A node deployment method for time difference positioning and direction finding of internal and external field targets

Abstract

A node deployment method for time difference positioning and direction finding of internal and external field targets, which takes the weighted sum of the average positioning accuracy improvement of the internal field area positioning and the average direction finding accuracy improvement of the external field area as the objective function of the station deployment optimization, takes the wireless sensor sensing capability as the constraint condition, improves the coverage rate of the internal field area, and deploys the distributed nodes for time difference positioning and direction finding of internal and external field targets; after the optimization deployment of the application, in the case of the change of the external field target source position and RDOA measurement error, the average positioning accuracy of the internal field area, the average direction finding accuracy of the external field target, and the coverage rate performance of the internal field area are all significantly improved, which improves the coverage range of the wireless sensor network while taking into account the internal field target positioning and external field target direction finding of the key area.

Description

Technical Field

[0001] This invention belongs to the field of spectrum monitoring technology, and in particular relates to a node deployment method that takes into account both internal and external target time difference positioning and direction finding. Background Technology

[0002] In the field of spectrum monitoring, passive positioning methods are techniques that directly correlate electromagnetic spectrum signals with their spatial location. Commonly used passive positioning methods include Time Difference of Arrival (TDOA) positioning and Angle of Arrival (AOA) cross-positioning. Among them, TDOA positioning can not only locate nearby targets but also perform direction finding for distant targets, and has been widely used in the field of spectrum monitoring.

[0003] The spatial geometry of a passive time-of-flight (TOF) localization and direction-finding (TOD) system is a core factor affecting the localization and TOD performance of the monitored area. In practical scenarios, when monitoring key areas, we need both indoor and outdoor target localization and direction finding, with the indoor field being more important than the outdoor field. Existing node deployment algorithms often focus on indoor positioning accuracy or treat indoor and outdoor positioning accuracy equally, ignoring the impact of larger outdoor positioning errors on node deployment. When the outdoor target is far from the wireless sensor network, its relative spatial geometry deteriorates, leading to increased outdoor positioning errors. In this case, using positioning accuracy as the objective function is not meaningful; considering the TOD results of the outdoor target is more meaningful. Furthermore, traditional node deployment algorithms all consider ideal configurations but ignore the limited maximum distance that each wireless sensor node can effectively sense or monitor. The following are relevant research papers.

[0004] In 2009, Wang Bo proposed using a genetic algorithm to optimize the deployment of sites for a passive time difference positioning (TDOA) system (Reference 1: Wang Bo. Optimal site deployment algorithm for TDOA positioning system based on genetic algorithm [J]. Systems Engineering and Electronics, 2009(9):2125-2128.). This method optimizes site deployment in a two-dimensional scene and requires the target source location to be known. In 2016, Zhou Cheng proposed maximizing the Fisher information matrix to obtain the optimal site deployment method for a positioning model based on time difference parameter measurement (Reference 2: Zhou Cheng. Research on optimal site deployment method for time difference positioning [J]. Journal of Xi'an University of Electronic Science and Technology, 2016,43(4):123-127.). This method indicates that the optimal site deployment is when the wireless sensor sites surround the target and are distributed at equal angles. In 2018, Dou Xueqian, for a positioning system based on TDOA measurement, used Geometric Dilution of Precision (GDOP) as the objective function (Reference 3: Dou Xueqian. Optimal station deployment method for multi-station external time difference positioning based on geometric dilution [J]. Electronic Information Countermeasures Technology, 2018, 33(5):37-40.), and used two solution algorithms, grid method and genetic algorithm, to optimize the deployment of stations. However, this method cannot meet the situation where near-field and far-field target sources exist simultaneously. In 2020, Xia Wei, for the passive time difference positioning method, in order to be more applicable to the real deployment environment, used the free space propagation loss model to represent the TDOA measurement error, and used the trace of the Cramer-Rao Lower Bound (CRLB) as the objective function for optimization deployment (Reference 4: Xia Wei. Research on optimal station deployment method for passive time difference positioning system [J]. Radar Science and Technology, 2020, 18(1):34-38.). In 2021, Wang Chengmin used the average GDOP of the target area as the objective function and employed the particle swarm optimization algorithm to find the optimal station deployment method for a multi-station passive time difference positioning system (Reference 5: Wang Chengmin. Optimization of station deployment for a multi-station passive positioning system based on particle swarm optimization algorithm [J]. Computer and Digital Engineering, 2021, 49(03):487-492.), which significantly reduced the positioning error in the target area. However, both methods are applicable to indoor or outdoor targets. When the target source is far from the wireless sensor, the curvature of its signal wavefront tends to be planar, resulting in a threshold effect in the positioning accuracy of the target source. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the purpose of this invention is to provide a node deployment method that takes into account both indoor and outdoor target time difference localization and direction finding. This method uses the sensing capability of wireless sensors as a constraint and optimizes the deployment by taking into account both indoor area localization and outdoor intrusion target direction finding. This improves the coverage of the wireless sensor network while taking into account indoor target localization and outdoor target direction finding in key areas, thus achieving the best node deployment results.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A node deployment method that combines time difference localization and direction finding for targets in both internal and external fields includes the following steps:

