Target source positioning method for non-Gaussian noise environment based on maximum entropy criterion

Abstract

The invention discloses a target source positioning method in a non-Gaussian noise environment based on a maximum entropy criterion. The method comprises the following steps: constructing a non-cooperative target source positioning scene; positioning a scene and collecting a distance difference measurement value; constructing a distance difference measurement model according to the obtained distance difference measurement value, and then obtaining a measurement model in a measurement value mixed noise and non-line-of-sight error form according to the distance difference measurement model; processing the distance difference measurement value; constructing a pseudo linear equation set, and forming a weighted least square problem; solving a target position and a weight coefficient vector of the least square problem; the solving method is used for alternately and iteratively solving to obtain a final estimation result; under the condition that the target source is non-cooperative, the coordinate position of the target source is effectively estimated by processing the time difference of arrival measured value obtained by the sensor system, and meanwhile, the influence of non-Gaussian noise on an estimation result is reduced; the method has the advantages of wide application range and good robustness.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication signal positioning, and in particular relates to a method for positioning a target source in a non-Gaussian noise environment based on a maximum entropy criterion. Background Art

[0002] As a positioning method based on time information, Time Difference of Arrival (TDOA) has attracted extensive attention from many researchers because it can provide relatively reliable positioning accuracy and has relatively low equipment cost. The basic principle of TDOA is to measure the arrival time difference of signals from the target to multiple receivers, model the time difference information between different receivers as multiple hyperbolas, and then calculate the specific position of the target by calculating the intersection of these hyperbolas. Due to its simple principle and low equipment cost, it has been widely used in many fields such as wireless communications, radar, sonar, and navigation systems.

[0003] Unlike positioning methods based on signal arrival time (TOA), TDOA relies on time difference information between receivers rather than the absolute arrival time of the signal. Therefore, the TDOA system only needs to ensure clock synchronization between each receiver, without the need for clock synchronization with the target. This feature reduces the complexity of the system and the requirements for clock accuracy. However, the TDOA positioning system also faces great challenges in complex signal propagation environments. Especially in cities, indoors or other complex scenes, the signal may be blocked or reflected by obstacles during transmission, thereby introducing non-line-of-sight (NLOS) errors. This error is usually much larger than general measurement noise and does not conform to the distribution characteristics of Gaussian noise, which seriously affects the positioning accuracy and performance of the positioning system.

[0004] Although many papers have been deeply studied on the target positioning problem in this non-Gaussian noise environment, most methods rely on accurate prior statistical information of measurement errors (OUYANG RW, WONG AK S. An enhanced TOA-based wireless location estimation algorithm for dense NLOS environments [C]. 2009 IEEE Wireless Communications and Networking Conference. IEEE, 2009: 1-6. and CHONG CC, WATANABE F, et al. NLOS identification and weighted least-squares localization for UWB systems using multipath channel statistics [J]. EURASIP Journal on Advances in Signal Processing, 2007, 2008: 1-14), using the statistical distribution, variance and mean of the error. However, these prior information are often difficult to obtain in actual scenarios, especially in dynamic environments, where measurement errors may change over time. To address this problem, researchers have proposed some improved methods, such as the method based on the maximum entropy criterion with variable center (WANG W and et al. Robust TDOA localization based on maximum correntropy criterion with variable center [J]. Signal Processing, 2023, 205: 108860), which can better handle non-Gaussian noise and improve positioning accuracy in the absence of prior information. Although this method solves the non-Gaussian noise problem to a certain extent, its computational complexity is high, requiring multiple iterations between the three sub-problems of target position, kernel function center, and kernel bandwidth, which has high computational complexity. In addition, in the sub-problem of solving the target position, the conventional processing of this method leads to additional unknown variables in the final objective function, which increases the computational complexity and causes multiple local solutions when the Laplace kernel is used as the kernel function. Summary of the invention

[0005] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a target source positioning method in a non-Gaussian noise environment based on the maximum entropy criterion. When the target source is non-cooperative, the arrival time difference measurement value obtained by processing the sensor system can effectively estimate the coordinate position of the target source, while reducing the influence of non-Gaussian noise on the estimation result; it has the advantages of wide application range and good robustness.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A method for locating a target source in a non-Gaussian noise environment based on a maximum entropy criterion comprises the following steps:

[0008] Step 1. Construct a non-cooperative target source localization scenario;

[0009] Step 2. Collect distance difference measurements using the non-cooperative target source localization scenario constructed in step 1;

[0010] Step 3. According to the distance difference measurement value obtained in step 2, a distance difference measurement model is constructed, and then a measurement model in the form of measurement value mixed noise and non-line-of-sight error is obtained according to the distance difference measurement model;

[0011] Step 4. For the measurement model of mixed noise and non-line-of-sight error, the distance difference measurement value is squared and differenced;

[0012] Step 5. According to the results of step 4, the distance difference measurement values ​​are squared and differenced, and a pseudo linear equation system is constructed to form a weighted least squares problem;

[0013] Step 6. Use the maximum entropy criterion framework to solve the target position and weight coefficient vector of the least squares problem described in step 5;

[0014] Step 7. According to the size of the non-cooperative target source positioning scene area, select a custom scaling factor β to scale the positioning scene; then alternately iterate the solution according to the solution method of step 6 to obtain the final estimation result.

