Amplitude-phase error and position error joint correction method and system based on ADMM

Abstract

The invention discloses an amplitude-phase error and position error joint correction method and system based on ADMM, and the method comprises the steps: building a radar array position error correction model according to a Capon direction finding principle; the constraints of the radar array position error correction model comprise array element position error constraints, phase error upper and lower limit constraints and amplitude-phase error total energy constraints of a radar array; and solving the radar array position error correction model by using an ADMM algorithm to obtain a corrected radar array position error and a corrected radar array amplitude-phase error. Based on an amplitude-phase and position error joint correction algorithm of the ADMM, Capon output power is maximized to realize error correction by applying energy and deviation threshold constraints to amplitude-phase errors and position errors, and the method is not only suitable for a single-correction-source scene but also suitable for a multi-correction-source scene.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and in particular relates to an amplitude-phase error and position error joint correction method and system based on ADMM. Background Art

[0002] Direction of arrival (DOA) is a technique for determining the direction of a signal source by receiving signals through an antenna array. DOA has important applications in wireless communications, radar systems, acoustic imaging, and seismic monitoring. However, the direction-finding performance of many DOA methods, such as the Multiple Signal Classification (MUSIC) algorithm and the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT), is based on the precise known array manifold. However, in practical applications, due to factors such as processing technology and aging, factors such as channel amplitude and phase errors and array element position errors are inevitable. This significantly reduces the performance of DOA algorithms that rely on precise array manifolds, and even causes errors.

[0003] The current radar array error correction algorithms are: (1) Subspace method, such as using the MUSIC spectrum estimation algorithm, based on a single auxiliary signal source, through the pre-compensation of the spatial spectrum direction finding array channel data, to achieve the correction of the array manifold and its covariance matrix. This method only considers the channel amplitude and phase error correction; (2) The least squares method, that is, estimating the error by performing a least squares fit on the received data. This method is simple to calculate, but it is only applicable to scenarios with small errors and small array sizes, and its use scenarios are limited. The maximum likelihood estimation, that is, estimating the error parameters through the maximum likelihood function, has better performance in high noise environments, but it requires assumptions about the statistical characteristics of the error. Summary of the invention

[0004] The purpose of the present invention is to overcome the problems of the existing amplitude-phase correction algorithm, and propose an amplitude-phase error and position error joint correction method and system based on ADMM.

[0005] In order to achieve the above object, the present invention adopts the following technical scheme: The combined correction method of amplitude, phase error and position error based on ADMM includes the following steps: A radar array position error correction model is established according to the Capon direction finding principle, wherein the constraint conditions of the radar array position error correction model include setting an element position error constraint of the radar array, an upper and lower limit constraint of the phase error, and a total energy constraint of the amplitude and phase error; The radar array position error correction model is solved using the ADMM algorithm to obtain the corrected radar array position error and the corrected radar array amplitude and phase errors.

[0006] Furthermore, the element position error constraint of the radar array is as follows:

[0007] in, To consider the position error in the actual scene, the radar array The position of the array element, is the upper limit of position offset, , For the An ideal error-free antenna position, For the The position error of each antenna; The phase error upper and lower limit constraints are as follows:

[0008] in, , Indicates The amplitude error of each antenna is For the The phase error of each antenna is and are the lower and upper bounds of the phase error, respectively. is the number of receiving array elements that make up the uniform linear radar array; The total energy constraint of the amplitude and phase error is as follows:

[0009] in, To consider the existence of amplitude and phase errors in actual scenes The channel amplitude and phase of the radar array with array elements, is the total energy.

[0010] Furthermore, the radar array position error correction model is shown as follows:

[0011] in, is the upper limit of position offset, is the total energy, , is the actual array manifold, For the direction of The receiving steering vector, is the element position error constraint of the radar array, are the upper and lower limits of the phase error, is the total energy constraint of amplitude and phase error.