[0008] Step 1: Construct a node deployment scenario for indoor area positioning and outdoor area direction finding, i.e., a wireless sensor network, which includes M wireless sensor nodes.

[0009] Step 2: For the indoor area, select the first node of the wireless sensor network as the reference node and calculate the signal source u in the indoor area. k The covariance matrix Q of the Time Difference of Arrival (TDOA) value and the TDOA measurement error relative to the wireless sensor. k ;

[0010] Step 3: For the external field region, calculate the signal source a in the external field region. k Compared to the Time of Arrival (TOA) value of the wireless sensor network, adding Gaussian measurement error yields the equivalent Time of Arrival (TOA) measurement value for each positioning node. Where, n i,k Let be a Gaussian variable with zero mean and variance s. 2 i,k Define n k ={n1,n2,…,n N}, its covariance matrix Γ q =diag{s 2 1,k ,s 2 2,k ,…,s 2 N,k}; Selecting the first node of the wireless sensor network as a reference, the signal source a is obtained. k The time difference of arrival (TDOA) measurement value indicates that all wireless sensor nodes are at the same level relative to signal source a. k Time Difference of Arrival (TDOA) Measurement Error Vector x k The covariance matrix is ​​R k ;

[0011] Step 4: Perform uniform sampling within the inner field area to obtain N. s sampling points u i i = 1, 2, ..., N s Calculate the Cramer-Rao lower bound (CRLB) for all sampled points and obtain its trace. The mean Cramero lower bound (CRLB) for the inner field area is:

[0012] Step 5: Perform uniform sampling within the outer field area to obtain N. o sampling points u i i = 1, 2, ..., N o Calculate the Cramer-Rao lower bound (CRLB) for all sampling points and obtain the trace of its direction-finding dimension. The mean Cramerlow lower bound (CRLB) for the outer field area is:

[0013] By using the Modified Polar Representation (MPR) method, the positions of sampling points in the field region are represented by azimuth, orientation, and inverse distance; thus, the Cramer-Rao lower bound of the sampling points in the field region under the MPR coordinate system is determined. Assume the wireless sensor reference node s1 is located at the origin of the coordinate system, then in

[0014]

[0015] L = [O (M-1)×2 ,1 M-1 / g o2 ].

[0016] θ o φ o and g o These represent the azimuth, elevation, and relative inverse distance of the target signal source in the field area relative to the wireless sensor node, respectively.

[0017] Step Six: Based on the importance of the objective, the average Cramer-Robber lower bound (CRLB) of the inner and outer field regions from Steps Four and Five is weighted and summed to obtain the result. ω1 and ω2 are the importance weights of the inner field region and the outer field region, respectively;

[0018] Step 7: Minimize the steps in Step 6 Let S be the objective function, S be the deployable area of ​​the wireless sensor nodes, S be the first constraint, and S be the sensing capability of the wireless sensors, i.e., the node coverage must be greater than or equal to the actual target coverage C. The node locations of the wireless sensor network are the decision variables, thus constructing an optimization problem. Represented as:

[0019]

[0020] stC1:s i ∈S, i=1,2,...,M

[0021] C2:ρ≥C

[0022] Step 8: Solve the optimization problem using the Particle Swarm Optimization (PSO) algorithm. The global optimal solution of the objective function is calculated, and finally the optimal deployment location of the wireless sensor network is output.

[0023] 2. The node deployment method that takes into account both internal and external target time difference positioning and direction finding as described in claim 1, characterized in that, in step one, the internal field area and the external field area together form the key monitoring area, the target in the internal field area is located, and the target in the external field area is direction found.

