Passive TDOA positioning method based on linear elimination weight and population center

Abstract

The application discloses a passive time difference positioning method based on linear elimination weight and population center, mainly solves the problems that the artificial honeybird algorithm has resource waste and a large number of repetitive behaviors when solving the time difference positioning problem, thereby reducing the population richness, easily falling into local convergence and affecting the positioning accuracy. The implementation scheme is as follows: firstly, on the basis of elimination and update of the artificial honeybird algorithm, the current elimination weight is calculated by using an elimination weight calculation formula, and then the candidate solution is updated by using an elimination update equation. Secondly, based on the population center, the distribution state of the current population is judged by calculating the historical step length of each individual and the distance from the population center, when the population is in a redundant state, the population center is used to replace the invalid individual, and the problem that the positioning efficiency is not high due to a large number of invalid behaviors in the late iteration of the prior art is overcome.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and more specifically relates to a passive time-difference positioning method based on linear elimination weights and population centers in the field of radar communication technology. This invention can be used for passive time-difference positioning to estimate the location of radiation source targets. Background Technology

[0002] Passive time difference (TDOA) positioning is a passive positioning technique that estimates the target based on the time difference (TDOA) of the radiation source's arrival at various positioning stations. Due to the maturity and high accuracy of time difference measurement technology, TDOA is widely used in radar and sonar technologies for target localization. The TDOA positioning problem is essentially a set of nonlinear equations, difficult to solve directly. Swarm intelligence algorithms, as a class of optimization algorithms, have been widely applied in the TDOA field in recent years due to their black-box characteristics—requiring no initial values ​​and only considering input and output. Various swarm intelligence algorithms, such as particle swarm optimization, tunic swarm optimization, and whale optimization, have been applied to solve the TDOA positioning problem for target localization estimation. However, these swarm intelligence algorithms are prone to getting trapped in local extrema during iterative solutions, thus affecting the positioning accuracy of target estimation.

[0003] The Artificial Hummingbird Algorithm, proposed by Zhao et al. in their paper "Artificial hummingbird algorithm: A new bio-inspired optimizer with its engineering applications" (Computer Methods in Applied Mechanics and Engineering, Volume 388, 2022, 114194, ISSN 0045-7825), derives a likelihood equation based on maximum likelihood estimation. This equation is then used as the function to be optimized. N initial target estimates are randomly generated. During each iteration, the current position is updated based on its relative merits to candidate positions. After all iterations, the optimal individual is the solution, representing the localization estimate of the radiation source target. This method verifies through test functions that the artificial hummingbird algorithm has a significantly higher accuracy than other swarm intelligence algorithms when solving optimization problems. However, this method still has two shortcomings: First, because the algorithm selectively updates, most individuals often remain unchanged during the iteration process, resulting in fewer actual individuals participating in population updates and a decrease in population richness. This can easily lead to local convergence when solving time difference positioning problems, affecting positioning accuracy. Second, it ignores the fact that the population is in a clustered state in the later stages of iteration, with most individuals located close to each other and some individuals exhibiting repetitive behaviors, which affects positioning efficiency. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the existing technology by proposing a passive time-difference positioning method based on linear elimination weights and population centers, which solves the problems of poor positioning accuracy and efficiency in the existing technology.

[0005] The technical approach to achieving the objective of this invention is as follows: Based on the artificial hummingbird algorithm, this invention designs a linear elimination weight that changes with the number of iterations, thereby increasing the proportion of individuals eliminated during iteration and addressing the problem of reduced participation in updates in the later stages of the artificial hummingbird algorithm. Based on the population center, this invention determines the current population distribution state by calculating the historical step length of each individual and its distance from the population center. When the population is in a redundant state, the population center replaces invalid individuals, reducing repetitive behavior and overcoming the problem of low localization efficiency caused by a large number of invalid behaviors in the later stages of iteration in existing technologies.

