the standard position during actual radar deployment. If the error cannot be accurately estimated and corrected, the measurement error of the observed target will increase, thus reducing the radar's target positioning accuracy. Currently, most technologies correct amplitude and phase consistency errors and inter-element coupling errors, while research on array pointing error correction is limited, and most studies focus on pointing error correction methods for uniform linear arrays. However, in reality, radar arrays are mostly area arrays, limiting the application of linear array pointing error correction methods. Existing technologies mostly consider array pointing error in the received signal or antenna pattern function, but the manifestation of array pointing error is complex and difficult to correct. There is no existing method to consider array pointing error in the normalized direction vector of the equation relating the cooperative target and the radar position and to solve for correction. Therefore, this invention provides an array pointing error correction method based on the relationship between the cooperative target and the radar position to solve the above-mentioned technical problems.

[0003] In their paper "A DBF Array Antenna Error Correction Method Based on Phase Difference" (Electronic Information Countermeasures Technology, 2023, 38(02): 71-79), Zhang Huijun et al. proposed a method for correcting the errors of array element position and phase center under different incident angles. The implementation steps are as follows: First, the correction software controls the servo so that the incident direction of the correction signal is the array normal direction. The relative positional relationship under different incident angles is simulated with a pre-set angular step. After the servo is in position, the correction software initiates the channel correction process, obtains the correction data of all channels reported by the processor, and acquires the amplitude and phase difference data of different array elements after correction at all incident angles. Using the theoretical array element spacing as the initial value, a search step is set according to the allowable array element spacing error. Finally, the array element spacing is reset according to the search step. Although this method can complete the correction even with phase center error, channel phase error, and array element position error, its limitation is that it is only applicable to linear arrays with arbitrary array element spacing. In reality, most radar arrays are area arrays, thus limiting the application scope of this method.

[0004] Xi'an University of Electronic Science and Technology disclosed an improved method for correcting the beam pointing error of an active phased array antenna in its patent application, "An Improved Correction Method for Beam Pointing Error of an Active Phased Array Antenna" (Patent Application No. CN 202410043287.X, Publication No. CN 117951433 A). The method involves obtaining the radiation pattern of the phased array antenna elements, obtaining a first function, deriving an improved correction angle formula for a uniform linear array or a uniform rectangular planar array of the array factor radiation pattern, obtaining the correction angle of the uniform linear array or uniform rectangular planar array of the array factor radiation pattern according to the improved correction angle formula, correcting the beam pointing of the array factor radiation pattern according to the correction angle, and multiplying the first function and the array factor radiation pattern function to obtain the actual beam pointing of the corrected composite radiation pattern of the phased array antenna. However, this method still has two shortcomings: First, it solves for the array pointing error by considering the antenna array pattern function, which is relatively complex, and the solution process uses approximation of the function, resulting in some error in the calculated correction angle. Second, this method requires calculating the synthetic pattern function and taking its first derivative, which involves a large amount of computation. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings and deficiencies of the aforementioned radar array pointing error correction techniques by proposing an array pointing error correction method based on the relationship between cooperative targets and radar positions. This method solves the problems of limited application scope, complex form of solving array pointing error using antenna array pattern functions, and large computational load in existing linear array pointing error correction methods.