[0024] 3. A node deployment method that combines time difference positioning and direction finding for targets in both internal and external fields, as described in claim 1, is characterized in that, in step two, the signal source u in the internal field area... k The covariance matrix Q of the measurement error relative to the time difference of arrival (TDOA) of the wireless sensor k It can be done To calculate, where B is the signal bandwidth, B n Let be the noise bandwidth of the wireless sensor node receiver, T be the duration of the received signal, and γ be the equivalent input signal-to-noise ratio of the two signals; let τ represent the estimated Time Difference of Arrival (TDOA). Then, the Cramer-Rao lower bound (CRLB) for the TDOA parameter estimation can be expressed as: Assuming that the signals received by each wireless sensor are independent and follow the same distribution characteristics, the specific expression for the covariance matrix Q can be derived as follows:

[0025]

[0026] 4. A node deployment method that combines internal and external target time difference positioning and direction finding according to claim 1, characterized in that, in step three, signal source a k The measured values ​​include measurement errors and follow a Gaussian distribution.

[0027] 5. A node deployment method that combines time difference positioning and direction finding for targets in both internal and external fields, as described in claim 1, characterized in that, in step four, the Cramero lower bound of the target signal source in the internal field area... in, It is the derivative of the true value of the Time Difference of Arrival (TDOA) with respect to the location of the signal source, characterizing the wireless sensor node's position relative to the signal source u. iSpatial resolution.

[0028] 6. A node deployment method that takes into account both internal and external target time difference positioning and direction finding according to claim 1, characterized in that the direction finding dimension in step five refers to the 2*2 matrix at the upper left corner of the Cramérault lower bound (CRLB) in a three-dimensional scene, and to the 1*1 matrix at the upper left corner of the Cramérault lower bound (CRLB) in a two-dimensional scene.

[0029] 7. A node deployment method for both internal and external target time difference positioning and direction finding according to claim 1, characterized in that, in step seven, the wireless sensor sensing capability refers to the degree to which the wireless sensor node perceives events or phenomena within its monitoring area; assuming the target monitoring area is D, and the number of wireless sensor nodes is N, the wireless sensor nodes are numbered and represented as a set S = {s1, s2, ..., s...} i}, i = 1, 2, ..., N, where the detection range of each wireless sensor node is a. i If the area of ​​the target detection region is A, then Let S2 = |A| be the maximum coverage area of ​​the wireless sensor node. Then the coverage rate of the monitoring area of ​​the WSN is... Let ρ represent the sensing capability of a wireless sensor.

[0030] 8. A node deployment method that combines time difference positioning and direction finding for targets in both internal and external fields, as described in claim 1, characterized in that step eight includes the following sub-steps:

[0031] 8.1) First, initialize: set the number of particle populations N, maximum number of iterations M, inertia factor ω, individual learning factor c1, group learning factor c2, single particle dimension D, the moving speed ν of all particles, and the initial position of all particles. The initial position of the particles is set according to the independent variable description under this model, that is, the first three particles in all populations are set to 0, and the initial positions of the remaining particles are randomly generated within the optimization constraints by a unified number generator.

[0032] 8.2) Select from step six As the fitness function of the particle swarm optimization algorithm, the initial fitness function values ​​of all particles in each swarm are calculated.

[0033] 8.3) Next, control the particles to move according to the velocity and position update formulas, generate new particles, and compare the fitness function value of the new particles with the initial fitness function value; in the optimization problem of step seven. In this study, the smaller the fitness value of a particle, the better its indoor positioning and outdoor direction finding performance. By comparing the fitness function values ​​of each particle, the optimal particle and its corresponding fitness function value are determined.

[0034] 8.4) If the number of iterations does not reach the preset value or the global optimal position does not meet the minimum limit, then repeat step 8.3 until the specified number of iterations is reached; finally, the particle with the lowest fitness in all populations is the optimal solution.

[0035] Compared with the prior art, the present invention has the following advantages:

[0036] Existing node deployment algorithms often focus on indoor positioning accuracy or treat indoor and outdoor positioning accuracy equally, ignoring the impact of larger outdoor positioning errors on node deployment. When the outdoor target is far from the wireless sensor network, its relative spatial geometry deteriorates, leading to increased outdoor positioning errors, making its positioning accuracy less meaningful as an objective function.