[0006] Based on the above ideas, the technical solution of the present invention is as follows:

[0007] Step 1: Generate the function to be optimized;

[0008] Step 2: Generate 30 estimates of the location of the radiation source target as candidate solutions for the function to be optimized;

[0009] Step 3: Update each candidate solution using the guided update and territory update equations in the artificial hummingbird algorithm;

[0010] Step 4: Determine if the current iteration number is divisible by the migration interval. If yes, proceed to step 5: Eliminate and update the candidate solutions; otherwise, proceed to step 6.

[0011] Step 5: Calculate the current elimination weight using the elimination weight calculation formula, and update the candidate solution using the elimination update equation;

[0012] Step 6: Determine the distribution of the current candidate solutions. If the average historical step size of the population is less than the average center distance of the population, the population is in a redundant state. Then proceed to step 7; otherwise, proceed to step 8.

[0013] Step 7: Perform substitution operations on invalid candidate solutions;

[0014] Step 8: Determine if the number of iterations has reached the maximum value. If yes, proceed to step 9; otherwise, increment the number of iterations by 1 and proceed to step 4.

[0015] Step 9: Output the target location estimate that minimizes f in the radiation source target location estimate.

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

[0017] First, when updating candidate solutions, this invention first calculates the current elimination weight using the elimination weight calculation formula, and then updates the candidate solutions using the elimination update equation. This increases the proportion of actual individuals participating in the population update, overcoming the problem in existing technologies where the number of actual individuals participating in the population update decreases in the later stages of the iteration due to the selective update, which makes the iteration prone to local extrema and affects positioning accuracy. This invention can avoid getting trapped in local extrema during the iteration process and improve the positioning accuracy of radiation source targets.

[0018] Second, the present invention determines whether the current population is in a redundant state based on the average historical step length and the average center distance of the population. When the population is in a redundant state, the population center is used to replace invalid individuals, thereby reducing repetitive behavior. This overcomes the shortcomings of the prior art, which ignores the aggregation in the later stages of population iteration, resulting in a large number of invalid repetitive behaviors. As a result, the present invention improves the positioning efficiency of radiation source targets. Attached Figure Description

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

[0020] Figure 2 This is a comparison chart of the simulation convergence characteristics of this invention;

[0021] Figure 3 This is a comparison chart of the simulation positioning deviation of the present invention;

[0022] Figure 4 This is a comparison chart of positioning errors under four-station positioning simulation of the present invention;

[0023] Figure 5 This is a comparison chart of positioning errors under five-station positioning simulation of the present invention. Detailed Implementation

[0024] The embodiments and effects of the present invention will be described in detail below with reference to the accompanying drawings.

[0025] Reference Figure 1 The implementation steps of this embodiment will be further described below.

[0026] Step 1: Generate the function to be optimized.

[0027] The function to be optimized refers to the mathematical relationship between the location of the radiation source target and the arrival time difference between the arrival time of the radiation source target signal to the positioning master station and each positioning auxiliary station. The maximum likelihood estimation method is used to obtain the likelihood function of the radiation source target location based on the mathematical relationship. The likelihood function is used as the function to be optimized, and the optimal solution that minimizes the value of the function is found.

[0028] The expression of the function to be optimized is as follows:

[0029]

[0030] Where f represents the function to be optimized, and M represents the number of positioning stations participating in time difference positioning, i.e., the number of the primary positioning station and all auxiliary positioning stations. s represents an estimate of the location of the radiation source target. i Let represent the position coordinates of the i-th positioning station, i = 2, ..., M, where i represents the serial number of the auxiliary positioning station, c represents the propagation speed of electromagnetic waves, and t represents the position coordinates of the i-th positioning station. i1 This represents the measured time difference between the arrival time of the radiation source target signal at the positioning station and the i-th auxiliary positioning station.

[0031] Step 2: Generate 30 estimates of the target location of the radiation source as candidate solutions for the function to be optimized.

