A mobile node blind-filling optimization deployment method considering internal and external fields

Abstract

A kind of mobile node blind-filling optimization deployment method considering inside and outside field, constructs the node deployment scene for inside field area positioning and outside field area direction finding, i.e.wireless sensor network, wireless sensor sensing capability is regarded as constraint, and optimization deployment method considering inside field area positioning and outside field intrusion target direction finding, improves the coverage of wireless sensor network while considering inside field target positioning and outside field target direction finding of key area, the weighted sum of inside field positioning accuracy and outside field direction finding accuracy according to the importance of inside and outside field is as objective function to optimize, can obtain the best node deployment result.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of spectrum monitoring, and particularly relates to a mobile node blind-filling optimization deployment method considering both internal and external fields. BACKGROUND

[0002] In the field of spectrum monitoring, the passive positioning method is a technical means of directly associating electromagnetic spectrum signals with their spatial positions. At present, the passive positioning and direction finding method based on the time difference (TDOA) parameter has been widely applied in many fields. Compared with the time of arrival (TOA) positioning, the TDOA technology only needs to synchronize between base stations and a common reference time, without synchronization between target nodes and base stations.

[0003] The spatial geometric configuration of the passive time difference positioning and direction finding system is a core factor affecting the positioning and direction finding performance of the monitoring area. For a sensor positioning network that has been deployed, due to a large monitoring area range or limited number of sensors, blind areas appear in the monitoring area and the positioning and direction finding accuracy is insufficient, so the mobile node blind-filling optimization deployment has always been a research hotspot.

[0004] Existing node deployment algorithms often aim at internal field positioning accuracy or treat internal and external field positioning accuracy as the same, ignoring the influence of large external field positioning error on node deployment. When the external target is far away from the sensor network, its relative spatial geometric configuration deteriorates, leading to an increase in external field positioning error, so it is not meaningful to consider the positioning accuracy as the target function at this time, and it is more meaningful to consider the direction finding result of the external target. In addition, the traditional node deployment algorithm considers ideal configuration, but ignores the fact that each sensor node can effectively sense or monitor a limited maximum distance. The following are related research literatures.

[0005] In 2016, Zhou Cheng obtained the optimal station arrangement method by maximizing the Fisher information matrix for the positioning model based on time difference parameter measurement (Reference 1: Zhou Cheng. Time difference positioning optimal station arrangement method research [J]. Journal of Xi'an University of Electronic Science and Technology, 2016, 43(4): 123-127.). The method shows that when the sensor sites surround the target and are equiangularly distributed, the station arrangement is optimal. In 2020, Xia Wei used the free space propagation loss model to represent the TDOA measurement error for the passive time difference positioning method in order to be more suitable for real deployment environment, and simultaneously optimized the deployment by taking the trace of the Cramér-Rao Lower Bound (CRLB) as the objective function (Reference 2: Xia Wei. Passive time difference positioning system optimal station arrangement method research [J]. Radar Science and Technology, 2020, 18(1): 34-38.). In 2021, Wang Chengmin took the average GDOP of the target area as the objective function and used the particle swarm algorithm to find the optimal station arrangement method of the multi-station passive time difference positioning system (Reference 3: Wang Chengmin. Particle swarm algorithm-based multi-machine passive positioning system optimal station arrangement [J]. Computer and Digital Engineering, 2021, 49(03): 487-492.), which significantly reduces the positioning error of the target area. However, these methods are suitable for in-field targets or out-field targets and do not consider the limited sensing ability of the sensor. When the target source is far away from the sensor, the curvature of the signal wavefront tends to be planar, resulting in a threshold effect on the positioning accuracy of the target source. SUMMARY

[0006] In order to overcome the shortcomings of the prior art, the purpose of the present application is to provide a node deployment method for time difference positioning and direction finding of in-field and out-field targets, which takes the weighted sum of the average positioning accuracy of in-field area positioning and the average direction finding accuracy of out-field area as the objective function of optimal station arrangement, and takes the sensor sensing ability as the constraint condition to realize the distributed node deployment for time difference positioning and direction finding of in-field and out-field targets. While achieving the above requirements, it also ensures the maximization of the sensor network coverage range, improves the sensor network coverage range while considering the in-field target positioning and out-field target direction finding of key areas.

