High-precision passive positioning method based on optimized position

Abstract

The invention discloses a high-precision passive positioning method based on position optimization, and the method comprises the steps: importing the initialization information of positioning stations, a positioning target and an area where the positioning target is located into a central station, and enabling the central station to calculate the positions of the central station and each positioning station, so as to deploy the initial positions of the central station and each positioning station; at the initial position, each positioning station sends detected lateral information to the central station, and the central station calculates to obtain a target position as a coarse-grained positioning result; judging whether the initial positions of the central station and the positioning stations are optimal positions or not, and if so, taking a coarse-grained positioning result as a current positioning result; if not, the central station calculates the optimal positions of the central station and the positioning stations so as to deploy the optimal positions of the central station and the positioning stations; and at the optimal position, each positioning station sends detected lateral information to the central station, and the central station calculates to obtain a target position as a high-precision positioning result. According to the invention, the positioning precision and efficiency can be improved.

Description

Technical Field

[0001] The present invention belongs to the field of electronic information technology, and in particular relates to a high-precision passive positioning method based on optimized position. Background Art

[0002] The accuracy of non-cooperative passive positioning systems, particularly cross-positioning technologies based on the angle of arrival (AoA), is affected by the performance and location of positioning stations. To improve positioning accuracy, signal processing and mathematical analysis are commonly used to continuously enhance positioning station performance. However, the selection of positioning device locations often relies on experience and intuition, lacking scientific and practical application, limiting the accuracy of non-cooperative passive positioning systems.

[0003] With the improvement of computer processing power, the problem of positioning station position optimization has also attracted attention. However, the current positioning station position optimization algorithms have little research on multi-station AOA positioning optimization models, and more focus on hybrid passive positioning scenarios. In addition, the iteration efficiency of most algorithms is low and they are prone to local convergence.

[0004] Therefore, there is an urgent need to provide a high-precision passive positioning method to improve the defects in the existing technology. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a high-precision passive positioning method based on optimized position. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] The present invention provides a high-precision passive positioning method based on optimized position, which is applied to a positioning scenario including one central station and n positioning stations, comprising:

[0007] Import the initialization information of the positioning station, the positioning target, and the area where the positioning target is located into the central station. The central station uses the intelligent optimization multi-station collaborative array method to calculate the position of the central station and each positioning station, and sends the position of each positioning station to each positioning station to deploy the initial position of the central station and each positioning station.

[0008] At the initial position, each positioning station sends the detected lateral information to the central station. The central station calls the density peak clustering algorithm fused with adaptive kernel density estimation to calculate the target position as the coarse-grained positioning result.

[0009] Determine whether the initial positions of the central station and each positioning station are optimal. If so, use the coarse-grained positioning result as the current positioning result. If not, the central station calls the collaborative agent array optimization algorithm based on the coarse-grained positioning result to calculate the optimal positions of the central station and each positioning station, and sends the optimal positions of each positioning station to each positioning station to deploy the optimal positions of the central station and each positioning station.

[0010] At the optimal position, each positioning station sends the detected lateral information to the central station. The central station calls the density peak clustering algorithm fused with adaptive kernel density estimation to calculate the target position as the high-precision positioning result.

[0011] Beneficial effects of the present invention:

[0012] The present invention provides a high-precision passive positioning method based on optimized position. First, the initial positions are deployed for the central station and the positioning stations. All positioning stations are deployed in accordance with the intelligent optimization multi-station collaborative array method, and the area where the largest target is located can be covered with the least number of positioning stations as much as possible; secondly, the target position is calculated as a coarse-grained positioning result based on the density peak clustering algorithm fused with adaptive kernel density estimation; thirdly, it is judged whether the coarse-grained positioning result is optimal. If not, the optimal position of the central station and each positioning station is calculated based on the collaborative agent array optimization algorithm; finally, the target position is calculated as a high-precision positioning result based on the optimal position of the central station and each positioning station. In the present invention, a method of collaboratively optimizing the positioning algorithm and the position of the point station is proposed, which can effectively improve the accuracy and efficiency of positioning.