[0032] The 30 estimates of the locations of the radiation source targets are obtained by the following formula:

[0033] X j =r·(ub-lb)+lb

[0034] Among them, X j Let represent the estimated location of the j-th radiation source target, j = 1, ..., 30, where j represents the index of the location estimate, r represents a random number randomly selected within the interval (0, 1), and ub and lb represent the upper and lower boundaries of the radiation source target area, respectively.

[0035] Step 3: Update each candidate solution using the guided update and territory update equations from the artificial hummingbird algorithm below:

[0036] [vt_max j ,tar]=max(VT(j,:))

[0037]

[0038]

[0039] Among them, vt_max j This represents the maximum access interval between the estimated location of the j-th radiation source and the estimated locations of other radiation sources, where tar represents the corresponding vt_max. j The index of the radiation source target location estimate is VT(j,:), which represents the access interval sequence of the j-th radiation source target location estimate to the other radiation source target location estimates. This represents the candidate value for estimating the location of the j-th radiation source target in the t-th iteration. Let X represent the estimated position of the j-th radiation source target in the t-th iteration, where Dec represents the direction vector, and X represents the direction vector. tar This indicates the corresponding vt_max j The radiation source target location estimate is f(·), which represents the function value obtained by substituting the radiation source target location estimate into the function to be optimized, f.

[0040] Step 4: Determine if the current iteration number is divisible by the migration interval. If yes, proceed to step 5; otherwise, proceed to step 6.

[0041] The migration interval is T = 2N, where N represents the number of estimated values ​​of the radiation source target location, and in the embodiment of the present invention, N = 30.

[0042] Step 5: Calculate the current elimination weight using the elimination weight calculation formula, and update the candidate solution using the elimination update equation.

[0043] The formula for calculating the elimination weight is as follows:

[0044]

[0045] Where P represents the elimination weight, t represents the current iteration number, and p max and p min p represents the upper and lower limits of the range of variation of the elimination weight, respectively. max =0.6, p min =0, Max_Times represents the maximum number of iterations, and in the embodiment of the present invention, Max_Times = 400.

[0046] The replacement and renewal equation is as follows:

[0047] XD = sort(f(X))

[0048] XD p =r·(ub-lb)+lb

[0049] Where XD represents the new sequence of position estimates obtained by substituting the radiation source target position estimates into the function f to be optimized, sorted from largest to smallest; sort(·) represents sorting from largest to smallest; and X represents the radiation source target position estimate sequence before sorting. p Let p represent the estimated location of the p-th radiation source target in XD, where p = 1, ..., N×P.

[0050] Step 6: Determine the distribution of the current candidate solutions. If the average historical step size is less than the average center distance, the population is in a redundant state. Then proceed to step 7. Otherwise, proceed to step 8.

[0051] The average historical step size and average center distance are obtained from the following formulas:

[0052]

[0053]

[0054] in, This represents the average historical step size of the population at the t-th iteration. This represents the value of the estimated location of the j-th radiation source target at the t-th iteration. This represents the average center distance of the population at the t-th iteration.

[0055] Step 7: Use the following substitution operation formula to perform substitution operations on invalid candidate solutions:

[0056]

[0057]

[0058] In an embodiment of the present invention, when the center distance of the estimated radiation source target location satisfies At that time, the estimated location of the radiation source target is considered invalid.

[0059] Step 8: Determine if the number of iterations has reached the maximum value. If yes, proceed to step 9; otherwise, increment the number of iterations by 1 and proceed to step 4.

[0060] Step 9: Output the target location estimate that minimizes f in the radiation source target location estimate.

[0061] The effects of this invention can be further illustrated by the following simulation.

[0062] 1. Simulation conditions:

[0063] The software platform for the simulation experiments of this invention is Windows 10 operating system and Matlab R2021b.