[0015] The specific method of step 1 is: in a non-cooperative target source positioning scenario, establish a p dimensional coordinate system as the reference coordinate system, and assume that there is 1 target source and N+1 radar sensors, which are used to receive the target source signal and obtain the signal arrival time. The real coordinate position of the radar sensor is known, and the real coordinate position of the target source is unknown. The clocks between the radar sensors are synchronized, and the relationship between the radar sensor and the target source is non-cooperative. The starting time of the target source transmitting the signal is unknown. Let the real coordinate position of the i-th radar sensor in the reference coordinate system be denoted as s i , where the N+1th radar sensor is recorded as the reference radar sensor, and the actual position of the target source in the reference coordinate system, i.e., the target position, is recorded as u o .

[0016] The specific method of step 2 is: collecting the specific time when the signal emitted by the target source arrives at each radar sensor, subtracting the specific time when the target source emission signal corresponding to the first N radar sensors arrives at each radar sensor from the specific time when the target source emission signal corresponding to the N+1th radar sensor arrives at the N+1th radar sensor, and obtaining the difference between the times; defining the difference between the times as the time difference measurement value; and then obtaining the distance difference measurement values ​​of the first N radar sensors with respect to the N+1th radar sensor according to the time difference measurement value and the known signal propagation speed, and recording the unnoised distance difference measurement value of the i-th radar sensor with respect to the N+1th radar sensor as Wherein, i=1,...,N.

[0017] The specific method of step 3 is: according to the unnoised distance difference measurement value set of the i-th radar sensor with respect to the N+1-th radar sensor in step 2 Construct a distance difference measurement model, which is described as: Then, according to the distance difference measurement model, the measurement model in the form of mixed noise and non-line-of-sight error is obtained: Will Substitution The measurement model in the form of mixed noise and non-line-of-sight error is described as: Among them, “|| ||” means taking the bi-norm, ||u o -s i || represents the actual distance from the target to the i-th radar sensor, ||u o -s N+1 || represents the actual distance from the target to the N+1th radar sensor, s N+1 represents the true coordinate position of the N+1th radar sensor in the reference coordinate system, d i Indicates the noisy distance difference measurement information of the source transmission signal reaching the i-th radar sensor and the N+1-th radar sensor, Indicates d i The non-line-of-sight error, Indicates d i of measurement noise.

[0018] The specific process of step 4 is as follows:

[0019] Measurement model for mixed noise in measurements and non-line-of-sight errors Will Move to the left side of the equation, square both sides and ignore the second-order noise and error terms on the right side of the equation Get the square form corresponding to the i-th radar sensor

[0020] The specific method of step 5 is: eliminate the norm term 2d in the square formula corresponding to the i-th radar sensor i ||u o -s N+1 ||, multiply both sides of the square corresponding to the i+1th radar sensor get

[0021] The square corresponding to the i-th radar sensor The difference between the two equations is: Further sorting out in, ξi is the error model; at this time, It is formulated as a weighted least squares problem and is described as: Among them, min() is the minimization function, (Ay) T WAy is the objective function, y is the optimization variable, and y=[u T ,1] T , u represents the target coordinate position variable, A is the introduced coefficient matrix Using the optimization variable y, the introduced coefficient matrix A, the error model ξ i Expressed as ξ i =A i y; where A i represents the vector composed of the i-th row elements of the introduced coefficient matrix A, s1 represents the real coordinate position of the first radar sensor in the reference coordinate system, s2 represents the real coordinate position of the second radar sensor in the reference coordinate system, and s N-1 represents the true coordinate position of the N-1th radar sensor in the reference coordinate system, s N represents the true coordinate position of the Nth radar sensor in the reference coordinate system, d1 represents the distance difference measurement value obtained between the first radar sensor and the reference radar sensor, d2 represents the distance difference measurement value obtained between the second radar sensor and the reference radar sensor, and d N-1 represents the distance difference measurement value obtained by the N-1th radar sensor and the reference radar sensor, d N represents the distance difference measurement value obtained by the Nth radar sensor and the reference radar sensor; W is the introduced weight matrix, w1 is the weight coefficient corresponding to d1, w N is d N The corresponding weight coefficient; the above weighted least squares problem In the example, the optimization variables y include the target position u o and weight coefficients w1,...,w N .