[0012] Furthermore, the radar array position error correction model is solved using the ADMM algorithm to obtain the corrected radar array position error and the corrected radar array amplitude and phase error as follows: The Lagrangian objective function of the ADMM algorithm is constructed through auxiliary variables and Lagrangian multipliers, and the constraint conditions of the radar array position error are written into the Lagrangian objective function of the ADMM algorithm to construct the radar array position error correction problem optimization model. After initializing the variables of the radar array position error correction problem optimization model, the ADMM algorithm is used to carry out alternating optimization until all variables reach the optimal solution, and the amplitude phase error and position error are output; The alternate optimization is carried out by the ADMM algorithm until all variables reach the optimal solution, including: The variable values ​​of the radar array position error correction problem optimization model are iteratively updated until the ADMM algorithm converges or the maximum number of iterations is reached.

[0013] Furthermore, the Lagrangian objective function is as follows:

[0014] The optimization model of the radar array position error correction problem is as follows:

[0015] in, is an auxiliary variable, The Lagrange multiplier of For custom step length.

[0016] Furthermore, one iteration update of the alternating optimization includes the following steps: Fix the values ​​of the auxiliary variables and Lagrange multipliers of the ADMM algorithm, and solve the optimal solution of the Lagrange objective function of the ADMM algorithm with respect to the remaining unfixed variables; Fix the value of the solved variable and find the optimal solution of the auxiliary variable; Fix the values ​​of all solved variables again and update the values ​​of the Lagrange multipliers; Completes the variable update in one iteration.

[0017] Furthermore, one iteration update of the alternating optimization is specifically as follows: fixed and , solved by bisection method , introduce auxiliary variables , solved by sub-ADMM ; fixed and , solved by the properties of quadratic functions ; Update Lagrange multipliers , the Lagrange multiplier is updated using the following formula:

[0018] Completes the variable update in one iteration.

[0019] The ADMM-based amplitude, phase error and position error joint correction system includes: A correction model establishment module is used to establish a radar array position error correction model according to the Capon direction finding principle, wherein the constraint conditions of the radar array position error correction model include setting an element position error constraint of the radar array, a phase error upper and lower limit constraint, and an amplitude and phase error total energy constraint; The correction error obtaining module is used to solve the radar array position error correction model using the ADMM algorithm to obtain the corrected radar array position error and the corrected radar array amplitude and phase errors.

[0020] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the ADMM-based joint correction method for amplitude, phase and position errors when executing the computer program.

[0021] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the ADMM-based amplitude-phase error and position error joint correction method is implemented.

[0022] Compared with the prior art, the present invention has the following beneficial technical effects: The present invention proposes an amplitude-phase error and position error joint correction method based on ADMM, and an amplitude-phase error and position error joint correction algorithm based on ADMM (Alternating Direction Method of Multipliers). By imposing energy and deviation threshold constraints on the amplitude-phase error and position error, the Capon output power is maximized to achieve error correction. The method is suitable for both single correction source scenarios and multi-correction source scenarios.

[0023] Furthermore, the present invention sets the output of Capon power, constrains the total energy of amplitude and phase errors, and the upper and lower limits of phase errors, establishes a new mathematical model, solves the model, introduces auxiliary variable separation constraint sets, and uses augmented Lagrangian function and ADMM for optimization, which is applied to error correction of radar antenna arrays. By setting auxiliary variables, complex constraints are transferred to the objective function, and finally the position error and amplitude and phase error are output, achieving high-performance joint correction of amplitude and phase errors and position errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The drawings described herein are for explanation purposes only and are not intended to limit the scope of the present invention in any way. In addition, the shapes and proportional dimensions of the components in the drawings are only for illustration purposes to help understand the present invention, and are not intended to specifically limit the shapes and proportional dimensions of the components of the present invention. In the drawings: Figure 1 It is a flow chart of the method for joint correction of amplitude and phase errors and position errors based on ADMM of the present invention.

[0025] Figure 2 It is a structural diagram of the amplitude-phase error and position error joint correction system based on ADMM of the present invention.

[0026] Figure 3 This is an electronic device diagram of the method for jointly correcting amplitude, phase error and position error based on ADMM of the present invention.

[0027] Figure 4 The power spectrum comparison of a single target source before and after correction in an embodiment of the present invention.