[0064] The time difference of arrival simulation data used in the simulation experiment of this invention were obtained from the positioning station shown in Table 1 and the radiation source target located at coordinates (15, 20, 10) km.

[0065] Table 1. Location coordinates of the positioning station

[0066] 1 [0,0,0] 2 [17,10,0] 3 [-17,10,0] 4 [0,-20,0] 5 [-17,-10,0]

[0067] 2. Simulation content and result analysis:

[0068] The simulation experiment of this invention uses the method of this invention (IAHA) and six existing technologies (AHA, IPSO, GA, SSA, WOA, and Chan algorithm) to perform time difference positioning of radiation source targets, and obtains the positioning deviation curve for each radiation source target.

[0069] In the simulation experiment of this invention, the six existing technologies used are:

[0070] Prior art 1 refers to the Artificial Hummingbird Algorithm proposed by Zhao et al. in their paper "Artificial hummingbird algorithm: A new bio-inspired optimizer with its engineering applications" (Computer Methods in Applied Mechanics and Engineering, Volume 388, 2022, 114194, ISSN 0045-7825), abbreviated as AHA time difference positioning algorithm.

[0071] Prior art 2 refers to the time difference localization algorithm based on particle swarm optimization proposed by KWK et al. in their paper "Particle swarm optimization for time-difference-of-arrival based localization" (2007 15th European Signal Processing Conference, Poznan, Poland, 2007, pp.414-417.), abbreviated as IPSO time difference localization algorithm.

[0072] The prior art 3 refers to the time difference positioning algorithm based on the adaptive genetic algorithm proposed by Wang Shenliang et al. in their paper "Application of Improved Adaptive Genetic Algorithm in TDOA Positioning" (Systems Engineering and Electronics Technology, 2019, 41(02):254-258.), abbreviated as GA time difference positioning algorithm.

[0073] Existing technology 4 refers to the time difference positioning technology based on the tunic group algorithm proposed by Chen Tao et al. in their paper "Passive Time Difference Positioning Based on the Tulip Group Algorithm" (Journal of Electronics and Information Technology, 2018, 40(07): 1591-1597.), abbreviated as SSA time difference positioning algorithm.

[0074] The prior art 5 refers to the time difference positioning algorithm based on the improved whale optimization algorithm proposed by Chen Guangwu et al. in their paper "Application of Improved Whale Optimization Algorithm in Passive Time Difference Positioning" (Sensors and Microsystems, 2022, 41(03):150-153+157), abbreviated as WOA time difference positioning algorithm.

[0075] Existing technology 6 refers to a time difference positioning algorithm proposed by YTChan et al. in the paper "A Simple and Efficient Estimator for Hyperbolic Location" (IEEE Trans on Signal Processing, 1994, 42(8): 1905-1915.), abbreviated as Chan algorithm.

[0076] To verify the experimental results of the simulation of this invention, the positioning errors of this invention and AHA were compared, the positioning errors of this invention and IPSO, GA, SSA, and WOA were compared, and the positioning errors of this invention and the Chan algorithm were compared.

[0077] A comparison of the positioning errors of this invention with those of the existing AHA technology.

[0078] By comparing the optimal solution values ​​of the present invention and AHA in each iteration, the convergence curves of the two algorithms are obtained, as follows: Figure 2 As shown. Figure 2 The horizontal axis represents the number of iterations, and the vertical axis represents the function value of the optimal radiation source target location estimate within the population. The solid black line represents the convergence curve obtained by this invention, and the dashed black line represents the convergence curve obtained by AHA.

[0079] from Figure 2 It can be seen that the present invention converges faster in the early stage of iteration, and tends to stabilize after 150 iterations, compared with the original artificial hummingbird algorithm which gradually stabilizes after about 220 iterations, and has a faster convergence rate.

[0080] This invention compares the positioning errors of existing technologies such as IPSO, GA, SSA, and WOA.