[0007] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0008] A mobile node blind-filling optimization deployment method considering in-field and out-field, specifically comprising the following steps:

[0009] Step 1: Construct a wireless sensor network for node deployment scenarios for in-field area positioning and out-field area direction finding, which includes M deployed wireless sensor nodes and N to-be-deployed mobile nodes;

[0010] Step two: For the inner field region, select the first node of the sensor network as the reference node, and calculate the inner field signal source a k The time difference of arrival (TDOA) value and the covariance matrix Q of the TDOA measurement error of the sensor relative to the time of arrival (TOA) value k ;

[0011] Step three: For the outer field region, calculate the outer field signal source o l The equivalent time of arrival (TOA) measurement value of each positioning node by adding a Gaussian measurement error to the time of arrival (TOA) value of the wireless sensor network where n i,l is a zero-mean Gaussian variable with variance s 2 i,l ; define n l ={n1, n2, …, n N}, and its covariance matrix Γ q =diag{s 2 1,l , s 2 2,l , …, s 2 N,l}; select the first node of the wireless sensor network as the reference, and obtain the time difference of arrival (TDOA) measurement value of the outer field signal source o l The covariance matrix R l of the time difference of arrival (TDOA) measurement error vector x l of all sensor nodes relative to the outer field signal source o l ;

[0012] Step four: Inner field region positioning: uniformly sample in the inner field region to obtain N k sampling points a k , k = 1, 2, …, N k , and calculate the Fisher information matrix determined by the wireless sensor network deployed in step one:

[0013]

[0014] and the Fisher information matrix determined by the deployed wireless sensor network and the mobile node:

[0015]

[0016] where tr{·} is the trace operator of the matrix, and are the s iand s j The time difference information matrix provided by the mobile node;

[0017] Step five: Calculate the trace P of the CRLB of the inner field region u (a k ) = tr{ (J u (a k )+ J -1 (a k )) u} and the trace P of the CRLB of the inner field region determined by the deployed wireless sensor network and the mobile node k ) = tr{ (J s (a k )+ J -1 (a l )) l}, which is:

[0018]

[0019] Indicates the improvement of the average positioning accuracy of the inner field region after deploying the mobile node;

[0020] Step six: Uniformly sample in the outer field region to obtain N l sample points o i , l = 1, 2, …, N j , and calculate the Fisher information matrix determined by the deployed wireless sensor network:

[0021]

[0022] and the Fisher information matrix determined by the deployed wireless sensor network and the mobile node:

[0023]

[0024] wherein, and are the s i in the deployed wireless sensor network and the s j in the mobile node, respectively;

[0025] By using the Modified Polar Representation (MPR) method, the azimuth angle, the direction angle and the inverse distance are used to represent the position of the sample point in the outer field region; then the CRLB of the sample point in the outer field region in the MPR coordinate system is Assuming that the wireless sensor reference node s1 is located at the coordinate origin, then wherein:

[0026]

[0027] L = [O (M-1)×2 ,1 M-1 / g o2 ].

[0028] θ o , φ o and g o represent azimuth angle, elevation angle and relative inverse distance of the field region sampling point relative to the wireless sensor node respectively;

[0029] Step seven: Calculate the CRLB of the field region and find the trace P of the direction finding dimension u (o l ) = tr{(J u (o l )) -1} and the trace P of the direction finding dimension of the CRLB determined by the deployed wireless sensor network and the mobile node P(o l ) = tr{(J u (o l )+J s (o l )) -1}, so we get:

[0030]

[0031] wherein, represents the average direction finding accuracy improvement of the inner field region after deploying the mobile node; N l represents the number of sampling points of the outer field region; represents the positioning accuracy improvement of the sampling point o l ;

[0032] Step eight: From the importance of the target, the average positioning accuracy improvement of the inner field region in step five and the average direction finding accuracy improvement of the outer field region in step seven are weighted and summed to get Fitness represents the objective function, and ω1 and ω2 are the importance weights of the inner field region and the outer field region respectively;

[0033] Step nine: Taking the minimization of Fitness in step eight as the objective function and the deployable region of the wireless sensor node as S2 as the first constraint condition, the sensing ability 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, an optimization problem is constructed is represented as:

[0034]

[0035] s.t.C1: s i∈S2, i=1,2,...,N

[0036] C2:ρ≥C

[0037] in, This indicates an improvement in the average positioning accuracy of the indoor area. This indicates improved direction finding accuracy in the field area; s i Indicates sensor coordinates;

[0038] Step 10: 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 mobile nodes is output.