[0028] Figure 5 This is a comparison of power spectra of multiple target sources before and after correction in an embodiment of the present invention. DETAILED DESCRIPTION

[0029] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0030] Embodiment 1 See also Figure 1 , the joint correction method of amplitude, phase error and position error based on ADMM includes the following steps: A radar array position error correction model is established according to the Capon direction finding principle, wherein the constraint conditions of the radar array position error correction model include setting an element position error constraint of the radar array, an upper and lower limit constraint of the phase error, and a total energy constraint of the amplitude and phase error; The radar array position error correction model is solved using the ADMM algorithm to obtain the corrected radar array position error and the corrected radar array amplitude and phase errors.

[0031] This embodiment can simultaneously correct the amplitude and phase errors and position errors of the radar array, avoid the error accumulation and mutual influence that may be caused by a single correction, achieve more accurate correction, and thus improve the overall performance of the radar system. The radar array position error correction model is established using the Capon direction finding principle, which can more accurately describe the error characteristics of the radar array. The Capon direction finding principle is based on a high-resolution direction finding algorithm, which can effectively suppress noise and interference and improve the direction finding accuracy. The ADMM algorithm, an efficient iterative optimization algorithm, is used to decompose the original problem into multiple sub-problems for parallel solution, which can significantly speed up the calculation speed. In the radar array error correction, the ADMM algorithm can quickly converge to the optimal solution, thereby saving calculation time and resources.

[0032] The element position error constraints of the radar array are as follows:

[0033] in, To consider the position error in the actual scene, the radar array The position of the array element, is the upper limit of position offset, , For the An ideal error-free antenna position, For the The position error of each antenna; The upper and lower limits of the phase error are as follows:

[0034] in, , Indicates The amplitude error of each antenna is For the The phase error of each antenna is and are the lower and upper bounds of the phase error, respectively. is the number of receiving array elements that make up the uniform linear radar array; The total energy constraints of amplitude and phase errors are as follows:

[0035] in, To consider the existence of amplitude and phase errors in actual scenes The channel amplitude and phase of the radar array with array elements, is the total energy.

[0036] The radar array position error correction model is shown as follows:

[0037] in, is the upper limit of position offset, is the total energy, , is the actual array manifold, For the direction of The receiving steering vector, is the element position error constraint of the radar array, are the upper and lower limits of the phase error, is the total energy constraint of amplitude and phase error.

[0038] The radar array position error correction model is solved using the ADMM algorithm, and the corrected radar array position error and the corrected radar array amplitude and phase error are obtained as follows: The Lagrangian objective function of the ADMM algorithm is constructed through auxiliary variables and Lagrangian multipliers, and the constraint conditions of the radar array position error are written into the Lagrangian objective function of the ADMM algorithm to construct the radar array position error correction problem optimization model. After initializing the variables of the radar array position error correction problem optimization model, the ADMM algorithm is used to carry out alternating optimization until all variables reach the optimal solution, and the amplitude phase error and position error are output; The ADMM algorithm is used to perform alternating optimization until all variables reach the optimal solution, including: The variable values ​​of the radar array position error correction problem optimization model are iteratively updated until the ADMM algorithm converges or the maximum number of iterations is reached.

[0039] The Lagrangian objective function is as follows:

[0040] The optimization model of radar array position error correction problem is as follows:

[0041] in, is an auxiliary variable, The Lagrange multiplier of For custom step length.

[0042] An iterative update of alternating optimization includes the following steps: Fix the values ​​of the auxiliary variables and Lagrange multipliers of the ADMM algorithm, and solve the optimal solution of the Lagrange objective function of the ADMM algorithm with respect to the remaining unfixed variables; Fix the value of the solved variable and find the optimal solution of the auxiliary variable; Fix the values ​​of all solved variables again and update the values ​​of the Lagrange multipliers; Completes the variable update in one iteration.

[0043] An iterative update of alternating optimization is as follows: fixed and , solved by bisection method , introduce auxiliary variables , solved by sub-ADMM ; fixed and , solved by the properties of quadratic functions ; Update Lagrange multipliers , the Lagrange multiplier is updated using the following formula:

[0044] Completes the variable update in one iteration.