[0006] The specific approach to achieving the objective of this invention is as follows: This invention utilizes a single radar to simultaneously measure at least one moving cooperative target, obtaining the azimuth, elevation, range, and measurement time for each cooperative target. A cooperative target refers to a target whose true position information can be obtained through other cooperative channels. For example, a target whose precise navigation position is continuously reported by a friendly aircraft via radio. The true position coordinates of all cooperative targets reported in the WGS-84 coordinate system are transformed to the radar's northeast-sky coordinate system. Then, the position coordinates of each cooperative target after coordinate system transformation are interpolated to obtain interpolated cooperative target position coordinates synchronized with the measurement parameters obtained by the radar station. Using the radar's azimuth, elevation, and range measurements of all cooperative targets, as well as the interpolated cooperative target position coordinates, a relationship equation between the radar and the cooperative target positions is constructed. This equation includes a normalized direction vector. The normalized direction vector is composed of trigonometric functions of the azimuth and elevation measurements and is used to represent the direction of the radar phased array antenna or the direction of signal propagation. The normalized direction vector is expanded using a first-order Taylor series at the array pointing error angle, and then substituted back into the constructed relational equation. The updated relational equation is expanded and rearranged. The relational equations formed by the L measurements of each cooperative target by the radar are combined, and the weighted least squares method is used to solve the equations to obtain the corrected array pointing error angle. The array pointing error is the angular deviation of the actual radar array antenna pointing relative to the radar's northeast-sky coordinate system. Since the radar array pointing error is considered in the normalized direction vector of the relational equation, its representation is simple; the array pointing error angle can be obtained by solving the relational equation between the radar and the cooperative target positions using weighted least squares. The solved array pointing error angle is used to correct the radar array pointing, and then the corrected radar is used to measure the cooperative target. Since the cooperative target can provide the true target position, it can be used as a reference for the effectiveness of the array pointing error correction. The effectiveness of the array pointing error correction is verified by comparing the measurement of the cooperative target obtained by the radar after correction with the actual position of the cooperative target. The closer the measurement of the cooperative target obtained by the radar after array pointing error correction is to the actual position provided by the cooperative target, the better the effect of array pointing error correction.

[0007] The specific steps of this invention include the following:

[0008] Step 1: A single radar simultaneously performs L measurements on N cooperative targets to obtain the measurement parameters for each target. The measurement parameters include azimuth measurement, elevation measurement, range measurement, and measurement time; N≥1; L≥2;

[0009] Step 2: Each cooperative target reports its current position coordinates in the WGS-84 coordinate system every t seconds. The position coordinates reported by N cooperative targets in the WGS-84 coordinate system every t seconds are converted to the position coordinates in the radar's northeast-sky coordinate system. The position coordinates of each cooperative target after coordinate system conversion are interpolated to obtain the interpolated position coordinates of the cooperative targets synchronized with the measurement parameters obtained by the radar station; 0 < t ≤ 1.

[0010] Step 3: Construct a normalized direction vector between the radar and each cooperative target, and then use the interpolated position coordinates of each cooperative target and the radar's measurements of each cooperative target to construct a relational equation.

[0011] Step 4: Perform a first-order Taylor expansion on the normalized direction vector at the array pointing error angle, and substitute the normalized direction vector after the first-order Taylor expansion into the relational equation constructed in step 3 to obtain the updated relational equation.

[0012] Step 5: Expand and rearrange the updated relational equations so that the left side of the relational equations is equal to the product of the array pointing error angle and the first derivative of the normalized direction vector at the array pointing error angle.

[0013] Step 6: Combine the relational equations formed by the L measurements of each cooperative target by the radar, calculate the weighting matrix when the radar measures N cooperative targets, and solve the equations using the weighted least squares method to obtain the corrected array pointing error angle.

[0014] Step 7: Determine whether the array pointing error angle is less than or equal to the accuracy set for the array pointing error. If yes, proceed to step 8; otherwise, proceed to step 3.

[0015] Step 8: Correct the radar array pointing error using the array pointing error angle.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] First, since this invention is based on the positional relationship between the radar and the cooperative target to correct the pointing error of the radar array, most of the existing technologies focus on the pointing error correction methods of uniform linear arrays. However, in reality, most radar arrays are area arrays. This invention overcomes the limitations of the application scope of linear array pointing error correction methods, making the application of this invention more extensive and realizing the pointing error correction of the radar array.

[0018] Secondly, since this invention considers the array pointing error in the normalized direction vector of the position relationship equation between the radar and the cooperative target, the array pointing error is simple and clear in form. The array pointing error angle can be obtained by solving the equation using weighted least squares. The array pointing error angle is then used to correct the radar array pointing, avoiding the problems of complex form and difficult solution and correction caused by considering the array pointing error from the antenna array pattern function in the prior art. This makes the solution of the array pointing error in this invention simpler and more convenient. Attached Figure Description

[0019] Figure 1 This is a flowchart of an embodiment of the present invention;

[0020] Figure 2 This is a simulation diagram of the present invention. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0022] Reference Figure 1 The implementation steps of the embodiments of the present invention will be described in further detail below.

