A method for position error correction based on maximum likelihood estimation

Abstract

The application discloses a position error correction method based on maximum likelihood estimation, comprising the following steps: acquiring radar error positions of each radar, positions of a correction source at each moment and distances between the radar and the correction source at each moment; obtaining a joint likelihood function of the distance between the radar and the correction source and the radar error position based on a joint likelihood function of the radar error positions of each radar and a joint likelihood function of the distances between each radar and the correction source at each moment; making the joint likelihood function of the distance between the radar and the correction source and the radar error position maximum to obtain a target function which needs to be minimized; and processing the target function by using a particle swarm algorithm to obtain a corrected position of the radar. The method of the application corrects the radar position by using a mobile correction source, does not need the accurate position of the correction source, corrects the radar position error by using the distances between each radar and the correction source at different moments and the error positions and the joint likelihood function of the distance between the radar and the correction source and the radar error position.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a position error correction method based on maximum likelihood estimation. Background Technology

[0002] In a networked radar system, the error in the radar station's own coordinates is a significant factor affecting the system's target positioning accuracy. Each radar has its own position coordinates, often provided by devices like GPS. However, GPS positioning itself has inherent errors; its coarse code accuracy can be as high as 100 meters, while its fine code accuracy can be as low as 10 meters. Furthermore, there are conversion errors during the unified coordinate transformation of each radar. Therefore, the radar's position coordinates are not entirely accurate and deviate from our unknown "true location." This deviation leads to a decrease in the positioning accuracy of the networked radar system. Therefore, it is necessary to correct the radar's position error before it can locate a target.

[0003] Currently, there are three main approaches to correcting radar position errors:

[0004] The first method is based on the traditional GPS position difference method. This method uses a correction source with an accurate and known position to provide valuable information, which is then used to correct the position error of the radar station.

[0005] The second method involves using a known but imprecise correction source to establish the positional relationship between the correction source and the radar, linearizing it, and estimating the radar's positional error using the minimum mean square error criterion, thereby correcting the position of each radar.

[0006] The third method is to use the target position to correct the radar position error. This method first uses the radar error position and a semi-definite relaxation method to roughly estimate the target position. Then, together with all the radar error positions, it is used as the initial iteration point to estimate the joint variable composed of all radar positions and target positions, and obtain the more accurate radar position after correction.

[0007] In existing technologies, radar position error correction methods that utilize precisely known correction sources are difficult to find precisely located correction sources, which is not realistic. Methods that use target position correction require first roughly locating the target position, and then combining the error positions of the target and the radar to correct the radar position. This method is cumbersome, and the target position is determined by the radar with position errors, which affects the final corrected radar position. Therefore, the correction accuracy is low.

[0008] Therefore, improving the accuracy of radar position correction has become an urgent problem to be solved. Summary of the Invention

[0009] To address the aforementioned problems in existing technologies, this invention proposes a position error correction method based on maximum likelihood estimation to improve the accuracy of radar position error correction, thereby enhancing the target tracking capability of networked radar systems. The technical problem to be solved by this invention is achieved through the following technical solution:

[0010] A position error correction method based on maximum likelihood estimation, the position error correction method comprising:

[0011] Obtain the radar error location of each radar, the location of the correction source at each time, and the distance between the radar and the correction source at each time, as measured by GPS.

[0012] Based on the joint likelihood function of the radar error position of each radar and the joint likelihood function of the distance between each radar and the correction source at each time, the joint likelihood function of the distance between the radar and the correction source and the radar error position is obtained.

[0013] Maximize the joint likelihood function of the distance between the radar and the correction source and the radar error location to obtain the objective function that needs to be minimized;

[0014] The objective function is processed using a particle swarm optimization algorithm to obtain the corrected position of the radar.