[0022] The specific method of step 6 is: using the maximum entropy criterion framework to solve the target position u of the least squares problem in step 5 o and weight coefficients w1,...,w N :

[0023] Entropy is used to represent the similarity between two random variables X and Y. The formula is: in, represents the mathematical expectation, κ σ () represents a kernel function with kernel bandwidth σ. There is a Silverman criterion that defines kernel bandwidth as σ = 1.06 × min {σ E,L / 1.34}×M -0.2 ; where σ E is the standard deviation between random variables X and Y, L is the interquartile range between the two variables, and M is the number of samples; when the random variable Y is zero, the random variable X can be expressed as a random error. Assuming that α represents the unknown variable related to the random variable X, the unknown variable is estimated by maximizing entropy. The formula is expressed as

[0024] Combined with the weighted least squares problem described in step 5 The unknown variable α is the optimization variable y in the weighted least squares problem; the mathematical expectation is approximated by a finite number of samples: It is denoted as the maximum entropy problem, where ξ i (y), i = 1, ..., N represents a finite number of error samples;

[0025] Using the Laplace kernel function Further transformation of the maximum entropy problem: Combine and The maximum entropy problem can be summarized as: The constant coefficient It has nothing to do with the optimization variable y and will be ignored in the following. According to the error function expression ξ in step 5 i =A i y, the objective function is further written as Based on the properties of convex conjugate functions, the weight matrix W is written as a weight coefficient vector w = [w1, ..., w N ] T , the objective function It is further transformed into a new augmented problem of solving the weight coefficient vector w, expressed as Among them, w i is d i The corresponding weight coefficient is, for The convex conjugate function of Substitute into the objective function get at this time Jointly solve the optimization variable y and the weight coefficient vector w, expressed as a joint optimization problem in, Represents the functional form of the optimization variable y and the weight coefficient vector w; due to the joint optimization problem It is difficult to solve, so the formula is transformed into two sub-problems and solved iteratively in sequence:

[0026] Sub-question 1:

[0027] When the weight coefficient vector w is known, the joint optimization problem can be simplified to in, Indicates w i At this time, since the joint optimization problem contains an absolute value term, it is also a non-convex problem. By introducing the intermediate variable τ i As |A i The upper bound of y| is obtained, and the joint optimization problem is transformed into a convex problem for solution; the final optimization problem of subproblem 1 is expressed as: Among them, st means subject to the constraint; after solving the final optimization problem of subproblem 1, the solution result is recorded as Represents the estimated value of the optimization variable y;

[0028] Sub-question 2:

[0029] When the optimization variable y is known, the joint optimization problem Simplified to At this time, the weight coefficient vector w has a corresponding closed-form solution The solution result is recorded as w, which represents the estimated value of the weight coefficient vector w.

[0030] The specific method of step 7 is: according to the size of the positioning scene area, a scaling factor β is selected by user-defined to scale the positioning scene;

[0031] Then set Solve step 6 subproblem 1 The results are directly brought into Solve subproblem 2 in step 6; solve subproblem 1 and subproblem 2 by alternating iterations. When the difference between the two iterative changes is less than 10 -10 Or when the number of iterations reaches 10, the final estimation result is considered to be obtained, that is, the optimal estimation value of the target source coordinate position, which is recorded as u * ,in, y * is the optimal estimate of y, Indicated by y * The subvector consisting of the 1st to pth elements of ; represents the estimated value of the weight coefficient vector w1, represents the estimated value of the weight coefficient vector w2, Represents the weight coefficient vector w N The estimated value of d2 is w2, and w2 is the weight coefficient vector corresponding to d2.

[0032] Compared with the prior art, the present invention has the following advantages:

[0033] 1) Most existing methods for target source positioning consider that the measurement noise follows Gaussian distribution, which leads to limited application scenarios of the proposed positioning methods; however, the present invention considers that the system works in a non-Gaussian environment, and proposes a corresponding positioning analysis method for this environment. By using the maximum entropy criterion framework, for the positioning scenario of non-Gaussian noise, the target position and weight coefficient are both treated as unknown quantities, and the two sub-problems are solved alternately in sequence. After the sub-problems converge, an estimate of the target position is obtained. This method is also applicable to the positioning scenario of Gaussian noise, and has a wide range of applicability and good robustness.

[0034] 2) The present invention considers the numerical relationship between the measurement values ​​from different radar sensors, and utilizes the characteristic that the measurement values ​​contain common norm terms through step 5 to perform difference to eliminate the non-convex norm terms, thereby simplifying subproblem 1 in step 6 and avoiding the problem that the algorithm converges to the local optimum due to the non-convex norm terms during the solution of subproblem 1, so that the positioning problem is suitable for solving using the Laplace kernel, which has a faster attenuation speed than solving it using the Gaussian kernel.