[0023] Step 1: A single radar performs 10 simultaneous measurements on 4 cooperative targets to obtain the measurement parameters for each cooperative target. The measurement parameters include azimuth measurement, elevation measurement, range measurement, and measurement time.

[0024] Step 2: Each cooperative target reports its current position coordinates in the WGS-84 coordinate system every 0.5 seconds. The position coordinates of the four cooperative targets reported in the WGS-84 coordinate system every 0.5 seconds are converted to the position coordinates in the radar's northeast-sky coordinate system. The position coordinates of each cooperative target after coordinate system conversion are interpolated to obtain the interpolated position coordinates of the cooperative targets synchronized with the measurement parameters obtained by the radar station.

[0025] The interpolation of the coordinates of each cooperative target position after coordinate system transformation is accomplished by the following formula:

[0026] g n,l =g n,k +(t n,l -t n,k )g n,v

[0027] Among them, g n,l This represents the interpolated position coordinates of the nth cooperative target after the radar's l-th measurement, where 1 ≤ n ≤ 4, 1 ≤ l ≤ 10, and g. n,k This represents the position coordinates of the nth cooperative target after the kth report of its own position coordinates in the WGS-84 coordinate system, transformed to the radar's northeast-sky coordinate system.n,l t represents the time of the l-th measurement by the radar of the n-th cooperative target. n,k G represents the moment when the nth cooperative target reports its own position coordinates in the WGS-84 coordinate system for the kth time. n,v Let v represent the velocity of the nth cooperative target.

[0028] Step 3: Construct a normalized direction vector between the radar and each cooperative target, and then use the interpolated position coordinates of each cooperative target and the radar's measurements of each cooperative target to construct a relational equation.

[0029] The normalized direction vector is as follows:

[0030]

[0031] Where e(·) represents the normalized direction vector, φ n,l Let θ represent the angle measurement vector obtained by the radar during the l-th measurement of the nth cooperative target, ω represent the initial estimate vector of the radar array pointing error angle before correction, Δδ represent the corrected radar array pointing error angle vector, and θ represent the corrected radar array pointing error angle vector. n,l Let θ represent the azimuth angle measurement obtained by the radar for the l-th measurement of the n-th cooperative target, θ represent the initial angle estimate of the radar array pointing error angle before correction, and Δθ represent the corrected radar array pointing error angle. This represents the elevation angle measurement obtained by the radar during the l-th measurement of the nth cooperative target. This represents the initial tilt angle estimate of the radar array pointing error angle before correction. This indicates the tilt angle of the corrected radar array pointing error.

[0032] The relational equation is as follows:

[0033] r n,l e(φ n,l +ω+△δ)=g n,l

[0034] Where, r n,l This represents the distance measurement obtained by the radar during the l-th observation of the nth cooperative target.

[0035] Step 4: Perform a first-order Taylor expansion on the normalized direction vector at the array pointing error angle, and substitute the normalized direction vector after the first-order Taylor expansion into the relational equation constructed in step 3 to obtain the updated relational equation.

[0036] Step 5: Expand and rearrange the updated relational equations so that the left side of the equations equals the product of the array pointing error angle and the first derivative of the normalized direction vector at the array pointing error angle.

[0037] The expansion and shifting operations are performed by the following formula:

[0038]

[0039] Among them, E n,l It represents the first derivative of the normalized direction vector of the radar's l-th observation of the nth cooperative target at the array pointing error angle.

[0040] Step 6: Combine the relational equations formed by the 10 measurements of each cooperative target by the radar, calculate the weighted matrix when the radar measures the four cooperative targets, and solve the equations using the weighted least squares method to obtain the corrected array pointing error angle.