[0015] In one embodiment of the present invention, the error at the radar error position follows a Gaussian distribution with a mean of 0 and a covariance of Q, and the error at the position of the correction source follows a Gaussian distribution with a mean of 0 and a covariance of Q. u , where, σ x Let σ be the standard deviation of the radar position error in the x-direction. y Let σ be the standard deviation of the radar position error in the y-direction. ux To correct the standard deviation of the source position error in the x-direction, σ uy To correct the standard deviation of the source position error in the y direction.

[0016] In one embodiment of the present invention, a joint likelihood function of the distance between the radar and the correction source and the radar error position is obtained based on the joint likelihood function of the radar error position of each radar and the joint likelihood function of the distance between each radar and the correction source at each time, including:

[0017] Obtain the joint vector s consisting of the true positions of N radars and the joint vector consisting of the radar error positions of N radars. Wherein, the joint vector s is represented as Joint vector Represented as s i Let i be the actual location of the i-th radar. The radar error position of the i-th radar, where T is the transpose;

[0018] Based on the joint vector s and the joint vector The joint likelihood function of the radar error location is obtained;

[0019] Based on the fact that the distance between each radar and the correction source at each time point follows a mean of the true distance and a covariance of σ, 2 Using a Gaussian distribution, construct the joint likelihood function of the distance between each radar and the correction source at each time step;

[0020] The joint likelihood function of the distance between the radar and the correction source and the radar error position is obtained based on the joint likelihood function of the radar error position and the joint likelihood function of the distance between each radar and the correction source at each time.

[0021] In one embodiment of the present invention, the joint likelihood function of the radar error location of the radar is expressed as:

[0022]

[0023] in, Let z be the joint likelihood function of the radar error position of the radar, and z be the joint vector formed by the true position of each radar and the true position of the correction source at each time moment.

[0024] The joint likelihood function of the distance between the radar and the correction source is expressed as:

[0025]

[0026] Where p(d|z) is the joint likelihood function of the distance between the radar and the correction source, d is the joint vector formed by the distances between each radar and the correction source at each time step, K is the total number of time steps, σ is the standard deviation of the laser ranging error, and d ij Let u be the distance between the i-th radar and the correction source at time j. j The true position of the source at time j is the correction point.

[0027] In one embodiment of the present invention, the joint likelihood function of the distance between the radar and the correction source and the radar error location is expressed as:

[0028]

[0029] in, It is the joint likelihood function of the distance between the radar and the correction source and the radar error location.

[0030] In one embodiment of the present invention, maximizing the joint likelihood function of the distance between the radar and the correction source and the radar error location to obtain the objective function to be minimized includes:

[0031] Taking the logarithm of the joint likelihood function of the distance between the radar and the correction source and the radar error location yields the objective function that needs to be minimized.

[0032] In one embodiment of the present invention, the objective function to be minimized is expressed as:

[0033]

[0034] Among them, A ij z = s i -u j B i z = s i .

[0035] In one embodiment of the present invention, a particle swarm optimization algorithm is used to process the objective function to obtain the corrected position of the radar, including:

[0036] Step 4.1: Initialize N within a preset range of the initial radar error position and the position of the correction source. s The position and velocity of each particle;

[0037] Step 4.2: Transform the objective function into a fitness function;

[0038] Step 4.3: Calculate the fitness function value for each particle based on the fitness function.

[0039] Step 4.4: Take the position of each particle as the individual extreme value Pbest, and take the particle with the smallest fitness function value as the population extreme value Gbest.

[0040] Step 4.5: Update the position and velocity of each particle based on the individual extreme value Pbest and the population extreme value Gbest;

[0041] Step 4.6: Based on the fitness function, recalculate the fitness function value for each particle using the updated particle position;

[0042] Step 4.7: Compare the updated fitness function value of each particle with the fitness function value corresponding to the individual extreme value of the particle in history, and select the position with the smallest fitness function value as the current individual extreme value of the particle. Compare the updated fitness function value of all particles with the fitness function value corresponding to the population extreme value of all particles in history, and select the position with the smallest fitness function value as the current population extreme value of all particles.