[0081] By comparing the optimal solution of this invention with that of IPSO, GA, SSA, and WOA in each iteration, a comparison chart of the convergence curves of the five algorithms is obtained, as shown in the figure. Figure 3 As shown. Among them, Figure 3 (a) is a convergence curve for orders 1-400. Figure 3 (b) is a deviation curve for 1-400 times.

[0082] Figure 3In (a), the horizontal axis represents the number of iterations, and the vertical axis represents the function value of the optimal radiation source target location estimate within the population. Figure 3 In (a), the black dashed line represents the convergence curve of IPSO, the black short line-dot represents the convergence curve of GA, the blue dashed line represents the convergence curve of SSA, the red dashed line represents the convergence curve of WOA, and the black solid line represents the convergence curve of the present invention.

[0083] from Figure 3 As can be seen from (a), the convergence curve of the present invention decreases at a rate significantly faster than that of other algorithms.

[0084] Figure 3 In (b), the horizontal axis represents the number of iterations, and the vertical axis represents the deviation between the algorithm's solution and the target radiation source to be located, in meters. The black dashed line represents the deviation curve of IPSO, the short black dotted line represents the deviation curve of GA, the blue dashed line represents the deviation curve of SSA, the red dashed line represents the deviation curve of WOA, and the black solid line represents the deviation curve of the present invention.

[0085] from Figure 3 As can be seen from (b), the positioning deviation of the radiation source target of the present invention is smaller than that of other algorithms.

[0086] The simulation compares the positioning errors of this invention and the Chan algorithm in different positioning scenarios.

[0087] The positioning errors of this invention and the Chan algorithm for radiation source targets were compared in scenarios with 4 positioning stations and 5 positioning stations, respectively. The comparison charts of the root mean square errors of the two algorithms in the two positioning scenarios are shown below. Figure 4 Figure 5 As shown. Among them, Figure 4 The positioning error curves of this invention and the Chan algorithm when using four positioning stations are shown. Figure 5 Positioning error curves of the present invention and the Chan algorithm with five positioning stations. Figure 4 and Figure 5 The horizontal axis represents the variance of the measurement noise in dB, and the vertical axis represents the root mean square error of the radiation source target estimation in dB. Figure 5 The curve marked with a triangle represents the root mean square error curve of this invention, and the curve marked with an asterisk represents the root mean square error curve of the Chan algorithm.

[0088] from Figure 4 As can be seen, when only the first four positioning stations in Table 1 participate in positioning, the Chan algorithm has no solution, while this invention can still solve the problem. From Figure 5 As can be seen, with five stations involved in the positioning, the positioning accuracy of the radiation source target of the present invention is higher than that of the Chan algorithm, which shows that the present invention can still achieve high positioning accuracy with a lower station deployment cost.

[0089] The above description is merely a specific example of the present invention and does not constitute any limitation on the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make modifications and changes in form and details without departing from the principles and structure of the invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A passive time-difference localization method based on linear elimination weights and population center, characterized in that, The population is updated by using a linear elimination weight that decreases linearly with the number of iterations. The population center and the positional distribution of each individual are used as the criteria for judgment, and replacement operations are performed on individuals in a redundant state. The specific steps of this localization method are as follows: Step 1: Generate the function to be optimized. By using the time difference of arrival between the radiation source target signal and the positioning master station and each positioning auxiliary station, construct the mathematical relationship between the radiation source target position and the time difference of arrival. Use the maximum likelihood estimation method to obtain the likelihood function of the radiation source target position based on the mathematical relationship, and use the likelihood function as the function to be optimized. The expression of the function to be optimized is as follows: ； Where f represents the function to be optimized, and M represents the number of positioning stations participating in time difference positioning, i.e., the number of the primary positioning station and all auxiliary positioning stations. This represents an estimate of the location of the radiation source target. This represents the position coordinates of the i-th positioning station. , where i represents the serial number of the auxiliary positioning station, and c represents the propagation speed of electromagnetic waves. The measured value represents the time difference between the arrival of the radiation source target signal at the positioning station and the i-th positioning auxiliary station; Step 2: Generate 30 estimates of the location of the radiation source target as candidate solutions for the function to be optimized; Step 3: Update each candidate solution using the guided update and territory update equations in the artificial hummingbird algorithm; Step 4: Determine if the current iteration number is divisible by the transition interval. If yes, proceed to step 5; otherwise, proceed to step 6. Step 5: Calculate the current elimination weight using the elimination weight calculation formula, and update the candidate solution using the elimination update equation; Step 6: Determine the distribution of the current candidate solutions. If the average historical step size is less than the average center distance, the population is in a redundant state. Then proceed to step 7; otherwise, proceed to step 8. Step 7: Perform substitution operations on invalid candidate solutions; Step 8: Determine if the number of iterations has reached the maximum value. If yes, proceed to step 9; otherwise, increment the number of iterations by 1 and proceed to step 4. Step 9: Output the target location estimate that minimizes f in the radiation source target location estimate.