[0039] In step one, the inner field area and the outer field area together form the key monitoring area. The targets in the inner field area are located, and the targets in the outer field area are oriented.

[0040] In step two, the signal source a in the inner field region... k The covariance matrix Q of the measurement error relative to the time difference of arrival (TDOA) of the sensor k pass To calculate, where B is the signal bandwidth, B n Let be the noise bandwidth of the sensor node receiving 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 TDOA parameter estimation is expressed as: Assuming that the signals received by each sensor are independent and follow the same distribution characteristics, the specific expression for Q can be derived as follows:

[0041]

[0042] In step three, the external signal source o l The measured values ​​include measurement errors and follow a Gaussian distribution.

[0043] In step four, in the indoor area positioning scenario, the actual position of the signal is represented by x, and the single positioning position estimate is represented by... The true value of the positioning parameter is represented by m, while the observed value affected by measurement error is represented by... here, The measurement error is assumed to follow a Gaussian distribution with a mean of zero, and the measurement error covariance matrix is ​​expressed as Q. m Based on this, the measured values Compared with the estimated value The joint probability density function can be expressed as:

[0044]

[0045] where k is a scalar; the second-order partial derivative of lnp(x; m) with respect to m is obtained The Fisher information matrix is:

[0046]

[0047] P u (a k )-P(a k )>0, introducing additional positioning nodes in the wireless sensor network positioning system can improve the positioning or direction finding accuracy.

[0048] P where, is the derivative of the true value of the time difference of arrival (TDOA) with respect to the position of the signal source, representing the spatial resolution of the sensor node to the signal source a k .

[0049] The direction finding dimension in step seven refers to the 2*2 matrix in the upper left corner of the Cramer-Rao lower bound (CRLB) in a three-dimensional scene, or the 1*1 matrix in the upper left corner of the Cramer-Rao lower bound (CRLB) in a two-dimensional scene.

[0050] In step nine, the sensor sensing capability refers to the degree of perception of the sensor node to the events or phenomena in its monitoring area; assuming that the target monitoring area is D and the number of sensor nodes is N, the sensor nodes are numbered and represented as a set S = {s1, s2,...,s i}, i = 1, 2,..., N, the detection range of each sensor node is a i , and the target detection area is A, then is the maximum coverage area of the wireless sensor node, and S2 = |A|, then the monitoring area coverage rate of the WSN is The sensing capability of the sensor is represented by p.

[0051] Step ten includes the following sub-steps:

[0052] 10.1) First, initialize and set the population size N of the particle swarm, the maximum number of iterations M, the inertia factor w, the individual learning factor c1, the group 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 description of the independent variable 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 within the optimization constraint range by a uniform digital generator;

[0053] 10.2) Select the As the fitness function of the particle swarm algorithm, the initial fitness function values of all particles in each group are calculated;

[0054] 10.3) Next, the control particles move according to the velocity and position update formula, generate new particles, and compare the fitness function values of the new particles with the initial fitness function values; in the optimization problem constructed in step nine , the greater the fitness value of the particle indicates that the inner field positioning and the outer field direction finding performance are improved; by comparing the fitness function values of each particle, the optimal particle and its corresponding fitness function value are determined;

[0055] 10.4) If the number of iterations does not reach the preset value or the global optimal position does not satisfy the minimum limit, step 10.3 is re-executed until the specified number of iterations is reached; finally, the particle with the minimum fitness in all populations is the optimal solution.

[0056] Compared with the prior art, the present application has the following advantages:

[0057] The present application aims at the mobile node deployment problem considering the inner and outer fields, considers the demand for improving the inner field positioning and the outer field direction finding performance in the actual scene, and the importance of the inner and outer field targets is different, the weighted sum of the average positioning accuracy improvement of the inner field area positioning and the average direction finding accuracy improvement of the outer field area is taken as the target function of the optimization station deployment, the wireless sensor sensing capability is taken as the constraint condition, the distributed node deployment considering the time difference positioning and direction finding of the inner and outer field targets is realized, the inner field monitoring area can be blind filled, and the advantages of considering the inner field positioning accuracy and the outer field direction finding accuracy are possessed.

[0058] The method of the present application improves the coverage rate of the inner field area by using the wireless sensor sensing capability as the constraint, and simulation results show that after the optimization deployment of the present application, in the case of the change of the outer field target source position and RDOA measurement error, the average positioning accuracy of the inner field area, the average direction finding accuracy of the outer field target and the coverage rate performance of the inner field area are significantly improved, and are better than the prior art.