[0037] 1. This invention optimizes deployment by using a weighted sum of indoor field positioning accuracy and outdoor field direction finding accuracy as the objective function, based on the relative importance of the indoor and outdoor fields. Furthermore, traditional node deployment algorithms consider ideal configurations but neglect the limited maximum sensing or monitoring distance of each wireless sensor node. This invention, constrained by the sensing capabilities of wireless sensors, delves into an optimized deployment method that balances indoor monitoring area positioning with outdoor intrusion target direction finding. This improves the coverage of the indoor monitoring area and offers the advantage of balancing indoor positioning accuracy with outdoor direction finding accuracy.

[0038] 2. The method of the present invention uses the sensing capability of wireless sensors as a constraint to improve the coverage of the inner field area. Simulation verification shows that the method of the present invention is superior to the prior art in terms of time difference positioning performance in the inner field area, time difference direction finding performance in the outer field area, and coverage of the inner field area under the changes of distance in the outer field area and RDOA measurement error.

[0039] In summary, this invention uses the sensing capabilities of wireless sensors as a constraint, and takes into account both indoor area positioning and outdoor intrusion target direction finding as an optimized deployment method, which can obtain the best node deployment results. Attached Figure Description

[0040] Figure 1 A schematic diagram illustrating the optimized deployment for both internal and external target time difference positioning and direction finding.

[0041] Figure 2 A comparative diagram of CRLB positioning for various interior field configurations.

[0042] Figure 3 RMSE for orientation measurement of the external field region for various configurations.

[0043] Figure 4 This is a schematic diagram showing the coverage of the interior area for various configurations.

[0044] Figure 5A comparative diagram of CRLB positioning for various interior field configurations.

[0045] Figure 6 RMSE for orientation measurement of the external field region for various configurations.

[0046] Figure 7 This is a schematic diagram showing the coverage of the interior area for various configurations. Detailed Implementation

[0047] The present invention will now be described in further detail with reference to the accompanying drawings.

[0048] Figure 1 This is a schematic diagram of the optimized deployment of the present invention. A node deployment method that takes into account both internal and external target time difference positioning and direction finding, the method specifically includes the following steps:

[0049] Step 1: Construct a node deployment scenario for indoor area positioning and outdoor area direction finding, i.e., a wireless sensor network, which includes M wireless sensor nodes.

[0050] Step 2: For the indoor area, select the first node of the wireless sensor network as the reference node and calculate the signal source u in the indoor area. k The covariance matrix Q of the Time Difference of Arrival (TDOA) value and the TDOA measurement error relative to the wireless sensor. k ;

[0051] Step 3: For the external field region, calculate the signal source a in the external field region. k Compared to the Time of Arrival (TOA) of the wireless sensor network, adding Gaussian measurement error yields the equivalent Time of Arrival (TOA) measurement value for each positioning node. Where, n i,k Let be a Gaussian variable with zero mean and variance s. 2 i,k Define n k ={n1,n2,…,n N}, its covariance matrix Γ q =diag{s 2 1,k ,s 2 2,k ,…,s 2 N,k}; Selecting the first node of the wireless sensor network as a reference, the signal source a is obtained. k The time difference of arrival (TDOA) measurement value indicates that all wireless sensor nodes are at the same level relative to signal source a. k Time Difference of Arrival (TDOA) Measurement Error Vector x k The covariance matrix is ​​Rk ;

[0052] Step 4: Perform uniform sampling within the inner field area to obtain N. s sampling points u i i = 1, 2, ..., N s Calculate the Cramer-Rao lower bound (CRLB) for all sampled points and obtain its trace. The mean Cramero lower bound (CRLB) for the inner field area is:

[0053] Step 5: Perform uniform sampling within the outer field area to obtain N. o sampling points u i i = 1, 2, ..., N o Calculate the Cramer-Rao lower bound (CRLB) for all sampling points and obtain the trace of its direction-finding dimension. The mean Cramerlow lower bound (CRLB) for the outer field area is:

[0054] By using the Modified Polar Representation (MPR) method, the positions of sampling points in the field region are represented by azimuth, orientation, and inverse distance; thus, the Cramer-Rao lower bound of the sampling points in the field region under the MPR coordinate system is determined. Assuming the wireless sensor reference node s1 is located at the origin, then in

[0055]

[0056] L = [O (M-1)×2 ,1 M-1 / g o2 ].