2. The passive time-difference localization method based on linear elimination weights and population centers as described in claim 1, characterized in that, The generation of 30 estimates of the radiation source target locations in step 2 is obtained by the following formula: ； in, This represents the estimated location of the j-th radiation source target. j represents the position estimation index, r represents a random number randomly selected within the interval (0,1], and ub and lb represent the upper and lower boundaries of the radiation source target area, respectively.

3. The passive time-difference localization method based on linear elimination weights and population centers as described in claim 2, characterized in that, The guided update and territory update equations described in step 3 are as follows: ； ； ； in, tar represents the maximum access interval between the estimated location of the j-th radiation source target and the estimated locations of other radiation source targets, where tar represents the corresponding The sequence number of the radiation source target location estimation. Let represent the sequence of access intervals between the location estimates of the j-th radiation source target and the location estimates of other radiation source targets. This represents the candidate value for estimating the location of the j-th radiation source target in the t-th iteration. This represents the estimated position of the j-th radiation source target at the t-th iteration, where Dec represents the direction vector. Indicates correspondence Estimation of the location of the radiation source target. This represents the function value obtained by substituting the estimated location of the radiation source target into the function f to be optimized.

4. The passive time-difference localization method based on linear elimination weights and population centers according to claim 3, characterized in that, The migration interval mentioned in step 4 is: , where N represents the number of estimated locations of the radiation source target.

5. The passive time-difference localization method based on linear elimination weights and population centers according to claim 4, characterized in that, The formula for calculating the elimination weight mentioned in step 5 is as follows: ； Where P represents the elimination weight, and t represents the current iteration number. and These represent the upper and lower limits of the range of change in the elimination weight, respectively. , Max_Times represents the maximum number of iterations.

6. The passive time-difference localization method based on linear elimination weights and population centers according to claim 5, characterized in that, The replacement and renewal equation mentioned in step 5 is as follows: ； ； in, This represents a new sequence of location estimates, rearranged from largest to smallest, based on the function values ​​obtained by substituting the radiation source target location estimates into the function to be optimized, f. This indicates the order from largest to smallest, where X represents the estimated sequence of radiation source target locations before sorting. This represents the estimated location of the p-th radiation source target in XD. .

7. The passive time-difference localization method based on linear elimination weights and population centers according to claim 6, characterized in that, The average historical step size and average center distance mentioned in step 6 are obtained by the following formula: ； ； in, This represents the average historical step size of the population at the t-th iteration. This represents the value of the estimated location of the j-th radiation source target at the t-th iteration. This represents the average center distance of the population at the t-th iteration.

8. The passive time-difference localization method based on linear elimination weights and population centers according to claim 7, characterized in that, The substitution operation formula described in step 7 is as follows: ； in, This represents the center position of the estimated radiation source target location at the t-th iteration.

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