[0043] Step 4.8: Repeat steps 4.5 to 4.7 for a preset number of iterations to obtain the final population extreme value, and take the final population extreme value as the optimal solution of the objective function;

[0044] Step 4.9: Select the first 2N data points from the optimal solution of the objective function as the correction positions of the radar, where N is the total number of radars.

[0045] In one embodiment of the present invention, the velocity update formula for the particle is:

[0046]

[0047] The position update formula for the particle is:

[0048]

[0049] in, Let n be the velocity of the nth particle in the (k+1)th iteration. Let n be the velocity of the nth particle in the kth iteration. This represents the position of the nth particle during the (k+1)th iteration. Let ω be the position of the nth particle in the kth iteration, c1 and c2 be the learning factors, r1 and r2 be random numbers in [0,1], Pbest be the individual extreme value corresponding to each particle in the history, and Gbest be the group extreme value corresponding to all particles in the history.

[0050] In one embodiment of the present invention, the fitness function is expressed as:

[0051]

[0052] Where σ is the standard deviation of the laser ranging error, K is the total number of moments, and d ij Let Q be the distance between the i-th radar and the correction source at time j, and let A be the covariance. ij z = s i -u j B i z = s i s i Let u be the actual location of the i-th radar. j To correct the true position of the source at time j, The radar error position of the i-th radar is given by z, which is the joint vector formed by the true position of each radar and the true position of the correction source at each time moment.

[0053] The beneficial effects of this invention are:

[0054] This invention utilizes the joint likelihood function of the radar error position of each radar and the joint likelihood function of the distance between each radar and the correction source at each time step to obtain the joint likelihood function of the distance between the radar and the correction source and the radar error position. The problem of maximizing the joint likelihood function of the distance between the radar and the correction source and the radar error position is transformed into an optimization problem. The optimization problem is then solved using a particle swarm optimization algorithm, thereby determining the radar's correction position. The method provided by this invention uses a moving correction source to correct the radar position, eliminating the need to know the precise location of the correction source. It uses the distance and error position between each radar and the correction source at different times to construct the joint likelihood function of the distance between the radar and the correction source and the radar error position to correct the radar position error. This invention transforms the solution of the maximum likelihood function into an optimization problem and solves the optimization problem using a particle swarm optimization algorithm, avoiding the approximation error of transforming a non-convex optimization problem into a convex optimization problem, thus improving the correction accuracy. Attached Figure Description

[0055] Figure 1 This is a schematic flowchart of a position error correction method based on maximum likelihood estimation provided in an embodiment of the present invention;

[0056] Figure 2 The diagram shows the position correction results of three radars using the method of this invention when the standard deviation of the radar position error in each direction is 10m.

[0057] Figure 3 This is a comparison chart of the results of 500 Monte Carlo experiments conducted on three radars using the method of this invention after correction, and before correction, under different standard deviations of radar position error.

[0058] Figure 4 This is a comparison chart of the fusion RMSE performance when the standard deviation of the radar position error in each direction is 10m, after the error position of three radars is corrected by the method of this invention and then the target is fused, and before the correction, the target is directly fused by the three radars and 500 Monte Carlo experiments are performed. Detailed Implementation

[0059] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0060] Example 1

[0061] This invention addresses the low accuracy of existing radar position error correction techniques by proposing a position error correction method based on maximum likelihood estimation. This method aims to improve the accuracy of radar position error correction, thereby enhancing the target tracking capability of networked radar systems. Please see below. Figure 1 , Figure 1This is a flowchart illustrating a position error correction method based on maximum likelihood estimation provided by an embodiment of the present invention. The present invention provides a position error correction method based on maximum likelihood estimation, which includes:

[0062] Step 1: Obtain the radar error position of each radar, the position of the correction source at each time, and the distance between the radar and the correction source at each time as measured by GPS (Global Positioning System). The radar error position is the measured radar position with error.