[0045] Embodiment 2 See also Figure 2 , A joint correction system of amplitude, phase error and position error based on ADMM. Including: A correction model establishment module is used to establish a radar array position error correction model according to the Capon direction finding principle, wherein the constraint conditions of the radar array position error correction model include setting an element position error constraint of the radar array, a phase error upper and lower limit constraint, and an amplitude and phase error total energy constraint; The correction error obtaining module is used to solve the radar array position error correction model using the ADMM algorithm to obtain the corrected radar array position error and the corrected radar array amplitude and phase errors.

[0046] This embodiment can adapt to different types of radar arrays and error conditions. Whether it is a small-scale radar array or a large-scale radar array, whether it is a simple error condition or a complex error condition, the system can provide an effective correction solution. Due to the use of the Capon direction finding principle and the ADMM algorithm, the system has a strong anti-interference ability. In a noisy and interference environment, the system can still maintain a high correction accuracy and stability.

[0047] Embodiment 3 See also Figure 3An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method for joint correction of amplitude, phase and position errors based on ADMM described in Embodiment 1 is implemented.

[0048] Embodiment 4 A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for jointly correcting amplitude, phase error and position error based on ADMM described in Embodiment 1 is implemented.

[0049] Embodiment 5 This embodiment provides a joint correction method for amplitude and phase errors and position errors based on ADMM. The specific mathematical model and implementation process are described as follows: Considered by A uniform linear array composed of receiving array elements, considering the position error in the actual scene, The position of an array element can be expressed as: (1) in, , For the An ideal error-free antenna position, For the The position error of the antenna.

[0050] In addition to the position error, there is usually a channel amplitude and phase error in practical applications. The channel amplitude and phase error is: (2) in, , Indicates The amplitude error of each antenna is For the The phase error of the antenna.

[0051] Considering both antenna position error and channel amplitude and phase error, the actual array manifold can be expressed as ,in For the direction of The receiving steering vector of . Assume that there is point target, the receiving data model of the narrowband far-field signal can be written as: (3) in, for The vector of reflection coefficients of the targets, is the orientation vector matrix, is additive noise.

[0052] According to the Capon direction finding principle, the peak of the spatial spectrum should appear in the direction of the known reference source, the phase error offset should be within a range, the total amplitude energy is determined, and the position error offset should be within a range. Based on the above considerations, the following correction model is constructed: (4) in, is the upper limit of position offset, is the total energy.

[0053] The Capon direction finding principle, also known as the minimum variance distortionless response (MVDR) direction finding principle, is a high-resolution direction of arrival (DOA) estimation method. The core idea of ​​the Capon algorithm is to achieve high-resolution detection of the desired signal and interference suppression through constrained beamforming under scenarios considering spatial noise and interference signals. The gain in the desired direction is set to a constant using a portion of the degrees of freedom, while the remaining degrees of freedom are used to form a zero point in the interference direction, thereby optimizing the array's received signal power.

[0054] The optimization steps for the above problems are as follows: Step 1: Introduce auxiliary variables To separate the constraints, we introduce the Lagrange multiplier Constructing Lagrangian functions , write the complex constraints in (4) into the objective function; Step 2: Initialize the initial values ​​of each variable in the Lagrangian function and carry out alternating optimization; Step 3: Fix , which can be solved by bisection method , introduce auxiliary variables , through the sub-ADMM to achieve The solution of Step 4: Fix , solved by the properties of quadratic functions ; Step 5: Update the Lagrange multiplier to obtain .

[0055] Repeat the above steps 2 to 5 until the convergence condition is met or the maximum number of iterations is reached, then stop the iteration. Finally, the amplitude and phase errors and position errors are output to achieve the correction of the radar array.

[0056] The following is an explanation of the specific implementation methods of the present invention in conjunction with the aforementioned ADMM computing framework: This embodiment establishes an error correction model with the help of Capon power output, and transfers the constraint conditions to the objective function through Lagrange multipliers and auxiliary variables to optimize the objective function.

[0057] Step 1: First introduce auxiliary variables , at this time, formula (4) can be changed to: (3) Create the Lagrangian function: (5) in, For the corresponding constraints The Lagrange multiplier of User-defined step size.