[0057] θ o φ o and g o These represent the azimuth, elevation, and relative inverse distance of the target signal source in the field area relative to the wireless sensor node, respectively.

[0058] Step Six: Based on the importance of the objective, the average Cramer-Robber lower bound (CRLB) of the inner and outer field regions from Steps Four and Five is weighted and summed to obtain the result. ω1 and ω2 are the importance weights of the inner field region and the outer field region, respectively;

[0059] Step 7: Minimize the steps in Step 6 Let S be the objective function, S be the deployable area of ​​the wireless sensor nodes, S be the first constraint, and S be the sensing capability of the wireless sensors, i.e., the node coverage must be greater than or equal to the actual target coverage C. The node locations of the wireless sensor network are the decision variables, thus constructing an optimization problem. Represented as:

[0060]

[0061] stC1:s i ∈S, i=1,2,...,M

[0062] C2:ρ≥C

[0063] Step 8: Solve the optimization problem using the Particle Swarm Optimization (PSO) algorithm. The global optimal solution of the objective function is calculated, and the optimal deployment location of the wireless sensor network is finally output.

[0064] Furthermore, in step one, the inner field area and the outer field area together constitute the key monitoring area. The targets in the inner field area are located, and the targets in the outer field area are oriented.

[0065] Furthermore, in step two, the signal source u in the inner field area k The covariance matrix Q of the measurement error relative to the time difference of arrival (TDOA) of the wireless sensor k It can be done To calculate, where B is the signal bandwidth, B n Let be the noise bandwidth of the wireless sensor node receiver, T be the duration of the received signal, and γ be the equivalent input signal-to-noise ratio of the two signals; let τ represent the estimated Time Difference of Arrival (TDOA). Then, the Cramer-Rao lower bound (CRLB) for the TDOA parameter estimation can be expressed as: Assuming that the signals received by each wireless sensor are independent and follow the same distribution characteristics, the specific expression for the covariance matrix Q can be derived as follows:

[0066]

[0067] Furthermore, in step three, signal source a k The measured values ​​include measurement errors and follow a Gaussian distribution.

[0068] Furthermore, in step four, the lower bound of the target signal source in the inner field area is determined. in, It is the derivative of the true value of the Time Difference of Arrival (TDOA) with respect to the location of the signal source, characterizing the wireless sensor node's position relative to the signal source u. i Spatial resolution.

[0069] Furthermore, in step five, the direction finding dimension refers to the 2*2 matrix at the top left corner of the Cramér-Rao lower bound (CRLB) in a 3D scene, and to the 1*1 matrix at the top left corner of the Cramér-Rao lower bound (CRLB) in a 2D scene.

[0070] Furthermore, in step seven, the sensing capability of a wireless sensor refers to the degree to which a wireless sensor node perceives events or phenomena within its monitoring area; assuming the target monitoring area is D and the number of wireless sensor nodes is N, the wireless sensor nodes are numbered and represented as a set S = {s1, s2, ..., s...} i}, i = 1, 2, ..., N, where the detection range of each wireless sensor node is a. i If the area of ​​the target detection region is A, then Let S2 = |A| be the maximum coverage area of ​​the wireless sensor node. Then the coverage rate of the monitoring area of ​​the WSN is... Let ρ represent the sensing capability of a wireless sensor.

[0071] Furthermore, step eight includes the following sub-steps:

[0072] 8.1) First, initialize the particle swarm by setting the population size N, maximum number of iterations M, inertia factor ω, individual learning factor c1, group learning factor c2, single particle dimension D, the moving speed ν of all particles, and the initial position of all particles. The initial position of the particles is set according to the independent variable description under this model, that is, the first three particles in all populations are set to 0, and the initial positions of the remaining particles are randomly generated within the optimization constraints by a unified number generator.

[0073] 8.2) Select from step six As the fitness function of the particle swarm optimization algorithm, the initial fitness function values ​​of all particles in each swarm are calculated.

[0074] 8.3) Next, control the particles to move according to the velocity and position update formulas, generate new particles, and compare the fitness function value of the new particles with the initial fitness function value; in the optimization problem of step seven. In this study, the smaller the fitness value of a particle, the better its indoor positioning and outdoor direction finding performance. By comparing the fitness function values ​​of each particle, the optimal particle and its corresponding fitness function value are determined.