[0041] The relationship equations formed by combining the 10 radar measurements of each cooperative target are accomplished by the following formula:

[0042] E n △δ=r n G n -e n

[0043] Among them, E n Let r be the matrix formed by the first derivative of the normalized direction vector in the relational equation consisting of all 10 radar measurements of the nth cooperative target. n G represents the matrix consisting of range measurements in the relational equation formed by all 10 radar measurements of the nth cooperative target. n e represents the matrix formed by interpolating the position coordinates of the cooperative target in the relational equation consisting of all 10 radar measurements of the nth cooperative target. n This represents the matrix formed by the normalized direction vectors in the relational equation consisting of all 10 radar measurements of the nth cooperative target.

[0044] The weighting matrix for the radar's measurement of four cooperative targets is obtained by the following formula:

[0045] W=R n -1

[0046] Where W represents the weighting matrix when the radar measures four cooperative targets, R n This represents a diagonal matrix composed of the error covariance matrices when the radar measures four cooperative targets.

[0047] The solution to the equation using the weighted least squares method is accomplished by the following formula:

[0048]

[0049] The superscript T indicates the transpose operation.

[0050] Step 7: Determine whether the array pointing error angle is less than or equal to the accuracy set for the array pointing error. If yes, proceed to step 8; otherwise, proceed to step 3.

[0051] Step 8: Correct the radar array pointing error using the array pointing error angle.

[0052] The aforementioned method of obtaining the array pointing error angle and correcting the radar array pointing error refers to:

[0053] θ b =ω+△δ

[0054] Where, θ b This indicates the radar array pointing direction after correction using the array pointing error angle.

[0055] The technical effects of the present invention will be explained in detail below with reference to simulation experiments.

[0056] 1. Simulation experimental conditions.

[0057] The software platform for the simulation experiment of this invention is: Windows 10 operating system and Matlab R2020a.

[0058] The simulation experiment of this invention assumes that there are four targets during the radar array correction process. The radar is assumed to be fixed at position [0m, 0m, 0m]. The initial states of the targets in the radar's northeast-sky coordinate system are [1000m, 100m / s, 3000m, 50m / s, 5000m, 100m / s] and [3000m, 200m / s, 2000m, 100m / s, 8000m, 50m / s], respectively.

[0059] [2000m, 100m / s, 5000m, 200m / s, 4000m, 100m / s], [5000m, 100m / s, 4000m, 50m / s, 3000m, 80m / s]. The radar sampling interval is set to 1 second, and the simulation duration is 10 seconds. The standard deviation of the radar ranging error is 10m, and the standard deviation of the angle measurement error is 0.5°. The radar base coordinate system's deviation from its own northeast-sky coordinate system in terms of array pointing angle is tilt α = 5° and rotation β = 5°.

[0060] 2. Simulation content and result analysis.

[0061] The simulation experiment of this invention is a simulation of the measurement of cooperative targets acquired by the radar before and after the radar array pointing error correction.

[0062] Simulation Experiment 1 of this invention uses the method of this invention to obtain the measurement values ​​of cooperative targets obtained by the radar after radar array pointing error correction and the reported positions of cooperative targets, as well as the measurement values ​​of cooperative targets obtained by the radar before radar array pointing error correction, plotted on the XOY plane as shown below. Figure 2 (a) shows two types of dot patterns and a straight line. Then, the cooperative target measurements obtained by the radar after radar array pointing error correction, the reported positions of the cooperative targets, and the cooperative target measurements obtained by the radar before radar array pointing error correction are plotted on the XOZ plane as shown below. Figure 2 (b) shows two types of dots and a straight line.

[0063] The following combination Figure 2 The simulation diagrams further illustrate the effects of the present invention.