[0013] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a flow chart of a high-precision passive positioning method based on optimized position provided by an embodiment of the present invention;

[0015] Figure 2 is another schematic diagram of a high-precision passive positioning method based on optimized position provided by an embodiment of the present invention;

[0016] Figure 3 This is a schematic diagram of the central station location initialization selection provided by an embodiment of the present invention;

[0017] Figure 4 This is a schematic diagram of initializing the position of a positioning station provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0019] In order to overcome the shortcomings of the above-mentioned existing methods, the present invention jointly designs the positioning algorithm and the positioning position optimization method, and proposes a high-precision passive positioning method based on optimized position. The positioning method includes four processes, namely the positioning station initial position deployment process, the coarse-grained positioning process, the positioning station position optimization process and the high-precision positioning process.

[0020] See Figure 1 , Figure 1 This is a flow chart of a high-precision passive positioning method based on optimized position provided by an embodiment of the present invention. Figure 2 This is another schematic diagram of a high-precision passive positioning method based on optimized position provided by an embodiment of the present invention. The high-precision passive positioning method based on optimized position provided by the present invention is applied to a positioning scenario including one central station and n positioning stations, including:

[0021] S101. Import the initialization information of the positioning station, positioning target and the area where the positioning target is located into the central station. The central station uses the intelligent optimization multi-station collaborative array method to calculate the position of the central station and each positioning station, and sends the position of each positioning station to each positioning station to deploy the initial position of the central station and each positioning station.

[0022] Specifically, in this embodiment, see Figure 3 , Figure 3 This is a schematic diagram of the central station location initialization selection provided by an embodiment of the present invention. The location deployment of the central station and each positioning station includes:

[0023] Taking the midpoint of the upper boundary of the area where the positioning target is located as the starting point, the vertical upper boundary is extended along the first direction for a distance d loc The point is taken as the initial position of the central station S0 to deploy the central station S0;

[0024] With the central station S0 as the center, the maximum communication distance d of the central station com Draw a circle O0 as the radius, and randomly select three locations with an interval of 120° on the circle O0 to deploy positioning stations S1, S2, and S3;

[0025] Positioning stations S1, S2 and S3 are respectively used as centers, and positioning stations are evenly deployed on a circle with the maximum communication distance of the positioning stations as the radius, until n positioning stations are deployed.

[0026] For details, see Figure 4 , Figure 4 This is a schematic diagram of the initialization of the positioning station provided by an embodiment of the present invention, with the positioning station S1 as the center and the maximum communication distance d of the positioning station S1 as the center. com1Draw a circle O1 as the radius, take the central station S0 as the starting point on the circle O1, and deploy positioning stations S4 and S5 at intervals of 120° clockwise;

[0027] With positioning station S2 as the center, the maximum communication distance d of positioning station S2 com2 Draw a circle O2 as the radius, take the central station S0 as the starting point on the circle O2, and deploy positioning stations S6 and S7 at intervals of 120° clockwise.

[0028] With positioning station S3 as the center, the maximum communication distance d of positioning station S3 com3 Draw a circle O3 as the radius, take the central station S0 as the starting point on the circle O3, and deploy positioning stations S8 and S9 at intervals of 120° clockwise.

[0029] With positioning station S4 as the center, the maximum communication distance d of positioning station S4 com4 Draw a circle O4 with the radius as the starting point, and randomly select a positioning station on the circle O4 as the starting point. Select a location with an interval of 120° and no positioning station to deploy positioning station S 10 ;

[0030] With positioning station S5 as the center, the maximum communication distance d of positioning station S5 com5 Draw a circle O5 with the radius as the starting point on circle O4, and select a randomly selected positioning station as the starting point. Deploy positioning stations S at locations with an interval of 120° and no positioning stations. 11 ;

[0031] With positioning station S6 as the center, the maximum communication distance d of positioning station S6 com6 Draw a circle O6 with the radius as the starting point, and randomly select a positioning station on the circle O6 as the starting point. Select a location with an interval of 120° and no positioning station to deploy positioning station S 12 ;