[0035] 3) The simulation experimental results of the method of the present invention show that the estimation accuracy of the target source position of the proposed method is much better than that of the positioning method for ordinary Gaussian noise, indicating that the method of the present invention has better performance in mean square error (MSE).

[0036] In summary, when the target source is non-cooperative, the present invention can effectively estimate the coordinate position of the target source by processing the arrival time difference measurement value obtained by the radar sensor system, while reducing the influence of non-Gaussian noise on the estimation result; it has the advantages of wide application range and good robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A comparison chart of the logarithmic mean square error (MSE) of the coordinate position estimation of the non-cooperative target source when N=6 between the method of the present invention (MCC) and the two-step weighted least squares (TSWLS) as the signal-to-noise ratio changes is given.

[0038] Figure 2 A comparison chart of the logarithmic mean square error (MSE) of the coordinate position estimation of the non-cooperative target source between the method of the present invention (MCC) and the two-step weighted least squares (TSWLS) when SNR=1 as the non-line-of-sight error upper limit changes is given.

[0039] Figure 3 A comparison chart of the logarithmic mean square error (MSE) of the coordinate position estimation of the non-cooperative target source when SNR=1 between the method of the present invention (MCC) and the two-step weighted least squares (TSWLS) is given as the number of sensors changes.

[0040] Figure 4 The figure is a flowchart of the method of the present invention. DETAILED DESCRIPTION

[0041] The present invention will be further described in detail below with reference to the accompanying drawings.

[0042] See also Figure 4 , a target source localization method in a non-Gaussian noise environment based on the maximum entropy criterion, comprising the following steps:

[0043] Step 1. Construct a non-cooperative target source positioning scenario; the specific method is:

[0044] In a non-cooperative target source localization scenario, establish a p The coordinate system of the dimension is used as the reference coordinate system, and it is assumed that there is a target source and N+1 A radar sensor is used to receive the target source signal and obtain the signal arrival time. The real coordinate position of the radar sensor is known, while the real coordinate position of the target source is unknown. The clocks between the radar sensors are synchronized, and the relationship between the radar sensor and the target source is non-cooperative. The start time of the target source transmitting the signal is unknown. Let the real coordinate position of the i-th radar sensor in the reference coordinate system be denoted as s i , where the N+1th radar sensor is recorded as the reference radar sensor, and the actual position of the target source in the reference coordinate system, i.e., the target position, is recorded as u o .

[0045] Step 2. Collect distance difference measurements using the non-cooperative target source localization scenario constructed in step 1; the specific method is:

[0046] The specific time when the signal emitted by the target source reaches each radar sensor is collected, and the specific time when the target source emission signal corresponding to the first N radar sensors reaches each radar sensor is subtracted from the specific time when the target source emission signal corresponding to the N+1th radar sensor reaches the N+1th radar sensor to obtain the difference between the times; the difference between the times is defined as the time difference measurement value; then, according to the time difference measurement value and the known signal propagation speed, the distance difference measurement value of the first N radar sensors with respect to the N+1th radar sensor is obtained, and the unnoised distance difference measurement value of the i-th radar sensor with respect to the N+1th radar sensor is recorded as Wherein, i=1,...,N.

[0047] Step 3. According to the distance difference measurement value obtained in step 2, a distance difference measurement model is constructed, and then a measurement model in the form of measurement value mixed noise and non-line-of-sight error is obtained according to the distance difference measurement model; the specific method is:

[0048] According to the unnoised distance difference measurement value set of the i-th radar sensor with respect to the N+1-th radar sensor in step 2 Construct a distance difference measurement model, which is described as: Then, according to the distance difference measurement model, the measurement model in the form of mixed noise and non-line-of-sight error is obtained: Will Substitution The measurement model in the form of mixed noise and non-line-of-sight error is described as: Among them, “|| ||” means taking the bi-norm, ||u o -s i || represents the actual distance from the target to the i-th radar sensor, ||u o -s N+1 || represents the actual distance from the target to the N+1th radar sensor, s N+1 represents the true coordinate position of the N+1th radar sensor in the reference coordinate system, d i Indicates the noisy distance difference measurement information of the source transmission signal reaching the i-th radar sensor and the N+1-th radar sensor, Indicates d i The non-line-of-sight error, Indicates d i of measurement noise.