[0063] Specifically, the initial radar error position of each radar is obtained from GPS. and the position of the correction source at each time point N represents the total number of radars, and K represents the total number of time slots. Due to the inaccuracy of GPS, both radar positions and correction source positions have certain errors. Assume that the radar position error follows a Gaussian distribution with a mean of 0 and a covariance of Q; and that the correction source position error follows a distribution with a mean of 0 and a covariance of Q. u The Gaussian distribution; the distance d from each radar to the correction source at each moment is obtained by laser ranging technology. ij For i = 1, 2, ..., N, j = 1, 2, ..., K, the ranging error has a mean of 0 and a variance of σ. 2 The Gaussian distribution.

[0064] Covariance Q is Covariance Q u for σ x Let σ be the standard deviation of the radar position error in the x-direction. y Let σ be the standard deviation of the radar position error in the y-direction. ux To correct the standard deviation of the source position error in the x-direction, σ uy To correct the standard deviation of the source position error in the y direction.

[0065] Step 2: Based on the joint likelihood function of the radar error position of each radar and the joint likelihood function of the distance between each radar and the correction source at each time, obtain the joint likelihood function of the distance between the radar and the correction source and the radar error position.

[0066] Step 2.1: Obtain the joint vector s consisting of the true positions of N radars and the joint vector consisting of the radar error positions of N radars. Wherein, the joint vector s is represented as Joint vector Represented as s i Let i be the actual location of the i-th radar. The radar error location of the i-th radar. Let z = [s] be the joint vector of the true positions of the correction sources at K time points. T ,u T ] T Let T be the joint vector formed by the true positions of each radar and the true positions of the correction sources at each time step, where T is the transpose.

[0067] Step 2.2: Based on the joint vector s and the joint vector The joint likelihood function of the radar error location is obtained.

[0068] Given that the radar error position depends only on the radar's true position, and that the radar error positions of each radar are independent and all follow a Gaussian distribution with mean equal to the true position and covariance Q, the joint likelihood function of the radar error positions can be expressed as:

[0069]

[0070] in, Let be the joint likelihood function of the radar error location.

[0071] Step 2.3: Based on the fact that the distance between each radar and the correction source at each time point follows a pattern where the mean is the true distance and the covariance is σ... 2 Using a Gaussian distribution, construct the joint likelihood function of the distance between each radar and the correction source at each time step.

[0072] Specifically, it is known that the distance between each radar and the correction source at each time point follows a pattern where the mean is the true distance and the covariance is σ. 2 Given a Gaussian distribution, the joint likelihood function of the distance between each radar and the correction source at each time step can be expressed as:

[0073]

[0074] Where p(d|z) is the joint likelihood function of the distance between the radar and the correction source, d is the joint vector formed by the distances between each radar and the correction source at each time step, and d = [d 11 ,d 12 ,...,d NK ] T d NK Let σ be the distance between the Nth radar and the correction source at time K, and let σ be the standard deviation of the laser ranging error.

[0075] Step 2.4: Based on the joint likelihood function of the radar error position and the joint likelihood function of the distance between each radar and the correction source at each time step, obtain the joint likelihood function of the distance between the radar and the correction source and the radar error position. The joint likelihood function of the distance between the radar and the correction source and the radar error position is expressed as:

[0076]

[0077] in, It is the joint likelihood function of the distance between the radar and the correction source and the location of the radar error.

[0078] Step 3: Maximize the joint likelihood function of the distance between the radar and the correction source and the radar error location to obtain the objective function that needs to be minimized. That is, by maximizing the joint likelihood function, it is transformed into an optimization problem.

[0079] Here, the logarithm of the joint likelihood function of the distance between the radar and the correction source and the radar error location is taken to obtain the objective function that needs to be minimized.

[0080] Specifically, taking the logarithm of the joint likelihood function of the distance between the radar and the correction source and the radar error location, we get:

[0081]

[0082] Where c is a constant term independent of s.