[0075] 8.4) If the number of iterations does not reach the preset value or the global optimal position does not meet the minimum limit, then repeat step 8.3 until the specified number of iterations is reached; finally, the particle with the lowest fitness in all populations is the optimal solution.

[0076] Simulation Analysis

[0077] 1. Simulation Experiment Conditions

[0078] The hardware platform for the simulation experiment of this invention is: AMD Ryzen 7 5800H processor with Radeon Graphics, clock speed of 3.20GHz, and 16.0GB of memory.

[0079] The software platform for the simulation experiment of this invention is: Windows 11 operating system and Matlab R2021b.

[0080] In the simulation, the wireless sensor network deployment area is set as R1:{x∈[-5,5],y∈[-5,5],z∈[-5,5]}, the inner field area is R2:{x∈[-7.5,7.5],y∈[-7.5,7.5],z∈[0.1]}, and the outer field area is R3:{(x 2 +y 2 +z 2 The values ​​are ∈ [20, 200], with units of km; the equivalent bandwidth of the signal in the inner field region is B = 200 kHz, the signal transmission power is 34 dBm, the noise equivalent bandwidth is B = 10 MHz, and the noise power spectral density is -110 dBm / Hz; the target measurement noise covariance matrix in the outer field region is... in The unit is m 2 In addition, ω1 and ω2 in the objective function are the importance weights of the inner and outer field regions, respectively. In this simulation, the inner field region is more important than the outer field region, so ω1 = 0.8 and ω2 = 0.2 are selected. The RMSE is used as the standard for measuring the outer field direction finding performance, defined as follows:

[0081]

[0082] Where K is the number of Monte Carlo simulations, K = 2000, θ k φ k Here, represents the azimuth and elevation angles obtained from the k-th simulation. The average CRLB is used as the performance metric for indoor positioning, defined as follows:

[0083]

[0084] Where r is the positioning parameter, u is the target source location, and the positioning parameter covariance matrix is ​​Q. r The number of target sources is N s .

[0085] 2. Simulation Content and Result Analysis

[0086] To verify the performance of the proposed method, four node location optimization deployment methods were used for comparison. These four methods were not constrained by sensing capabilities during the deployment process. They were DES deployment, rectangular deployment, arc deployment, and triangular deployment. DES deployment was the result of optimization deployment using the particle swarm optimization algorithm with the weighted sum of the average positioning accuracy of the inner and outer fields as the objective function, without sensing capability constraints. Rectangular, arc, and triangular are three classic regular station configurations.

[0087] Figure 2 , Figure 3 , Figure 4 The simulation results are shown in the figure, which sets the distance of the field area from the coordinate origin to vary from 20km to 200km and the RDOA measurement error of the field area to 1m. The MPR configuration refers to the configuration obtained by the optimized deployment method proposed in this invention. Figure 2 A comparative diagram of CRLB positioning for various interior configurations; Figure 3 RMSE for orientation measurement of the external field region for various configurations; Figure 4 This is a schematic diagram showing the coverage of the interior area for various configurations.

[0088] like Figure 2 , 3 As shown in Figure 4, the MPR configuration effectively improves the performance of time difference localization for indoor targets, the performance of time difference direction finding for outdoor targets, and the coverage of the indoor area compared to other wireless sensor node deployment configurations. Figure 2 In the test, when Range = 100km, the MPR configuration improved the interior field positioning CRLB by 1.83dB, 5.21dB, 4.15dB, and 4.92dB respectively compared to the DES, rectangular, arc-shaped, and triangular configurations. Figure 3 In the MPR configuration, when Range = 100km, the angle estimation performance is improved by 0.0058 degrees, 0.0124 degrees, 0.0196 degrees, and 0.1579 degrees respectively compared to the DES, rectangular, arc, and triangular configurations. However, due to the excessively large RMSE error in the triangular configuration's external field direction finding, [further improvements are needed]. Figure 3 The curve is omitted in the text. Figure 4 In the simulation, when Range = 100km, the MPR configuration improved the inner field coverage by 4.9%, 19.8%, 10.8%, and 4.1% compared to the DES, rectangular, arc-shaped, and triangular configurations, respectively. Simulation results show that the MPR configuration outperforms the DES and other configurations in terms of inner field time difference positioning performance, outer field time difference direction finding performance, and inner field coverage.