[0032] With positioning station S7 as the center, the maximum communication distance d of positioning station S7 com7 Draw a circle O7 with the radius as the starting point, and select a randomly selected positioning station on the circle O7 as the starting point. Deploy positioning stations S at locations with an interval of 120° and no positioning stations. 13 ;

[0033] With positioning station S8 as the center, the maximum communication distance d of positioning station S8 com8 Draw a circle O8 with the radius as the starting point, and select a randomly selected positioning station on the circle O8 as the starting point. Deploy positioning stations S at locations with an interval of 120° and no positioning stations. 14 ;

[0034] With positioning station S9 as the center, the maximum communication distance d of positioning station S9 com9Draw a circle O9 with the radius as the starting point, and randomly select a positioning station on the circle O9 as the starting point. Select a location with an interval of 120° and no positioning station to deploy positioning station S 15 .

[0035] S102. At the initial position, each positioning station sends the detected lateral information to the central station. The central station calls the density peak clustering algorithm fused with adaptive kernel density estimation to calculate the target position as the coarse-grained positioning result.

[0036] Specifically, this embodiment includes:

[0037] The central station collects the lateral information detected by each positioning station to calculate the intersection of the lateral lines and construct the data set X = {(x1, y1), (x2, y2), ..., (x n ,y n )};

[0038] The natural nearest neighbor method is used to calculate the natural nearest neighbor points of each lateral line intersection in the data set, and the natural nearest neighbor point set knn(x i ); calculate the nearest neighbor relationship NNN(x i ,y i ), whose expression is:

[0039]

[0040] According to the natural neighbor point set knn(x i ), and the nearest neighbor relationship NNN(x i ,y i ), calculate the local density of each lateral line intersection in the data set;

[0041] Calculate the relative distances between each lateral line intersection in the dataset based on the local density of each lateral line intersection in the dataset;

[0042] Calculate the decision value of each lateral line intersection in the data set based on local density and relative distance;

[0043] A decision diagram is drawn based on the decision values ​​of each lateral line intersection in the data set; optionally, for each lateral line intersection, its local density is used as the horizontal coordinate value and its relative distance is used as the vertical coordinate value, and the coordinate diagram is drawn as the decision diagram;

[0044] Select multiple cluster centers from the decision graph, obtain the nearest neighbor points of each cluster center, and construct a set of clusters corresponding to each cluster center; each cluster center corresponds to a target; optionally, the point in the upper right corner of the decision graph that is farthest from other points is used as the cluster center;

[0045] Calculate the average value of each lateral line intersection point in each cluster set to obtain the target position W, which is expressed as:

[0046]

[0047] Where N represents the total number of lateral line intersections in each cluster set, x i ' represents the horizontal coordinate of the i-th lateral line intersection point in the cluster set, y i ' represents the ordinate of the intersection point of the i-th lateral line in the cluster set; optionally, points in the dataset X that are not natural neighbors of the points in the cluster are assigned to the cluster set where the nearest cluster center point is located;

[0048] In this embodiment, calculating the local density of each lateral line intersection in the data set includes:

[0049] The truncated kernel method is used to find the intersection of the lateral lines (x i ,y i )’s natural neighbor point (i.e., in knn(x i ) in the figure, and the Gaussian kernel method is used to process the lateral line intersection point (x i ,y i ) (i.e., in the dataset X but not in knn(x i ) in the figure) and get the lateral line intersection point (x i ,y i ) local density ρ i , whose expression is:

[0050]

[0051] Where a represents the maximum value of the local density of the truncated kernel among all the lateral line intersections, b represents the maximum value of the Gaussian kernel density among all the lateral line intersections, and d ij Indicates the intersection point of the lateral lines (x i ,y i ) and (x j ,y j ), χ(x j ) represents a piecewise function, and its expression is:

[0052]

[0053] Among them, xj ∈NNN(x i ) represents the lateral line intersection point (x j ,y j ) is the lateral line intersection point (x i ,y i )’s natural neighbors, Indicates the intersection point of the lateral lines (x j ,y j ) is the lateral line intersection point (x i ,y i )’s non-natural neighbors.