[0058] Step 2: Initialize the initial values ​​of each variable in the Lagrangian function , carry out alternating optimization; Step 3, Fix ,at this time and is a variable, ignoring additional constants, equation (5) can be written as follows: (6) in, , .

[0059] Error in position Under known circumstances, equation (6) degenerates into the following problem: (7) Expand the above formula, combine similar terms and integrate to get: (8) in, , .

[0060] The Lagrangian function of equation (8) is defined as: (9) Taking the derivative of the above formula and setting it to 0 can obtain the optimal : (10) Considering , you can get information about Function: (11) Optimal Can be obtained from Obtained from the root. Performing feature decomposition, we have: (12) in, is a diagonal matrix of matrix eigenvalues, and ; In addition, the eigenvector Forming the feature matrix .

[0061] then, (13) when , and (14) is a monotonically increasing function, so in the interval There is a unique zero solution in the memory, which can be obtained by simple bisection , and substituting it into (10), we can obtain The optimal solution of .

[0062] get After finding the optimal solution, consider the position Substitute (10) into (6), ignore irrelevant constants, and we can get The update formula is: (15) in,

[0063] To solve equation (15), an auxiliary variable is introduced , then formula (15) can be transformed into: (16) Based on formula (16), the Lagrangian function is introduced: (17) in, For equality constraints The corresponding Lagrange multiplier is, User-defined step size.

[0064] The solution of the augmented Lagrangian function described by equation (17) is still completed by the alternating direction multiplier method. Based on this method, the following iterative steps Step a-Step c can be obtained.

[0065] Step a: Update

[0066] Based on the given , , solve ,at this time is a variable, and the rest are constants. Formula (17) can be equivalent to: (18) Formula (18) is highly nonlinear, so we consider using BFGS to solve it. The specific implementation is to first construct The objective function file can then be solved using the fminunc function in MATLAB.

[0067] Step b: Based on the given , , solve ,at this time is a variable, and the rest are constants. Formula (17) can be changed to: (19) The closed analytical form of formula (19) is: (20) Step c: Update the Lagrange multiplier (twenty one) Step 4, Fix , solve

[0068] At this time only is a variable, and the rest are constants. According to formula (5), (twenty two) Splitting a vector into scalars gives: (twenty three) in, .

[0069] The solution is: (twenty four) Step 5, Update : (25) The mathematical model and optimization process of this embodiment are implemented through the above process, and then verified by computer simulation.

[0070] Experiment 1: Mainly verify the calibration performance of the proposed method for the amplitude and phase errors and array element position errors in the array. The simulation parameters are set as follows: assuming that there is a uniform linear array with 16 array elements; the incident direction of the signal source is 30°, the signal-to-noise ratio is 10dB, and the number of snapshots is 200. The amplitude error at the receiving end is Randomly distributed between The array element position error is randomly distributed between The simulation results of power comparison of single target source before and after correction and power comparison of multi-target source before and after correction are shown as follows: Figure 4 and Figure 5 shown.

[0071] Figure 4 The power spectrum of Capon output before correction, after correction and with known errors is shown in the figure. It can be clearly seen from the figure that when there are amplitude and phase errors and array element position errors, the target pointing is offset and the sidelobe level is extremely high. Comparing the power spectrum after correction with the power spectrum with known errors, it can be seen that the two are close to overlapping, which strongly illustrates the effectiveness of the proposed method.

[0072] Figure 5 Describes the comparison of power spectra before and after correction and with known errors in the case of multiple signal sources. As can be seen from the figure, before correction, the target cannot be pointed correctly and the sidelobe level is raised due to the channel amplitude and phase errors and array element position errors; after correction, the target is pointed correctly and the sidelobe level is suppressed, and the results overlap to a large extent with the known error case. Therefore, it can be proved that the method is still applicable in the case of multiple correction sources and can obtain better results.

[0073] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0074] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0075] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0076] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention is described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation of the present invention can still be modified or replaced by equivalents, and any modification or equivalent replacement that does not deviate from the spirit and scope of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A joint correction method for amplitude, phase error and position error based on ADMM, characterized in that: The following steps are involved: A radar array position error correction model is established according to the Capon direction finding principle, wherein the constraint conditions of the radar array position error correction model include setting an element position error constraint of the radar array, an upper and lower limit constraint of the phase error, and a total energy constraint of the amplitude and phase error; The radar array position error correction model is solved using the ADMM algorithm to obtain the corrected radar array position error and the corrected radar array amplitude and phase errors.