[0064] Figure 2 In (a), the horizontal axis represents the distance between the cooperative target and the radar along the X-axis, in meters, and the vertical axis represents the distance between the cooperative target and the radar along the Y-axis, in meters. Figure 2 In (a), the black straight line represents the actual trajectory of the reported position of each cooperative target, the blue dot represents the position of each cooperative target after the radar measurement of each cooperative target is converted to the XOY plane of the rectangular coordinate system before the radar array pointing error correction, and the red dot represents the position of each cooperative target after the radar measurement of each cooperative target is converted to the XOY plane of the rectangular coordinate system after the radar array pointing error is corrected using the method of the present invention.

[0065] from Figure 2 As can be seen in (a), after the radar array pointing error is corrected by the array pointing error calculated by the method of the present invention, the positions of each cooperative target measured and reported by the radar in the XOY plane are closer to the true values ​​of the cooperative targets than the positions of each cooperative target measured and reported by the radar before correction. The correction effect of the method of the present invention is obvious.

[0066] Figure 2 (b) The horizontal axis represents the distance between the target and the radar in the X-axis direction, in meters, and the vertical axis represents the distance between the target and the radar in the Z-axis direction, in meters. Figure 2 In (b), the black straight line represents the actual trajectory of the reported position of each cooperative target, the blue dot represents the position of each cooperative target after the radar's measurement of each cooperative target is converted to the XOZ plane of the rectangular coordinate system before the radar array pointing error correction, and the red dot represents the position of each cooperative target after the radar's measurement of each cooperative target is converted to the XOZ plane of the rectangular coordinate system after the radar array pointing error is corrected using the method of the present invention.

[0067] from Figure 2As can be seen in (b), after the radar array pointing error is corrected by the array pointing error calculated by the method of the present invention, the measured and reported positions of each cooperative target obtained by the radar in the XOZ plane are closer to the true values ​​of the cooperative targets than the measured and reported positions of each cooperative target obtained by the radar before correction. The correction effect of the method of the present invention is obvious.

Claims

1. A method for correcting array pointing error based on the relationship between cooperative targets and radar positions, characterized in that, Using radar measurements of azimuth, elevation, and range for all cooperative targets, the reported true position coordinates of all cooperative targets are transformed into position coordinates in the radar's northeast-sky coordinate system. A positional relationship equation between the radar and the cooperative targets is constructed, which includes a normalized direction vector, taking into account array pointing errors. The steps of this error correction method are as follows: Step 1: A single radar simultaneously performs L measurements on N cooperative targets to obtain the measurement parameters for each cooperative target. The measurement parameters include azimuth measurement, elevation measurement, range measurement, and measurement time. N≥1; L≥2; Step 2: Each cooperative target reports its current position coordinates in the WGS-84 coordinate system every t seconds. The position coordinates reported by N cooperative targets in the WGS-84 coordinate system every t seconds are converted to the position coordinates in the radar's northeast-sky coordinate system. The position coordinates of each cooperative target after coordinate system conversion are interpolated to obtain the interpolated position coordinates of the cooperative targets synchronized with the measurement parameters obtained by the radar station; 0 < t ≤ 1. Step 3: Construct a normalized direction vector between the radar and each cooperative target, and then use the interpolated position coordinates of each cooperative target and the radar's measurements of each cooperative target to construct a relational equation; Step 4: Perform a first-order Taylor expansion on the normalized direction vector at the array pointing error angle, and then substitute the normalized direction vector after the first-order Taylor expansion into the relational equation constructed in step 3 to obtain the updated relational equation. Step 5: Expand and rearrange the updated relational equations so that the left side of the relational equations is equal to the product of the array pointing error angle and the first derivative of the normalized direction vector at the array pointing error angle. Step 6: Combine the relational equations formed by the L measurements of each cooperative target by the radar, calculate the weighting matrix when the radar measures N cooperative targets, and solve the equations using the weighted least squares method to obtain the corrected array pointing error angle. Step 7: Determine whether the array pointing error angle is less than or equal to the accuracy set for the array pointing error. If yes, proceed to step 8; otherwise, proceed to step 3. Step 8: Correct the radar array pointing error using the array pointing error angle.