[0054] In this embodiment, calculating the relative distances between the intersection points of the lateral lines in the data set includes:

[0055] Construct local density greater than the intersection point of the lateral line (x i ,y i ) of the local density of the lateral line intersection point set I i ;

[0056] Calculate the lateral line intersection point (x i ,y i ) of the relative distance δ i , whose expression is:

[0057]

[0058] in, Represents the empty set.

[0059] In this embodiment, the lateral line intersection point (x i ,y i )’s decision value γ i The expression is:

[0060] γ i =ρ i δ i ;

[0061] Among them, ρ i Indicates the intersection point of the lateral lines (x i ,y i ) local density, δ i Indicates the intersection point of the lateral lines (x i ,y i ) relative distance.

[0062] S103. Determine whether the initial positions of the central station and each positioning station are optimal positions. If so, use the coarse-grained positioning result as the current positioning result. If not, the central station calls the collaborative agent deployment optimization algorithm based on the coarse-grained positioning result to calculate the optimal positions of the central station and each positioning station, and sends the optimal positions of each positioning station to each positioning station to deploy the optimal positions of the central station and each positioning station.

[0063] Specifically, this embodiment includes:

[0064] According to the initial position s of the central station and each positioning station i =(x i ,y i ), construct the first particle, whose expression is:

[0065] X1=[((x1,y1),(x2,y2),…,(x L ,y L ))];

[0066] Based on the lth particle, the l+1th particle is calculated, and its expression is:

[0067]

[0068] Where l = 2,…,L, L represents the total number of particles, and mod(·) represents the modulo operation;

[0069] Based on all the calculated particles, a particle swarm is constructed, and the initial fitness value Fit(X) of each particle is calculated;

[0070] The current fitness value of the particle is used as the individual optimal fitness value pb, and the optimal fitness value gb of the particle swarm is updated. The expressions are:

[0071] pb k =max(Fit(X k ));

[0072] gb k =max(Fit(p));

[0073] Among them, Fit(p) represents the fitness value of particle swarm p;

[0074] At the preset number of iterations iter max In the calculation, the particle with the largest fitness value is obtained, and the position of the central station corresponding to the particle and each positioning station is regarded as the optimal position.

[0075] In this embodiment, the expression of the initial fitness value Fit(X) of the particle is:

[0076]

[0077]

[0078] Where X=[x1,y1,...,x n ,y n ] represents the position coordinates of the central station and each positioning station, D represents the area where the target is located, s represents the set of lateral line intersection points in the cluster set of the positioning fuzzy area, M represents the number of discrete points, GDOP(s) represents the geometric precision factor at s, m represents the number of radiation source targets, e x and e y Indicates the coordinates of the center point of the area where the target is located, n indicates the number of central stations and each positioning station, G indicates the connectivity between the central station and the positioning station or any two positioning stations. The signals between any two positioning stations can reach each other, or the signals between the central station and the positioning station can reach each other, that is, any two points in the positioning network are connected. G indicates a connectivity graph. The signals between any two positioning stations cannot reach each other, or the signals between the central station and the positioning station can reach each other. G indicates that it is not a connectivity graph.

[0079] In this embodiment, the particle with the largest fitness value is calculated, including:

[0080] Calculate the dynamic inertia weight coefficient w(i), which is expressed as:

[0081]

[0082] Among them, w max Indicates the maximum value of the inertia weight coefficient, w min Indicates the minimum value of the inertia weight coefficient;

[0083] Update the current particle's velocity v according to the dynamic inertia weight coefficient i+1 and position X i+1 , whose expression is:

[0084] v i+1 =ω×v i +c1×rand()×(pb i -X i )+c2×rand()×(gb-X i );

[0085] X i+1 =X i +v i+1 ;

[0086] Among them, ω represents the inertia factor, c1 represents the individual learning factor, c2 represents the group learning factor, rand() represents the random number, X irepresents the position of the particle at the last moment, v i represents the velocity of the particle at the previous moment;

[0087] Update the particle's fitness value Fit(X);

[0088] According to the updated fitness value of the particle, the individual optimal fitness value pb of the particle and the optimal fitness value gb of the particle swarm are updated.