[0089] Figure 5 , Figure 6 , Figure 7To set the measurement error of the target source RDOA in the field area to vary from -30dB to 40dB in 10dB intervals, the simulation results are shown at a distance of 80km from the coordinate origin in the field area. Figure 5 A comparative diagram of CRLB positioning for various interior configurations; Figure 6 RMSE for orientation measurement of the external field region for various configurations; Figure 7 This is a schematic diagram showing the coverage of the interior area for various configurations.

[0090] Depend on Figure 5 , 6 As shown in Figure 7, the proposed method configuration in this section effectively improves indoor target time difference localization performance, outdoor target time difference direction finding performance, and indoor area coverage compared to other wireless sensor node deployment configurations. Figure 5 In the study, when the RDOA measurement error was 20dB, the MPR configuration improved the internal field positioning CRLB by 2.19dB, 2.29dB, 3.06dB, and 3.36dB compared to the DES, arc, triangular, and rectangular configurations, respectively. Figure 6 In the study, when the RDOA measurement error was 20 dB, the MPR configuration improved the angle estimation performance by 0.010 degrees, 2.411 degrees, 0.186 degrees, and 0.067 degrees compared to the DES, arc, triangular, and rectangular configurations, respectively. Figure 7 In the simulation, when the RDOA measurement error is 10dB, the MPR configuration improves the inner field coverage by 5.0%, 10.7%, 4.1%, and 19.8% compared to the DES, arc, triangular, and rectangular configurations, respectively. Simulation results show that the MPR configuration outperforms the DES and other configurations in terms of inner field time difference positioning performance, outer field time difference direction finding performance, and inner field coverage.

Claims

1. A node deployment method for both internal and external field target time difference positioning and direction finding, characterized in that, Specifically comprising the following steps: Step one: constructing a node deployment scenario for positioning in the inner field area and direction finding in the outer field area, i.e. a wireless sensor network, which includes M wireless sensor nodes; Step two: for the inner field area, select the first node of the wireless sensor network as the reference node, calculate the inner field area signal source u k The time difference of arrival TDOA value and the covariance matrix Q of the time difference of arrival TDOA measurement error of the wireless sensor relative to the time difference of arrival TDOA value k ; Step three: calculate the field area signal source a for the field area k The equivalent time of arrival value TOA measurement value of each positioning node is obtained by adding a Gaussian measurement error to the time of arrival value TOA of the wireless sensor network Wherein, n i,k is a zero-mean Gaussian variable, and the variance is s 2 i,k ; define n k ={n1, n2, …, n N}, and the covariance matrix G q =diag{s 2 1,k ,s 2 2,k ,…,s 2 N,k}; select the first node of the wireless sensor network as a reference to obtain the time difference of arrival TDOA measurement value of the signal source a k , and the covariance matrix R k of the time difference of arrival TDOA measurement error vector x k of the signal source a k of all wireless sensor nodes is Step four: uniformly sampling in the inner field region to obtain N s sample points u i , i = 1, 2, …, N s , calculating the Cramer-Rao lower bound CRLB of all sample points and obtaining the trace to get C(u i ), i = 1, 2, …, N s , then the average Cramer-Rao lower bound CRLB of the inner field region is Step five: uniformly sampling in the outer field region to obtain N o sampling points u i ,i=1,2,…,N o , calculate the CRLB of all sampling points and obtain the trace of the direction finding dimension to obtain C(u j ),i=1,2,…,N o , then the average CRLB of the outer field region is By using the modified polar representation (MPR) method, the position of the sampling point in the outer field region is represented by the azimuth angle, the direction angle and the inverse distance. The Cramer-Rao lower bound of the sampling point in the outer field region in the MPR coordinate system Let the wireless sensor reference node s1 be located at the coordinate origin, then wherein L = [O (M-1)×2 ,1 M-1 / g o2 ]. θ o , φ o , and g o represent the azimuth angle, the elevation angle and the relative inverse distance of the field region target signal source with respect to the wireless sensor node, respectively; Step six: From the target importance, the average CRLB of the inner field and the outer field in step four and step five are weighted and summed to obtain C a (u o ) = ω1C as (u o ) + ω2C ao (u o ), ω1, ω2 are the importance weights of the inner field and the outer field respectively; Step seven: Minimize C a (u o ) as the objective function, the deployment area of the wireless sensor node as the first constraint condition, the sensing capability of the wireless sensor as the second constraint condition, i.e., the node coverage is greater than or equal to the actual set target coverage C, and the node position of the wireless sensor network as the decision variable to construct an optimization problem P 1 , which is represented as: s.t. C1: s i ∈ S, i = 1, 2,..., M C2: p >= C Step eight: solve the optimization problem P by using particle swarm algorithm PSO 1 , calculate the global optimal solution of the objective function, and finally output the optimal deployment position of the wireless sensor network.