[0049] Step 4. For the measurement model of mixed noise and non-line-of-sight error, the distance difference measurement value is squared and differenced. The specific process is as follows:

[0050] Measurement model for mixed noise in measurements and non-line-of-sight errors Will Move to the left side of the equation, square both sides and ignore the second-order noise and error terms on the right side of the equation Get the square form corresponding to the i-th radar sensor

[0051] Step 5. According to the results of step 4, the distance difference measurement values ​​are squared and differenced, and a pseudo-linear equation system is constructed to form a weighted least squares problem; the specific method is:

[0052] Eliminate the norm term 2d in the square formula corresponding to the i-th radar sensor i ||u o -s N+1 ||, multiply both sides of the square corresponding to the i+1th radar sensor get

[0053] The square corresponding to the i-th radar sensor The difference between the two equations is Further sorting out in, ξ iis the error model; at this time, It is formulated as a weighted least squares problem and is described as: Among them, min() is the minimization function, (Ay) T WAy is the objective function, y is the optimization variable, and y=[u T ,1] T , u represents the target coordinate position variable, A is the introduced coefficient matrix Using the optimization variable y, the introduced coefficient matrix A, the error model ξ i Expressed as ξ i =A i y; where A i represents the vector composed of the i-th row elements of the introduced coefficient matrix A, s1 represents the real coordinate position of the first radar sensor in the reference coordinate system, s2 represents the real coordinate position of the second radar sensor in the reference coordinate system, and s N-1 represents the true coordinate position of the N-1th radar sensor in the reference coordinate system, s N represents the true coordinate position of the Nth radar sensor in the reference coordinate system, d1 represents the distance difference measurement value obtained between the first radar sensor and the reference radar sensor, d2 represents the distance difference measurement value obtained between the second radar sensor and the reference radar sensor, and d N-1 represents the distance difference measurement value obtained by the N-1th radar sensor and the reference radar sensor, d N represents the distance difference measurement value obtained by the Nth radar sensor and the reference radar sensor; W is the introduced weight matrix, w1 is the weight coefficient corresponding to d1, w N is d N The corresponding weight coefficient; the above weighted least squares problem In the example, the optimization variables y include the target position u o and weight coefficients w1,...,w N .

[0054] Step 6. Use the maximum entropy criterion framework to solve the target position and weight coefficient vector of the least squares problem described in step 5; the specific method is:

[0055] Use the maximum entropy criterion framework to solve the target position u of the least squares problem described in step 5 o and weight coefficients w1,...,w N :

[0056] Entropy is used to represent the similarity between two random variables X and Y. The formula is: in, represents the mathematical expectation, κ σ() represents a kernel function with kernel bandwidth σ. There is a Silverman criterion that defines kernel bandwidth as σ = 1.06 × min {σ E ,L / 1.34}×M -0.2 ; where σ E is the standard deviation between random variables X and Y, L is the interquartile range between the two variables, and M is the number of samples; when the random variable Y is zero, the random variable X can be expressed as a random error. Assuming that α represents the unknown variable related to the random variable X, the unknown variable is estimated by maximizing entropy. The formula is expressed as

[0057] Combined with the weighted least squares problem described in step 5 The unknown variable α is the optimization variable y in the weighted least squares problem; the mathematical expectation is approximated by a finite number of samples: It is denoted as the maximum entropy problem, where ξ i (y), i = 1, ..., N represents a finite number of error samples;

[0058] Using the Laplace kernel function Further transformation of the maximum entropy problem: Combine The maximum entropy problem can be summarized as: The constant coefficient It has nothing to do with the optimization variable y and will be ignored in the following. According to the error function expression ξ in step 5 i =A i y, the objective function is further written as Based on the properties of convex conjugate functions, the weight matrix W is written as a weight coefficient vector w = [w1, ..., w N ] T , the objective function It is further transformed into a new augmented problem of solving the weight coefficient vector w, expressed as Among them, w i is d i The corresponding weight coefficient is, for The convex conjugate function of Substitute into the objective function get at this time Jointly solve the optimization variable y and the weight coefficient vector w, expressed as a joint optimization problem in, Represents the functional form of the optimization variable y and the weight coefficient vector w; due to the joint optimization problem It is difficult to solve, so the formula is transformed into two sub-problems and solved iteratively in sequence:

[0059] Sub-question 1:

[0060] When the weight coefficient vector w is known, the joint optimization problem can be simplified to in, Indicates w i At this time, since the joint optimization problem contains an absolute value term, it is also a non-convex problem. By introducing the intermediate variable τ i As |A i The upper bound of y| is obtained, and the joint optimization problem is transformed into a convex problem for solution; the final optimization problem of subproblem 1 is expressed as: Among them, st means subject to the constraint; after solving the final optimization problem of subproblem 1, the solution result is recorded as Represents the estimated value of the optimization variable y;

[0061] Sub-question 2:

[0062] When the optimization variable y is known, the joint optimization problem Simplified to At this time, the weight coefficient vector w has a corresponding closed-form solution The solution result is Represents the estimated value of the weight coefficient vector w.