[0089] S104. At the optimal position, each positioning station sends the detected lateral information to the central station. The central station calls the density peak clustering algorithm fused with adaptive kernel density estimation to calculate the target position as a high-precision positioning result.

[0090] In summary, the present invention provides a high-precision passive positioning method based on optimized position. First, the initial positions are deployed for the central station and the positioning stations. All positioning stations are deployed in accordance with the intelligent optimization multi-station collaborative array method, and the area where the largest target is located can be covered with the least number of positioning stations as much as possible; secondly, the target position is calculated as a coarse-grained positioning result based on the density peak clustering algorithm fused with adaptive kernel density estimation; thirdly, whether the coarse-grained positioning result is optimal is judged. If not, the optimal position of the central station and each positioning station is calculated based on the collaborative agent array optimization algorithm; finally, the target position is calculated as a high-precision positioning result based on the optimal position of the central station and each positioning station. In the present invention, a method of collaboratively optimizing the positioning algorithm and the position of the point station is proposed, which can effectively improve the accuracy and efficiency of the positioning system.

[0091] It should be noted that, in this document, relational terms such as first and second are used solely to distinguish one entity or operation from another, and do not necessarily require or imply any actual relationship or order between these entities or operations. Furthermore, the terms "comprise," "include," or any other variations thereof are intended to encompass non-exclusive inclusion, such that an article or device comprising a list of elements includes not only those elements but also other elements not explicitly listed. Without further limitation, an element defined by the phrase "comprising a..." does not preclude the presence of additional identical elements in the article or device comprising the element. Terms such as "connected" or "connected" are not limited to physical or mechanical connections but may include electrical connections, whether direct or indirect. References to orientations or positional relationships, such as "upper," "lower," "left," and "right," are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate description and simplify the description of the present invention. They do not indicate or imply that the device or element referred to must have, be constructed, or operate in a specific orientation, and are therefore not to be construed as limiting the present invention.

[0092] In the description of this specification, the reference terms "one embodiment," "some embodiments," "example," "specific example," or "some examples" mean that the specific features or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification.

[0093] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A high-precision passive positioning method based on optimized position, applied to a positioning scenario including one central station and n positioning stations, characterized in that: include: Importing the initialization information of the positioning station, the positioning target, and the area where the positioning target is located into the central station, the central station uses the intelligent optimization multi-station collaborative array method to calculate the position of the central station and each of the positioning stations, and sends the position of each of the positioning stations to each of the positioning stations to deploy the initial positions of the central station and each of the positioning stations; At the initial position, each positioning station sends the detected lateral information to the central station, and the central station calls the density peak clustering algorithm fused with adaptive kernel density estimation to calculate the target position as the coarse-grained positioning result; Determine whether the initial positions of the central station and each of the positioning stations are optimal positions. If so, use the coarse-grained positioning result as the current positioning result. If not, the central station calls the collaborative agent array optimization algorithm based on the coarse-grained positioning result to calculate the optimal positions of the central station and each of the positioning stations, and sends the optimal positions of each of the positioning stations to each of the positioning stations to deploy the optimal positions of the central station and each of the positioning stations. At the optimal position, each positioning station sends the detected lateral information to the central station, and the central station calls the density peak clustering algorithm fused with adaptive kernel density estimation to calculate the target position as a high-precision positioning result.

2. The high-precision passive positioning method based on optimized position according to claim 1, characterized in that: The method of importing the initialization information of the positioning station, the positioning target, and the area where the positioning target is located into the central station, and the central station using the intelligent optimization multi-station collaborative array method to calculate the position of the central station and each of the positioning stations includes: Taking the midpoint of the upper boundary of the area where the positioning target is located as the starting point, the vertical upper boundary is extended along the first direction by a distance d loc The point is used as the initial position of the central station S0 to deploy the central station S0; With the central station S0 as the center, the maximum communication distance d of the central station com Draw a circle O0 as the radius, and randomly select three locations with an interval of 120° on the circle O0 to deploy positioning stations S1, S2, and S3; Positioning stations are evenly deployed on a circle with the maximum communication distance of the positioning station as the radius, with the positioning station S1, the positioning station S2 and the positioning station S3 as the center, until n positioning stations are deployed.