[0083] Let the objective function be:

[0084] Therefore, maximizing the logarithm of the expression is equivalent to minimizing the objective function.

[0085] Define the following matrix:

[0086] A ij =[0 2×2(i-1) I 0 2×2(N+j-i-1) -I 0 2×2(K-j) ], i=1,...,N, j=1,2,...,K

[0087] B i =[0 2×2(i-1) I 0 2×2(N+K-i) ], i = 1, ..., N

[0088] Where I is a 2×2 identity matrix.

[0089] but:

[0090] A ij z = s i -u j

[0091] B i z = s i

[0092] Therefore, the objective function to be minimized is:

[0093]

[0094] Step 4: Use the particle swarm optimization algorithm to process the target function to obtain the radar's corrected position.

[0095] Step 4.1: Initialize the particles. Initialize N within the preset range of the radar's initial error position and the position of the correction source. s The position of each particle and speed Let n be the initial position of the nth particle. Let be the initial velocity of the nth particle.

[0096] Here, the preset range is the vicinity of the initial radar error position and the position of the correction source. This embodiment does not specifically limit this range, and those skilled in the art can set it according to actual needs.

[0097] Step 4.2: Transform the objective function into a fitness function. The initial fitness function is expressed as:

[0098]

[0099] Step 4.3: Calculate the fitness function value for each particle based on the fitness function.

[0100] Step 4.4: Take the position of each particle as the individual extreme value Pbest, and take the particle with the smallest fitness function value as the population extreme value Gbest.

[0101] Step 4.5: Update the position and velocity of each particle based on the individual extreme value Pbest and the group extreme value Gbest.

[0102] Here, the particle velocity update formula is:

[0103]

[0104] The particle position update formula is:

[0105]

[0106] in, Let n be the velocity of the nth particle in the (k+1)th iteration. Let n be the velocity of the nth particle in the kth iteration. This represents the position of the nth particle during the (k+1)th iteration. Let ω be the position of the nth particle in the kth iteration, c1 and c2 be the learning factors, r1 and r2 be random numbers in [0,1], Pbest be the individual extreme value corresponding to each particle in the history, and Gbest be the group extreme value corresponding to all particles in the history.

[0107] Step 4.6: Based on the fitness function, recalculate the fitness function value for each particle using the updated particle positions. The fitness function is expressed as:

[0108]

[0109] Step 4.7: Compare the updated fitness function value of each particle with the fitness function value corresponding to the individual extreme value of that particle in history, and select the position with the smallest fitness function value as the current individual extreme value of that particle. Compare the updated fitness function value of all particles with the fitness function value corresponding to the population extreme value of all particles in history, and select the position with the smallest fitness function value as the current population extreme value of all particles.

[0110] Step 4.8: Repeat steps 4.5 to 4.7 for the preset number of iterations to obtain the final population extreme value, and take the final population extreme value as the optimal solution of the objective function.

[0111] Step 4.9: Select the first 2N data points from the optimal solution of the objective function as the radar's correction position.

[0112] Please see Figure 1 , Figure 2 and Figure 3 , Figure 1 The position correction results of the method of the present invention for three radars when the standard deviation of the position error in each direction of the radar is 10m; Figure 1 This indicates that the radar position corrected using the method of the present invention is closer to the true position. Figure 2 The figure shows the comparison results of 500 Monte Carlo experiments conducted on three radars after correction using the method of this invention, with the radar position errors before correction under different standard deviations of radar position errors. Figure 2 This indicates that the radar position error corrected using the method of the present invention is significantly smaller than the radar position error before correction. Figure 3 The figure shows a comparison of the RMSE performance of the target fusion after the error position of three radars is corrected using the method of this invention and then the target is fused, and before the correction, the target is directly fused by the three radars and 500 Monte Carlo experiments are performed. Figure 3 This indicates that the accuracy of radar position correction followed by target fusion using the method of this invention is closer to the accuracy of target target fusion when the radar has no position error, suggesting that the radar position corrected using this method has better target tracking performance.