[0063] Step 7. According to the size of the non-cooperative target source positioning scene area, select a custom scaling factor β to scale the positioning scene; then alternately iterate the solution according to the solution method of step 6 to obtain the final estimation result; the specific method is:

[0064] According to the size of the positioning scene area (the sensor location in the simulation is in the range of [-2.5, 2.5] km × [-2.5, 2.5] km, and the non-cooperative source target location is in the range of [-0.5, 0.5] km × [-0.5, 0.5] km), a custom scaling factor β is selected to scale the positioning scene;

[0065] Then set Solve step 6 subproblem 1 The results are directly brought into Solve subproblem 2 in step 6; solve subproblem 1 and subproblem 2 by alternating iterations. When the difference between the two iterative changes is less than 10 -10 Or when the number of iterations reaches 10, the final estimation result is considered to be obtained, that is, the optimal estimation value of the target source coordinate position, which is recorded as u * ,in, y * is the optimal estimate of y, Indicated by y * The subvector consisting of the 1st to pth elements of ; represents the estimated value of the weight coefficient vector w1, represents the estimated value of the weight coefficient vector w2, Represents the weight coefficient vector w N The estimated value of d2 is w2, and w2 is the weight coefficient vector corresponding to d2.

[0066] Simulation experiment:

[0067] In order to verify the feasibility and effectiveness of the method of the present invention, a simulation test was carried out on the method of the present invention.

[0068] Assume that there are N+1 radar sensors and 1 non-cooperative source target in two-dimensional space, where the sensor position is randomly generated in the range of [-2.5, 2.5] km × [-2.5, 2.5] km, and the non-cooperative source target position is randomly generated in the range of [-0.5, 0.5] km × [-0.5, 0.5] km; the measurement noise of the distance measurement value is assumed to have a mean of 0 and a covariance matrix of Q = σ 2 I N , where σ 2 is the noise power of the distance measurement noise, The non-line-of-sight error is randomly generated in the range of [-0.5, 0.5] km.

[0069] Based on the above parameter settings, the simulation test tested the performance of the proposed method under three conditions: different signal-to-noise ratios, different non-line-of-sight error upper limits, and different numbers of radar sensors, including the mean square error of the proposed method. To verify the robustness of the method at the same time, ten random scenes were generated, and 100 Monte Carlo experiments were performed on each scene, and all the results were integrated and averaged to obtain the final mean square error. To verify the performance of the method, a two-step weighted least squares method for Gaussian noise was also introduced for comparison.

[0070] Figure 1 A comparison chart of the logarithmic mean square error (MSE) of the coordinate position estimation of the non-cooperative target source when N=6 between the method of the present invention (MCC) and the two-step weighted least squares (TSWLS) as the signal-to-noise ratio changes is given.

[0071] Figure 2 A comparison chart of the logarithmic mean square error (MSE) of the coordinate position estimation of the non-cooperative target source between the method of the present invention (MCC) and the two-step weighted least squares (TSWLS) when SNR=1 as the non-line-of-sight error upper limit changes is given.

[0072] Figure 3 A comparison chart of the logarithmic mean square error (MSE) of the coordinate position estimation of the non-cooperative target source when SNR=1 between the method of the present invention (MCC) and the two-step weighted least squares (TSWLS) is given as the number of sensors changes.

[0073] from Figure 1 It can be seen from the figure that, as the measurement noise signal-to-noise ratio changes, the performance of the method of the present invention in estimating the target position is better than that of the two-step weighted least squares method at the given signal-to-noise ratio level; as the signal-to-noise ratio changes, the performance of the two methods does not change significantly, the two-step weighted least squares method maintains the target position estimation at about 45.5dB, and the method of the present invention maintains the target position estimation at about 44dB. The method of the present invention has an advantage of about 1.5dB over the two-step weighted least squares method; Figure 2 It can be seen from the figure that as the upper limit of the non-line-of-sight error changes, the performance of the inventive method for target position estimation is better than that of the two-step weighted least squares method at the given non-line-of-sight error level; as the non-line-of-sight error level increases, the performance of the two-step weighted least squares method and the inventive method for target position estimation deteriorates, but the inventive method has an advantage of 1.5dB-2.5dB over the two-step weighted least squares method for target position estimation; Figure 3 It can be seen that as the number of radar sensors changes, the performance of the method of the present invention in estimating the target position is better than the two-step weighted least squares method under the given number of radar sensors; as the number of sensors increases, although more non-line-of-sight errors are introduced, the estimation performance of the target position of the two methods is generally better, and the method of the present invention has always maintained an advantage of nearly 2dB. In summary, the method of the present invention can effectively suppress the impact of non-line-of-sight errors on target positioning performance within the tested range, and is more robust than existing methods.