[0059] In summary, the present application can realize the mobile node optimization deployment method considering the inner field area positioning and the outer field intrusion target direction finding, and obtain the best node deployment result. DETAILED DESCRIPTION

[0060] Figure 1 The figure is a mobile node blind filling diagram considering the inner and outer fields.

[0061] Figure 2 The figure is an inner field area average positioning accuracy improvement diagram.

[0062] Figure 3 The figure is an outer field area average direction finding accuracy improvement diagram.

[0063] Figure 4 The figure is for the coverage rate of the inner field area.

[0064] Figure 5 The figure is for the average positioning accuracy of the inner field area.

[0065] Figure 6 The figure is for the average direction finding accuracy of the outer field area.

[0066] Figure 7 The figure is for the coverage rate of the inner field area. DETAILED DESCRIPTION

[0067] The application will be further described in detail below with reference to the accompanying drawings.

[0068] Figure 1 The figure is for the mobile node blind-filling method of the application considering the inner and outer field areas, and the method specifically comprises the following steps:

[0069] Step one: constructing the wireless sensor network of the node deployment scene facing the inner field area positioning and the outer field area direction finding, which comprises M deployed wireless sensor nodes and N to-be-deployed mobile nodes;

[0070] Step two: for the inner field area, selecting the first node of the sensor network as the reference node, calculating the inner field signal source a k The time difference of arrival (TDOA) value of the sensor and the covariance matrix Q of the time difference of arrival (TDOA) measurement error k ;

[0071] Step three: for the outer field area, calculating the outer field signal source o l The equivalent time of arrival (TOA) measurement value of each positioning node by adding the Gaussian measurement error to the time of arrival (TOA) value of the wireless sensor network Wherein, n i,l is a zero-mean Gaussian variable, and the variance is s 2 i,l ; defining n l ={n1, n2, V, n N}, and the covariance matrix Γ q =diag{s 2 1,l ,s 2 2,l ,…,s 2 N,l}; selecting the first node of the wireless sensor network as the reference to obtain the outer field signal source ol The time difference of arrival TDOA measurement value of the field source o l The time difference of arrival TDOA measurement error vector x l The covariance matrix of the field source o l ;

[0072] Step four: uniformly sample in the inner field area to obtain N k sampling points a k , k = 1, 2, …, N k , and calculate the Fisher information matrix determined by the wireless sensor network deployed in step one for all sampling points:

[0073]

[0074] And the Fisher information matrix determined by the deployed wireless sensor network and the mobile node:

[0075]

[0076] Where tr{·} is the trace operator of the matrix, and are the time difference information matrices provided by s i in the deployed wireless sensor network and s j in the mobile node, respectively;

[0077] Step five: calculate the trace P u (a k ) = tr{(J u (a k )) -1} of the Cramer-Rao lower bound CRLB in the inner field area and the trace P(a k ) = tr{(J u (a k )+J s (a k )) -1} of the Cramer-Rao lower bound CRLB determined by the deployed wireless sensor network and the mobile node, to obtain:

[0078]

[0079] Indicates the average positioning accuracy improvement of the inner field area after deploying the mobile node;

[0080] Step six: uniformly sample in the outer field area to obtain N l sampling points o l , l = 1, 2, …, N l, the Fisher information matrix of all sampling points determined by the deployed wireless sensor network is calculated:

[0081]

[0082] and the Fisher information matrix of all sampling points determined by the deployed wireless sensor network and the mobile node is:

[0083]

[0084] where, and are the Fisher information matrix provided by the s i and s j in the deployed wireless sensor network and the mobile node, respectively.

[0085] By using the Modified Polar Representation (MPR) method, the position of the sampling points in the field region is represented by the azimuth angle, the direction angle and the inverse distance; then the Cramer-Rao lower bound of the sampling points in the field region under the MPR coordinate system is Assuming that the wireless sensor reference node s1 is located at the coordinate origin, then where:

[0086]

[0087] L = [O (M-1)×2 ,1 M-1 / g o2 ].

[0088] θ o , φ o and g o represent the azimuth angle, the elevation angle and the relative inverse distance of the sampling points in the field region relative to the wireless sensor node, respectively.