[0113] This invention utilizes the joint likelihood function of the radar error position of each radar and the joint likelihood function of the distance between each radar and the correction source at each time step to obtain the joint likelihood function of the distance between the radar and the correction source and the radar error position. The problem of maximizing the joint likelihood function of the distance between the radar and the correction source and the radar error position is transformed into an optimization problem. The optimization problem is then solved using a particle swarm optimization algorithm, thereby determining the radar's correction position. The method provided by this invention uses a moving correction source to correct the radar position, eliminating the need to know the precise location of the correction source. It uses the distance and error position between each radar and the correction source at different times to construct the joint likelihood function of the distance between the radar and the correction source and the radar error position to correct the radar position error. This invention transforms the solution of the maximum likelihood function into an optimization problem and solves the optimization problem using a particle swarm optimization algorithm, avoiding the approximation error of transforming a non-convex optimization problem into a convex optimization problem, thus improving the correction accuracy.

[0114] Networked radar systems integrate multiple radars of different types, enabling multi-radar collaborative detection and fully leveraging the advantages of joint detection to effectively improve the detection capabilities of individual radars. However, in practical networked radar systems, inaccurate localization of the radar's own position results in positional errors for individual radars in addition to inherent measurement errors. This error can cause significant deviations between the tracks of the same target on different radars, leading to ambiguity and difficulties in track correlation and fusion. In severe cases, it can even result in phantom targets, severely degrading the performance of the entire detection system and negating the inherent advantages of networked radar. Therefore, effective radar position error correction methods are crucial for improving the detection capabilities of networked radar systems. The position error correction method based on maximum likelihood estimation provided in this invention can be used to correct radar position errors in networked radar systems, thereby improving the radar's target detection accuracy and enhancing the target tracking capability of the networked radar system.

[0115] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0116] Although this application has been described herein in conjunction with various embodiments, those skilled in the art, by reviewing the accompanying drawings, disclosure, and appended claims, will understand and implement other variations of the disclosed embodiments in carrying out the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. A single processor or other unit can implement several functions listed in the claims. While different dependent claims may recite certain measures, this does not mean that these measures cannot be combined to produce good results.

[0117] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A position error correction method based on maximum likelihood estimation, characterized in that, The position error correction method includes: Obtain the radar error location of each radar, the location of the correction source at each time, and the distance between the radar and the correction source at each time, as measured by GPS. Based on the joint likelihood function of the radar error position of each radar and the joint likelihood function of the distance between each radar and the correction source at each time, the joint likelihood function of the distance between the radar and the correction source and the radar error position is obtained. Maximize the joint likelihood function of the distance between the radar and the correction source and the radar error location to obtain the objective function that needs to be minimized; The objective function is processed using a particle swarm optimization algorithm to obtain the corrected position of the radar; wherein, Based on the joint likelihood function of the radar error position of each radar and the joint likelihood function of the distance between each radar and the correction source at each time, the joint likelihood function of the distance between the radar and the correction source and the radar error position is obtained, including: Get The joint vector formed by the actual positions of the radars and The joint vector formed by the radar error positions of the radar units , where the joint vector Represented as joint vector Represented as , For the first The actual location of the radar No. The location of radar error in the radar system. For transpose; Based on the joint vector and joint vector The joint likelihood function of the radar error location is obtained; Based on the fact that the distance between each radar and the correction source at each time point follows a mean of the true distance and a covariance of... Using a Gaussian distribution, construct the joint likelihood function of the distance between each radar and the correction source at each time step; The joint likelihood function of the distance between the radar and the correction source and the radar error position is obtained based on the joint likelihood function of the radar error position and the joint likelihood function of the distance between each radar and the correction source at each time. The joint likelihood function of the radar error location is expressed as: in, Let be the joint likelihood function of the radar error location of the radar. The joint vector formed by the true position of each radar and the true position of the correction source at each time moment; The joint likelihood function of the distance between the radar and the correction source is expressed as: in, Let be the joint likelihood function of the distance between the radar and the correction source. This is the joint vector formed by the distances between each radar and the correction source at each time point. The total number of moments. This represents the standard deviation of the laser ranging error. For the first Time of the first The distance between the radar and the correction source For the first The true position of the source is constantly corrected.