2. The array pointing error correction method based on the relationship between cooperative targets and radar positions according to claim 1, characterized in that, The interpolation of the coordinates of each cooperative target position after coordinate system transformation, as described in step 2, is accomplished by the following formula: g n,l =g n,k +(t n,l -t n,k )g n,v Among them, g n,l This represents the position coordinates of the nth cooperative target after interpolation, synchronized with the lth radar measurement, 1≤n≤N, 1≤l≤L, g n,k This represents the position coordinates of the nth cooperative target after the kth report of its own position coordinates in the WGS-84 coordinate system, transformed to the radar's northeast-sky coordinate system. n,l t represents the time of the l-th measurement by the radar of the n-th cooperative target. n,k G represents the moment when the nth cooperative target reports its own position coordinates in the WGS-84 coordinate system for the kth time. n,v Let v represent the velocity of the nth cooperative target.

3. The array pointing error correction method based on the relationship between cooperative targets and radar positions according to claim 2, characterized in that, The normalized direction vector mentioned in step 3 is as follows: Where e(·) represents the normalized direction vector, φ n,l Let θ represent the angle measurement vector obtained by the radar during the l-th measurement of the nth cooperative target, ω represent the initial estimate vector of the radar array pointing error angle before correction, Δδ represent the corrected radar array pointing error angle vector, and θ represent the corrected radar array pointing error angle vector. n,l Let θ represent the azimuth angle measurement obtained by the radar for the l-th measurement of the n-th cooperative target, θ represent the initial angle estimate of the radar array pointing error angle before correction, and Δθ represent the corrected radar array pointing error angle. This represents the elevation angle measurement obtained by the radar during the l-th measurement of the nth cooperative target. This represents the initial tilt angle estimate of the radar array pointing error angle before correction. This indicates the tilt angle of the corrected radar array pointing error.

4. The array pointing error correction method based on the relationship between cooperative targets and radar positions according to claim 3, characterized in that, The relational equation mentioned in step 3 is as follows: r n,l e(φ n,l +ω+△δ)=g n,l Where, r n,l This represents the distance measurement obtained by the radar during the l-th observation of the nth cooperative target.

5. The array pointing error correction method based on the relationship between cooperative targets and radar positions according to claim 4, characterized in that, The expansion and transposition operations described in step 5 are performed by the following formula: Among them, E n,l It represents the first derivative of the normalized direction vector of the radar's l-th observation of the nth cooperative target at the array pointing error angle.

6. The array pointing error correction method based on the relationship between cooperative targets and radar positions according to claim 5, characterized in that, The relationship equations formed by the L measurements of each cooperative target by the radar in step 6 are combined by the following formula: E n △δ=r n G n -e n Among them, E n Let r be the matrix formed by the first derivative of the normalized direction vector in the relational equation consisting of all L measurements of the nth cooperative target by the radar. n G represents the matrix consisting of range measurements in the relational equation formed by all L measurements of the nth cooperative target by the radar. n Let e ​​be the matrix formed by interpolating the position coordinates of the cooperative target in the relational equation consisting of all L measurements of the nth cooperative target by the radar. n This represents the matrix formed by the normalized direction vectors in the relational equation consisting of all L measurements of the nth cooperative target by the radar.

7. The array pointing error correction method based on the relationship between cooperative targets and radar positions according to claim 6, characterized in that, The weighting matrix for calculating radar measurements of N cooperative targets, as described in step 6, is obtained by the following formula: W=R n -1 Where W represents the weighting matrix when the radar measures N cooperative targets, R n This represents a diagonal matrix composed of the error covariance matrices when the radar measures N cooperative targets.

8. The array pointing error correction method based on the relationship between cooperative targets and radar positions according to claim 7, characterized in that, The solution to the equation using the weighted least squares method described in step 6 is accomplished by the following formula: The superscript T indicates the transpose operation.

9. The array pointing error correction method based on the relationship between cooperative targets and radar positions according to claim 8, characterized in that, Step 8, which refers to correcting the radar array pointing error using the array pointing error angle, means: i b =ω+△δ Where, θ b This indicates the radar array pointing direction after correction using the array pointing error angle.

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