2. The node deployment method for both internal and external field target time difference positioning and direction finding according to claim 1, characterized in that, In the step one, the inner field area and the outer field area together constitute a key monitoring area, and the target in the inner field area is positioned and the target in the outer field area is direction found.

3. The node deployment method for both internal and external field target time difference positioning and direction finding according to claim 1, characterized in that, In step two, the signal source u in the inner field area k The covariance matrix Q of the measurement error relative to the time difference of arrival (TDOA) of the wireless sensor k It can be done To calculate, where B is the signal bandwidth, B n Let be the noise bandwidth of the receiving node of the wireless sensor node, T be the duration of the received signal, and γ be the equivalent input signal-to-noise ratio of the two signals; let τ represent the estimated time difference of arrival (TDOA). Then, the Cramer-Rao lower bound (CRLB) for the estimation of the TDOA parameter can be expressed as: Assuming that the signals received by each wireless sensor are independent and follow the same distribution characteristics, the specific expression for the covariance matrix Q can be derived as follows:

4. The node deployment method for target time-difference positioning and direction finding in both internal and external fields according to claim 1, characterized in that, In the third step, the signal source a k The measured values contain measurement errors, which are subject to a Gaussian distribution.

5. The node deployment method for both internal and external field target time difference positioning and direction finding according to claim 1, characterized in that, The Cramér-Rao lower bound of the target signal source in the inner field region in step four i = 1, 2, …, N s wherein, is the derivative of the true value of the time difference of arrival TDOA with respect to the signal source position, characterizing the spatial resolution of the wireless sensor node for the signal source u i .

6. The node deployment method for both internal and external field target time difference positioning and direction finding according to claim 1, characterized in that, The direction finding dimension in the step five refers to a 2*2 matrix in the upper left corner of the CRLB in a three-dimensional scene, and refers to a 1*1 matrix in the upper left corner of the CRLB in a two-dimensional scene.

7. The node deployment method for both internal and external field target time difference positioning and direction finding according to claim 1, characterized in that, In step seven, the wireless sensor sensing capability refers to the degree to which a wireless sensor node perceives events or phenomena within its monitoring area. Assuming the target monitoring area is D and the number of wireless sensor nodes is N, the wireless sensor nodes are numbered and represented as a set S = {s1, s2, ..., s...}. i }, i = 1, 2, ..., N, where the detection range of each wireless sensor node is a. i If the area of ​​the target detection region is A, then Let S2 = |A| be the maximum coverage area of ​​the wireless sensor node. Then the coverage rate of the monitoring area of ​​the WSN is... Let r represent the sensing capability of a wireless sensor.

8. The node deployment method for both internal and external field target time difference positioning and direction finding according to claim 1, characterized in that, The step eight includes the following sub-steps: 8.1) First initialization: setting the population size N of the particle swarm, the maximum iteration number M, the inertia factor ω, the individual learning factor c1, the population learning factor c2, the dimension number D of a single particle, the moving speed v of all particles, and the initial position of all particles, wherein the initial position of the particles is set according to the independent variable description under the model, i.e. the first three particles in all populations are set to 0, and the initial positions of the remaining particles are randomly generated in the optimization constraint range by a uniform digital generator; 8.2) Select C in step six a (u o ) = ω1C as (u o ) + ω2C ao (u o ) as the fitness function of the particle swarm algorithm, and calculate the initial fitness function value of all particles in each group Fitness = C a (u o ) = ω1C as (u o ) + ω2C ao (u o ); 8.3) Next, control the particles to move according to the velocity and position update formula, generate new particles, and compare the fitness function value of the new particles with the initial fitness function value; in the optimization problem P 1 of step seven, the smaller the fitness value of the particle indicates the better the internal field positioning and external field direction finding performance; by comparing the fitness function values of the particles, the optimal particle and its corresponding fitness function value are determined; 8.4) If the iteration number does not reach the preset value or the global optimal position does not satisfy the minimum limit, re-execute step 8.3 until the specified iteration number is reached; finally, the particle with the minimum fitness in all populations is the optimal solution.

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