Claims

1. A method for locating a target source in a non-Gaussian noise environment based on the maximum entropy criterion, characterized in that: The following steps are involved: Step 1. Construct a non-cooperative target source localization scenario; Step 2. Collect distance difference measurements using the non-cooperative target source localization scenario constructed in step 1; Step 3. According to the distance difference measurement value obtained in step 2, a distance difference measurement model is constructed, and then a measurement model in the form of measurement value mixed noise and non-line-of-sight error is obtained according to the distance difference measurement model; Step 4. For the measurement model of mixed noise and non-line-of-sight error, the distance difference measurement value is squared and differenced; Step 5. According to the results of step 4, the distance difference measurement values ​​are squared and differenced, and a pseudo linear equation system is constructed to form a weighted least squares problem; Step 6. Use the maximum entropy criterion framework to solve the target position and weight coefficient vector of the least squares problem described in step 5; Step 7. According to the size of the non-cooperative target source positioning scene area, a custom scaling factor β is selected to scale the positioning scene; Then, the solution is iterated alternately according to the solution method in step 6 to obtain the final estimation result.

2. According to claim 1, a method for locating a target source in a non-Gaussian noise environment based on the maximum entropy criterion is characterized in that: The specific method of step 1 is: in a non-cooperative target source positioning scenario, a p-dimensional coordinate system is established as a reference coordinate system, and it is assumed that there is 1 target source and N+1 radar sensors for receiving target source signals and obtaining signal arrival time. The real coordinate position of the radar sensor is known, and the real coordinate position of the target source is unknown. The clock synchronization between the radar sensors is set, and the radar sensor and the target source are in a non-cooperative relationship. The starting time of the target source transmitting the signal is unknown. Assume that the real coordinate position of the i-th radar sensor in the reference coordinate system is denoted as s i , where the N+1th radar sensor is recorded as the reference radar sensor, and the actual position of the target source in the reference coordinate system, i.e., the target position, is recorded as u o .

3. The method for locating a target source in a non-Gaussian noise environment based on the maximum entropy criterion according to claim 1, characterized in that: The specific method of step 2 is: collecting the specific time when the signal emitted by the target source arrives at each radar sensor, subtracting the specific time when the target source emission signal corresponding to the first N radar sensors arrives at each radar sensor from the specific time when the target source emission signal corresponding to the N+1th radar sensor arrives at the N+1th radar sensor, and obtaining the difference between the times; defining the difference between the times as the time difference measurement value; and then obtaining the distance difference measurement values ​​of the first N radar sensors with respect to the N+1th radar sensor according to the time difference measurement value and the known signal propagation speed, and recording the unnoised distance difference measurement value of the i-th radar sensor with respect to the N+1th radar sensor as Wherein, i=1,...,N.

4. The method for locating a target source in a non-Gaussian noise environment based on the maximum entropy criterion according to claim 1, characterized in that: The specific method of step 3 is: according to the unnoised distance difference measurement value set of the i-th radar sensor with respect to the N+1-th radar sensor in step 2 Construct a distance difference measurement model, which is described as: Then, according to the distance difference measurement model, the measurement model in the form of mixed noise and non-line-of-sight error is obtained: Will Substitution The measurement model in the form of mixed noise and non-line-of-sight error is described as: Among them, "||||" means taking the bi-norm, ||u o -s i || represents the actual distance from the target to the i-th radar sensor, ||u o -s N+1 || represents the actual distance from the target to the N+1th radar sensor, s N+1 represents the true coordinate position of the N+1th radar sensor in the reference coordinate system, d i Indicates the noisy distance difference measurement information of the source transmission signal reaching the i-th radar sensor and the N+1-th radar sensor, Indicates d i The non-line-of-sight error, Indicates d i of measurement noise.

5. The method for locating a target source in a non-Gaussian noise environment based on the maximum entropy criterion according to claim 1, characterized in that: The specific process of step 4 is as follows: Measurement model for mixed noise in measurements and non-line-of-sight errors Will Move to the left side of the equation, square both sides and ignore the second-order noise and error terms on the right side of the equation Get the square form corresponding to the i-th radar sensor 6. The method for locating a target source in a non-Gaussian noise environment based on the maximum entropy criterion according to claim 1, characterized in that: The specific method of step 5 is: eliminate the norm term in the square formula corresponding to the i-th radar sensor Multiply both sides of the square corresponding to the i+1th radar sensor get The square corresponding to the i-th radar sensor The difference between the two equations is: Further sorting out in, ξ i is the error model; at this time, It is formulated as a weighted least squares problem and is described as: Among them, min() is the minimization function, (Ay) T WAy is the objective function, y is the optimization variable, and y=[u T ,1] T , u represents the target coordinate position variable, A is the introduced coefficient matrix Using the optimization variable y, the introduced coefficient matrix A, the error model ξ i Expressed as ξ i =A i y; among them, A i represents the vector composed of the i-th row elements of the introduced coefficient matrix A, s1 represents the real coordinate position of the first radar sensor in the reference coordinate system, s2 represents the real coordinate position of the second radar sensor in the reference coordinate system, and s N-1 represents the true coordinate position of the N-1th radar sensor in the reference coordinate system, s N represents the true coordinate position of the Nth radar sensor in the reference coordinate system, d1 represents the distance difference measurement value obtained between the first radar sensor and the reference radar sensor, d2 represents the distance difference measurement value obtained between the second radar sensor and the reference radar sensor, and d N-1 represents the distance difference measurement value obtained by the N-1th radar sensor and the reference radar sensor, d N represents the distance difference measurement value obtained by the Nth radar sensor and the reference radar sensor; W is the introduced weight matrix, w1 is the weight coefficient corresponding to d1, w N is d N The corresponding weight coefficient; the above weighted least squares problem In the example, the optimization variables y include the target position u o and weight coefficients w1,...,w N .