[0089] Step seven: calculate the Cramer-Rao lower bound CRLB of the field region and the trace P of the direction finding dimension u (o l ) = tr{(J u (o l )) -1} and the trace P of the direction finding dimension of the Cramer-Rao lower bound CRLB determined by the deployed wireless sensor network and the mobile node is P (o l ) = tr{(J u (o l )+J s (o l )) -1}, so we get:

[0090]

[0091] wherein, represents the average direction finding precision improvement of the inner field area after deploying the mobile node; N l represents the number of sampling points in the outer field area; represents the positioning precision improvement of the sampling point o l .

[0092] Step eight: from the target importance, the average positioning precision improvement of the inner field area in step five and the average direction finding precision improvement of the outer field area in step seven are weighted and summed to obtain Fitness represents the target function, and ω1 and ω2 are the importance weights of the inner field area and the outer field area, respectively;

[0093] Step nine: taking the Fitness in step eight as the objective function and the deployable area of the wireless sensor node as S2 as the first constraint condition, the wireless sensor perception capability 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, an optimization problem is constructed is represented as:

[0094]

[0095] s.t.C1: s i ∈ S2, i = 1, 2, …, N

[0096] C2: ρ ≥ C

[0097] wherein, represents the average positioning precision improvement of the inner field area, represents the direction finding precision improvement of the outer field area; s i represents the sensor coordinates;

[0098] Step ten: the optimization problem is solved by using a particle swarm algorithm PSO to calculate the global optimal solution of the target function, and finally the optimal deployment position of the mobile node is output.

[0099] Further, in the step one, the inner field area and the outer field area jointly constitute a key monitoring area, the targets in the inner field area are positioned, and the targets in the outer field area are direction found.

[0100] Further, in the step two, the inner field area signal source a k relative to the time difference of arrival TDOA measurement error covariance matrix Q k is calculated by , wherein B is a signal bandwidth, and B nThe noise bandwidth of the receiving end node for the sensor node is T, the time duration of the received signal, and γ is the equivalent input signal-to-noise ratio of the two-way signal; τ represents the time difference of arrival (TDOA) estimation value, and the Cramer-Rao lower bound (CRLB) of the time difference of arrival (TDOA) parameter estimation is represented as: Under the assumption that the signals received by each sensor are independent of each other and follow the same distribution characteristics, the specific expression of Q can be derived as:

[0101]

[0102] Further, in step three, the field signal source o l The measurement value contains measurement error, which follows a Gaussian distribution.

[0103] Further, in step four, in the positioning scene in the indoor field area, the actual position of the signal is represented as x, and the single positioning position estimation is represented as The positioning parameter true value is represented as m, and the observed value affected by the measurement error is represented as Here, The measurement error of m is assumed to follow a Gaussian distribution with a mean of zero, and the measurement error covariance matrix is represented as Q m ; on this basis, the joint probability density function of the measurement value and the estimation value can be represented as

[0104]

[0105] where k is a scalar; the second-order partial derivative of lnp(x; m) with respect to m is obtained as The Fisher information matrix is:

[0106]

[0107] Further, in step five, P u (a k )-P(a k )>0, and the introduction of additional positioning nodes in the wireless sensor network positioning system can improve the positioning or direction finding accuracy.

[0108] Further, in step five, the where is the derivative of the time difference of arrival (TDOA) true value with respect to the signal source position, representing the spatial resolution of the sensor node for the signal source a k .

[0109] Furthermore, in step seven, the direction finding dimension refers to the 2*2 matrix at the top left corner of the Cramér-Rao lower bound (CRLB) in a three-dimensional scene, and to the 1*1 matrix at the top left corner of the Cramér-Rao lower bound (CRLB) in a two-dimensional scene.

[0110] Furthermore, in step nine, the sensor's sensing capability refers to the degree to which a sensor node perceives events or phenomena within its monitoring area; assuming the target monitoring area is D and the number of sensor nodes is N, the sensor nodes are numbered and represented as a set S = {s1, s2, ..., s...} i}, i = 1, 2, ..., N, where the detection range of each 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 the sensor.

[0111] Furthermore, step ten includes the following sub-steps:

[0112] 10.1) 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.

[0113] 10.2) Select the option from step eight. As the fitness function of the particle swarm optimization algorithm, the initial fitness function value of all particles in each swarm is calculated;

[0114] 10.3) 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 constructed in step nine... In this process, the larger the fitness value of a particle, the greater the improvement in its indoor field positioning and outdoor field direction finding performance; by comparing the fitness function values ​​of each particle, the optimal particle and its corresponding fitness function value are determined.