2. The position error correction method based on maximum likelihood estimation according to claim 1, characterized in that, The error at the radar error location has a mean of 0 and a covariance of . The error of the position of the correction source follows a Gaussian distribution with a mean of 0 and a covariance of . , where, , , For radar position error in x Standard deviation of direction For radar position error in y Standard deviation of direction To correct the source position error in x Standard deviation of direction To correct the source position error in y Standard deviation of direction.

3. The position error correction method based on maximum likelihood estimation according to claim 2, characterized in that, The joint likelihood function of the distance between the radar and the correction source and the location of the radar error is expressed as: in, It is the joint likelihood function of the distance between the radar and the correction source and the radar error location.

4. The position error correction method based on maximum likelihood estimation according to claim 3, characterized in that, Maximizing the joint likelihood function of the distance between the radar and the correction source and the radar error location to obtain the objective function to be minimized includes: Taking the logarithm of the joint likelihood function of the distance between the radar and the correction source and the radar error location yields the objective function that needs to be minimized.

5. The position error correction method based on maximum likelihood estimation according to claim 4, characterized in that, The objective function to be minimized is expressed as: in, , .

6. The position error correction method based on maximum likelihood estimation according to claim 1, characterized in that, The objective function is processed using a particle swarm optimization algorithm to obtain the corrected position of the radar, including: Step 4.1: Initialize within a preset range of the initial radar error position and the position of the correction source. The position and velocity of each particle; Step 4.2: Transform the objective function into a fitness function; Step 4.3: Calculate the fitness function value for each particle based on the fitness function. Step 4.4: Take the position of each particle as its individual extreme value. The particle with the smallest fitness function value among all the particles is taken as the population extreme value. ; Step 4.5: Based on the individual extreme values and group extreme values Update the position and velocity of each particle; Step 4.6: Based on the fitness function, recalculate the fitness function value for each particle using the updated particle position; Step 4.7: Compare the updated fitness function value of each particle with the fitness function value corresponding to the individual extreme value of the particle in history, and select the position with the smallest fitness function value as the current individual extreme value of the particle. Compare the updated fitness function value of all particles with the fitness function value corresponding to the population extreme value of all particles in history, and select the position with the smallest fitness function value as the current population extreme value of all particles. Step 4.8: Repeat steps 4.5 to 4.7 for a preset number of iterations to obtain the final population extreme value, and take the final population extreme value as the optimal solution of the objective function; Step 4.9: Select the top 2 from the optimal solutions of the objective function. One data point is used as the correction position for the radar, wherein, This represents the total number of radars.

7. The position error correction method based on maximum likelihood estimation according to claim 6, characterized in that, The velocity update formula for the particle is: The position update formula for the particle is: in, For the first During the nth iteration n The speed of each particle For the first During the nth iteration n The speed of each particle For the first During the nth iteration n The position of each particle. For the first During the nth iteration n The position of each particle. For inertial weights, As a learning factor, A random number in [0,1] This represents the individual extreme value corresponding to each particle in history. This represents the population extremum corresponding to all particles in history.

8. The position error correction method based on maximum likelihood estimation according to claim 7, characterized in that, The fitness function is expressed as follows: in, Represents the fitness function. This represents the standard deviation of the laser ranging error. The total number of moments. For the first Time of the first The distance between the radar and the correction source For covariance, ， ， ， ， in, for The identity matrix, N This represents the total number of radars.

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