2. The method for joint correction of amplitude, phase error and position error based on ADMM according to claim 1, characterized in that: The element position error constraints of the radar array are as follows: in, To consider the position error in the actual scene, the radar array The position of the array element, is the upper limit of position offset, , For the An ideal error-free antenna position, For the The position error of each antenna; The phase error upper and lower limit constraints are as follows: in, , Indicates The amplitude error of each antenna is For the The phase error of each antenna is and are the lower and upper bounds of the phase error, respectively. is the number of receiving array elements that make up the uniform linear radar array; The total energy constraint of the amplitude and phase error is as follows: in, To consider the existence of amplitude and phase errors in actual scenes The channel amplitude and phase of the radar array with array elements, is the total energy.

3. The method for joint correction of amplitude, phase error and position error based on ADMM according to claim 2, characterized in that: The radar array position error correction model is shown in the following formula: in, is the upper limit of position offset, is the total energy, , is the actual array manifold, For the direction of The receiving steering vector, is the element position error constraint of the radar array, are the upper and lower limits of the phase error, is the total energy constraint of amplitude and phase error.

4. The method for joint correction of amplitude, phase error and position error based on ADMM according to claim 3, characterized in that: The radar array position error correction model is solved using the ADMM algorithm to obtain the corrected radar array position error and the corrected radar array amplitude and phase error as follows: The Lagrangian objective function of the ADMM algorithm is constructed through auxiliary variables and Lagrangian multipliers, and the constraint conditions of the radar array position error are written into the Lagrangian objective function of the ADMM algorithm to construct the radar array position error correction problem optimization model. After initializing the variables of the radar array position error correction problem optimization model, the ADMM algorithm is used to carry out alternating optimization until all variables reach the optimal solution, and the amplitude phase error and position error are output; The alternate optimization is carried out by the ADMM algorithm until all variables reach the optimal solution, including: The variable values ​​of the radar array position error correction problem optimization model are iteratively updated until the ADMM algorithm converges or the maximum number of iterations is reached.

5. The method for joint correction of amplitude, phase error and position error based on ADMM according to claim 4, characterized in that: The Lagrangian objective function is as follows: The optimization model of the radar array position error correction problem is as follows: in, is an auxiliary variable, The Lagrange multiplier of For custom step length.

6. The method for joint correction of amplitude, phase error and position error based on ADMM according to claim 5, characterized in that: One iteration update of the alternating optimization comprises the following steps: Fix the values ​​of the auxiliary variables and Lagrange multipliers of the ADMM algorithm, and solve the optimal solution of the Lagrange objective function of the ADMM algorithm with respect to the remaining unfixed variables; Fix the value of the solved variable and find the optimal solution of the auxiliary variable; Fix the values ​​of all solved variables again and update the values ​​of the Lagrange multipliers; Completes variable updates in one iteration.

7. The method for joint correction of amplitude, phase error and position error based on ADMM according to claim 6, characterized in that: The specific iterative update of the alternating optimization is: fixed and , solved by bisection method , introduce auxiliary variables , solved by sub-ADMM ; fixed and , solved by the properties of quadratic functions ; Update Lagrange multipliers , the Lagrange multiplier is updated using the following formula: Completes variable updates in one iteration.

8. A joint correction system for amplitude, phase error and position error based on ADMM, characterized in that: include: A correction model establishment module is used to establish a radar array position error correction model according to the Capon direction finding principle, wherein the constraint conditions of the radar array position error correction model include setting an element position error constraint of the radar array, a phase error upper and lower limit constraint, and an amplitude and phase error total energy constraint; The correction error obtaining module is used to solve the radar array position error correction model using the ADMM algorithm to obtain the corrected radar array position error and the corrected radar array amplitude and phase errors.

9. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the ADMM-based joint correction method for amplitude, phase, and position errors as described in any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the method for joint correction of amplitude, phase error and position error based on ADMM as described in any one of claims 1 to 7.

Images