[0115] 10.4) 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 10.3 until the specified number of iterations is reached; finally, the particle with the lowest fitness in all populations is the optimal solution.

[0116] Simulation Analysis

[0117] 1. Simulation Experiment Conditions

[0118] The hardware platform of the simulation experiment of the application is: the processor is AMD Ryzen 7 5800H with Radeon Graphics, the main frequency is 3.20GHz, and the memory is 16.0GB.

[0119] The software platform of the simulation experiment of the application is: Windows 11 operating system and Matlab R2021b.

[0120] In the simulation, the deployment area of the deployed sensor network and the mobile node is set to S:{x∈[-3,3],y∈[-3,3],z∈[0,0.2]}, the outer field area is O:{(x 2 +y 2 +z 2 )∈[10,200]} and the inner field area is A:{x∈[-7.5,7.5],y∈[-7.5,7.5],z∈[-0.05]} in units of km; M=5 unmanned aerial vehicle nodes are selected to form a normalized positioning and direction finding network to monitor the inner and outer field areas, and N=1 unmanned aerial vehicle node is selected to perform mobile blind filling in the inner and outer field areas; the range of the azimuth angle and the pitch angle of the outer field area is set to θ o =[26°,34°] and φ o =[54°,64°]. The signal equivalent bandwidth B of the inner field area is 200KHz, the signal transmission power is 34dBm, the noise equivalent bandwidth B is 10MHz, and the noise power spectral density is-110dBm / Hz; the target measurement noise covariance matrix of the outer field area is wherein the unit is m 2 ; in addition, ω1 and ω2 in the objective function are the importance weights of the inner field area and the outer field area respectively, in this simulation, the importance of the inner field area is higher than that of the outer field area, therefore ω1=0.8 and ω2=0.2 are selected; the inner field positioning performance measurement index adopts the average positioning accuracy improvement in step five, the outer field direction finding performance measurement index adopts the average direction finding accuracy improvement in step seven, and the inner field area coverage performance measurement index adopts the difference between the coverage rate after deploying the mobile node and the coverage rate without deploying the mobile node, that is, the inner field area coverage rate improvement.

[0121] 2. Simulation content and result analysis

[0122] To verify the performance of the method, three node position optimization deployment methods are used as a comparison, which are not subject to the constraints of sensing ability in the deployment process, respectively, DES deployment, top deployment and random deployment; DES deployment is to use the weighted sum of the average positioning accuracy improvement in the inner and outer fields as the objective function without the constraint of sensing ability, and the particle swarm optimization algorithm is used to optimize the deployment result; in the top deployment, the unmanned aerial vehicle tends to be deployed above the inner field area, and its position can be obtained by the following steps: (1) finding the inscribed circle of the deployment area; (2) the position coordinates of the unmanned aerial vehicle are , wherein is the center of the inscribed circle, is the radius of the inscribed circle, z max and z min are the maximum and minimum values of the altitude of the unmanned aerial vehicle respectively, and rand generates a random number uniformly distributed between (0, 1); in the random deployment, the position of the unmanned aerial vehicle in the deployment area is random.

[0123] Figure 2 , Figure 3 , Figure 4 is the simulation result figure when the distance coordinate of the set outer field area is changed from 20km to 200km, and the RDOA measurement error of the outer field area is set to 1m, and MPR configuration refers to the configuration obtained by optimizing the deployment of the method; Figure 2 is the inner field area average positioning accuracy improvement; Figure 3 is the outer field area average direction finding accuracy improvement; Figure 4 is the inner field area coverage rate improvement.

[0124] As shown in Figure 2 , 3 and 4, the MPR configuration can effectively improve the inner field target TDOA positioning performance, the outer field target TDOA direction finding performance and the inner field area coverage rate compared with other sensor node station deployment configurations. In Figure 2 , when Range = 50km, the inner field area average positioning accuracy of the MPR configuration is improved by 0.21dB, 0.27dB and 0.36dB compared with the DES configuration, the vertex deployment configuration and the random deployment configuration. In Figure 3 , when Range = 50km, the average direction finding accuracy of the MPR configuration is improved by 2.16dB, 2.87dB and 2.85dB compared with the DES configuration, the vertex deployment configuration and the random deployment configuration. In addition, in Figure 4 , when Range = 50km, the inner field area coverage rate of the MPR configuration is improved by 1.6%, 5.7% and 8.2% compared with the DES configuration, the vertex deployment configuration and the random deployment configuration. The simulation shows that the MPR configuration is superior to the DES configuration and other configurations in terms of inner field TDOA positioning performance, outer field TDOA direction finding performance and inner field area coverage rate.