7. The method for locating a target source in a non-Gaussian noise environment based on the maximum entropy criterion according to claim 1, characterized in that: The specific method of step 6 is: using the maximum entropy criterion framework to solve the target position u of the least squares problem in step 5 o and weight coefficients w1,...,w N : Entropy is used to represent the similarity between two random variables X and Y. The formula is: in, represents the mathematical expectation, κ σ () represents a kernel function with kernel bandwidth σ. There is a Silverman criterion that defines kernel bandwidth as σ = 1.06 × min {σ E ,L / 1.34}×M -0.2 ; where σ E is the standard deviation between random variables X and Y, L is the interquartile range between the two variables, and M is the number of samples; when the random variable Y is zero, the random variable X can be expressed as a random error. Assuming that α represents the unknown variable related to the random variable X, the unknown variable is estimated by maximizing entropy. The formula is expressed as Combined with the weighted least squares problem described in step 5 The unknown variable α is the optimization variable y in the weighted least squares problem; the mathematical expectation is approximated by a finite number of samples: It is denoted as the maximum entropy problem, where ξ i (y), i = 1, ..., N represents a finite number of error samples; Using the Laplace kernel function Further transformation of the maximum entropy problem: Combine and The maximum entropy problem can be summarized as: The constant coefficient It has nothing to do with the optimization variable y and will be ignored in the following. According to the error function expression ξ in step 5 i =A i y, the objective function is further written as Based on the properties of convex conjugate functions, the weight matrix W is written as a weight coefficient vector w = [w1, ..., w N ] T , the objective function It is further transformed into a new augmented problem of solving the weight coefficient vector w, expressed as Among them, w i is d i The corresponding weight coefficient is, for The convex conjugate function of Substitute into the objective function get at this time Jointly solve the optimization variable y and the weight coefficient vector w, expressed as a joint optimization problem in, Represents the functional form of the optimization variable y and the weight coefficient vector w; due to the joint optimization problem It is difficult to solve, so the formula is transformed into two sub-problems and solved iteratively in sequence: Sub-question 1: When the weight coefficient vector w is known, the joint optimization problem can be simplified to in, Indicates w i At this time, since the joint optimization problem contains an absolute value term, it is also a non-convex problem. By introducing the intermediate variable τ i As |A i The upper bound of y| is obtained, and the joint optimization problem is transformed into a convex problem for solution; the final optimization problem of subproblem 1 is expressed as: Among them, st means subject to the constraint; after solving the final optimization problem of subproblem 1, the solution result is recorded as Represents the estimated value of the optimization variable y; Sub-question 2: When the optimization variable y is known, the joint optimization problem Simplified to At this time, the weight coefficient vector w has a corresponding closed-form solution The solution result is Represents the estimated value of the weight coefficient vector w.

8. The method for locating a target source in a non-Gaussian noise environment based on the maximum entropy criterion according to claim 1, characterized in that: The specific method of step 7 is: according to the size of the positioning scene area, a scaling factor β is selected by user-defined to scale the positioning scene; Then set Solve step 6 subproblem 1 The results are directly brought into Solve subproblem 2 in step 6; solve subproblem 1 and subproblem 2 by alternating iterations. When the difference between the two iterative changes is less than 10 -10 Or when the number of iterations reaches 10, the final estimation result is considered to be obtained, that is, the optimal estimation value of the target source coordinate position, which is recorded as u * ,in, y * is the optimal estimate of y, Indicated by y * The subvector consisting of the 1st to pth elements of ; represents the estimated value of the weight coefficient vector w1, represents the estimated value of the weight coefficient vector w2, Represents the weight coefficient vector w N The estimated value of d2 is w2, and w2 is the weight coefficient vector corresponding to d2.

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