[0125] Figure 5 、 Figure 6 、 Figure 7 The simulation result figure of the MPR configuration compared with other sensor node deployment configurations in the outfield area with the RDOA measurement error varying from -30dB to 40dB with an interval of 10dB at the distance coordinate of 10km from the origin point; Figure 5 The average positioning accuracy improvement in the infield area; Figure 6 The average direction finding accuracy improvement in the outfield area; Figure 7 The coverage rate improvement in the infield area.

[0126] Figure 5 、 6 As shown in FIGS. 6, 7 and 8, the MPR configuration can effectively improve the infield target TDOA positioning performance, outfield target TDOA direction finding performance and infield area coverage rate compared with other sensor node deployment configurations. Figure 5 In the simulation, when the RDOA measurement error is 1m, the MPR configuration can improve the infield area average positioning accuracy by 0.06dB, 0.17dB and 0.31dB compared with the DES configuration, the vertex deployment configuration and the random deployment configuration. Figure 6 In the simulation, when the RDOA measurement error is 1m, the MPR configuration can improve the average direction finding accuracy by 1.84dB, 1.24dB and 1.59dB compared with the DES configuration, the vertex deployment configuration and the random deployment configuration. Figure 7 In the simulation, when the RDOA measurement error is 1m, the MPR configuration can improve the infield area coverage rate by 7.4%, 4.1% and 7.4% compared with the DES configuration, the vertex deployment configuration and the random deployment configuration. The simulation shows that the MPR configuration is superior to the DES configuration and other configurations in terms of infield TDOA positioning performance, outfield TDOA direction finding performance and infield area coverage rate.

Claims

1. A method for the deployment of a mobile node for the optimization of blind filling in both internal and external fields, characterized in that, Specifically comprising the following steps: Step one: constructing a wireless sensor network for the node deployment scene of the inner field area positioning and the outer field area direction finding, which includes M deployed wireless sensor nodes and N to-be-deployed mobile nodes; Step two: for the inner field area, select the first node of the sensor network as the reference node, calculate the inner field signal source a k The time difference of arrival TDOA value and the covariance matrix Q of the time difference of arrival TDOA measurement error relative to the sensor k ; Step three: calculate the out-field signal source o l 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,l is a zero-mean Gaussian variable, and the variance is s 2 i,l ; define n l ={n1, n2, K, n N}, and the covariance matrix Γ q =diag{s 2 1,l ,s 2 2,l ,K,s 2 N,l}; select the first node of the wireless sensor network as a reference to obtain the time difference of arrival TDOA measurement value of the out-field signal source o l , and the covariance matrix R l of the time difference of arrival TDOA measurement error vector x l of the out-field signal source o l of all sensor nodes is Step four: In-field area positioning: uniform sampling in the in-field area, obtaining N k sampling points a k ,k = 1,2,K,N k , calculate the Fisher information matrix of all sampling points determined by the wireless sensor network deployed in step one: And the Fisher information matrix determined by the deployed wireless sensor network and the mobile node: where tr{·} is the trace operator of a matrix, and are the s i and s j provided time difference information matrix; Step five: Compute the trace P of the CRLB in the inner field region u (a k ) = tr{J u (a k ) -1} and the trace P(a k ) = tr{J u (a k ) + J s (a k ) -1} of the CRLB jointly determined by the deployed wireless sensor network and the mobile node, we have: P1 A The figure shows the improvement of the average positioning accuracy in the inner field after deploying mobile nodes. Step six: uniformly sampling in the field region to obtain N l sampling points o l , l = 1, 2, K, N l , and calculating the Fisher information matrix determined by the deployed wireless sensor network for all sampling points And the Fisher information matrix determined by the deployed wireless sensor network and the mobile node: wherein, and are the s i and s j provided Fisher information matrix; 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 Assuming that the wireless sensor reference node s1 is 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 sampling point with respect to the wireless sensor node, respectively; Step seven: Compute the CRLB for the field region and find the trace P(o u (o l ) = tr{(J u (o l )) -1} and the trace P(o l ) = tr{(J u (o l )+ J s (o l )) -1} of the CRLB direction finding dimension determined by the deployed wireless sensor network and mobile nodes, thus we have: wherein: represents the average direction-finding accuracy improvement of the inner field area after deploying the mobile node; N l represents the number of sampling points in the outer field area; represents the positioning accuracy improvement of the sampling point o l . Step eight: From the importance of the target, the average positioning accuracy improvement in the inner field region and the average direction finding accuracy improvement in the outer field region in step five and step seven are weighted and summed to obtain Fitness represents the target function, and ω1 and ω2 are the importance weights of the inner field region and the outer field region, respectively. Step nine: wireless sensor node deployment area S2 as the constraint one, wireless sensor perception ability as the constraint two, that is, the node coverage is greater than or equal to the actual set target coverage C, the node position of the wireless sensor network as the decision variable, the optimization problem is constructed with the minimum fitness in step eight as the objective function is represented as: s.t. C1: s i ∈ S2, i = 1, 2,..., N C2: p >= C wherein, represents the improvement of the average positioning accuracy in the inner field area, represents the improvement of the direction finding accuracy in the outer field area; s i represents the sensor coordinates; Step ten: solve the optimization problem by using particle swarm optimization (PSO) The global optimal solution of the objective function is calculated, and finally the optimal deployment position of the mobile node is output.

2. The method of claim 1, wherein, In the step one, the inner field area and the outer field area jointly 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 method of claim 1, wherein, In the step two, the inner field area signal source a k Covariance matrix Q of TDOA measurement error relative to the sensor k is calculated by , where B is the signal bandwidth, B n is the noise bandwidth of the receiving end node of the sensor node, T is the duration of the received signal, and γ is the equivalent input signal-to-noise ratio of the two signals; τ represents the TDOA estimation value, and the Cramer-Rao lower bound (CRLB) of the TDOA parameter estimation is represented as: Under the assumption that the signals received by each sensor are independent of each other and follow the same distribution characteristics, the specific expression of Q can be derived as:

4. The method of claim 1, wherein, In the third step, the external field signal source o l The measured values contain measurement errors, which are subject to a Gaussian distribution.

5. The method of claim 1, wherein, In step four, in the positioning scenario in an indoor field, the actual position of the signal is denoted as x, and the single positioning position estimation is denoted as The true value of the positioning parameter is denoted as m, and the observed value affected by the measurement error is denoted as Here, The measurement error of is assumed to follow a Gaussian distribution with zero mean, and the measurement error covariance matrix is denoted as Q m On this basis, the joint probability density function of the measurement value and the estimation value can be expressed as: where k is a scalar; take the second-order partial derivative of lnp(x; m) with respect to m, to get The Fisher information matrix is:

6. The method of claim 1, wherein, P in step five u (a k )-P(a k ) > 0, introducing additional positioning nodes in a wireless sensor network positioning system can improve positioning or direction finding accuracy.

7. The method of claim 1, wherein, As described in step five 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 sensor node for the signal source a k .

8. The method of claim 1, wherein, The direction finding dimension in the step seven refers to the 2*2 matrix of the left upper corner of the Cramer-Rao lower bound (CRLB) in a three-dimensional scene, and refers to the 1*1 matrix of the left upper corner of the Cramer-Rao lower bound (CRLB) in a two-dimensional scene.

9. The method of claim 1, wherein, In step nine, the sensor sensing capability refers to the degree of sensing of events or phenomena in the monitoring area of the sensor node; assuming that the target monitoring area is D, the number of sensor nodes is N, the sensor nodes are numbered and represented as a set S = {s1, s2,..., s i}, i = 1, 2,..., N, the detection range of each sensor node is a i , the target detection area is A, then is the maximum coverage area of the wireless sensor node, and S2 = |A|, then the monitoring area coverage rate of the WSN is The sensing capability of the sensor is represented by r.

10. The method of claim 1, wherein, The step ten includes the following sub-steps: 10.1) First initialization, set the population size N of the particle swarm, the maximum iteration number M, the inertia factor omega, the individual learning factor c1, the group 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, that is, 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; 10.2) Selecting the best of step eight As the fitness function of the particle swarm algorithm, and calculate the initial fitness function value of all particles in each group; 10.3) 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; the optimization problem constructed in step nine In the optimization problem constructed in step nine, the greater the fitness value of a particle indicates that the inner field positioning and the outer field direction finding performance are improved more; by comparing the fitness function values of the particles, the optimal particle and its corresponding fitness function value are determined; 10.4) If the iteration number does not reach the preset value or the global optimal position does not satisfy the minimum limit, re-execute step 10.3 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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