3. The high-precision passive positioning method based on optimized position according to claim 1, characterized in that: Each of the positioning stations sends the detected lateral information to the central station, and the central station calls a density peak clustering algorithm fused with adaptive kernel density estimation to calculate the target position, including: The central station collects the lateral information detected by each positioning station to calculate the lateral line intersection point and constructs a data set X = {(x1, y1), (x2, y2), ..., (x n ,y n )}; The natural nearest neighbor method is used to calculate the natural nearest neighbor points of each lateral line intersection in the data set, and a natural nearest neighbor point set knn(x i ); Calculate the nearest neighbor relationship NNN(x i ,y i ), whose expression is: According to the natural neighbor point set knn(x i ), and the nearest neighbor relationship NNN(x i ,y i ), calculating the local density of each lateral line intersection in the data set; Calculating relative distances between respective lateral line intersections in the data set based on local densities of the respective lateral line intersections in the data set; calculating a decision value for each lateral line intersection point in the data set based on the local density and the relative distance; Drawing a decision diagram based on the decision values ​​of each lateral line intersection point in the data set; Selecting multiple cluster center points from the decision graph, obtaining the nearest neighbor points of each cluster center point, and constructing cluster sets corresponding to each cluster center point; wherein each cluster center point corresponds to a target; The average value of each lateral line intersection point in each cluster set is calculated to obtain the target position W, which is expressed as: Where N represents the total number of lateral line intersections in each cluster set, x i ' represents the horizontal coordinate of the i-th lateral line intersection point in the cluster set, y i ' represents the vertical coordinate of the i-th lateral line intersection point in the cluster set.

4. The high-precision passive positioning method based on optimized position according to claim 3, characterized in that: Calculating the local density of each lateral line intersection point in the data set includes: The truncated kernel method is used to find the intersection of the lateral lines (x i ,y i ) is processed by the natural neighboring points, and the Gaussian kernel method is used to process the lateral line intersection point (x i ,y i ) is processed to obtain the lateral line intersection point (x i ,y i ) local density ρ i , whose expression is: Where a represents the maximum value of the local density of the truncated kernel among all the lateral line intersections, b represents the maximum value of the Gaussian kernel density among all the lateral line intersections, and d ij Indicates the intersection point of the lateral lines (x i ,y i ) and (x j ,y j ), χ(x j ) represents a piecewise function, and its expression is: Among them, x j ∈NNN(x i ) represents the lateral line intersection point (x j ,y j ) is the lateral line intersection point (x i ,y i )’s natural neighbors, Indicates the intersection point of the lateral lines (x j ,y j ) is the lateral line intersection point (x i ,y i )’s non-natural neighbors.

5. The high-precision passive positioning method based on optimized position according to claim 3, characterized in that: Calculating the relative distances between the intersection points of the lateral lines in the data set includes: Construct local density greater than the intersection point of the lateral line (x i ,y i ) of the local density of the lateral line intersection point set I i ; Calculate the lateral line intersection point (x i ,y i ) of the relative distance δ i , whose expression is: in, Represents the empty set.

6. The high-precision passive positioning method based on optimized position according to claim 3, characterized in that: The lateral line intersection point (x i ,y i )’s decision value γ i The expression is: c i =ρ i d i ; Among them, ρ i Indicates the intersection point of the lateral lines (x i ,y i ) local density, δ i Indicates the intersection point of the lateral lines (x i ,y i ) relative distance.

7. The high-precision passive positioning method based on optimized position according to claim 1, characterized in that: The central station calls the collaborative agent array optimization algorithm based on the coarse-grained positioning result to calculate the optimal position of the central station and each of the positioning stations, including: According to the initial positions of the central station and each of the positioning stations, the first particle is constructed, and its expression is: X1=[((x1,y1),(x2,y2),…,(x L ,y L ))]; Based on the lth particle, the l+1th particle is calculated, and its expression is: Where l = 2,…,L, L represents the total number of particles, and mod(·) represents the modulo operation; Based on all the calculated particles, a particle swarm is constructed, and the initial fitness value Fit(X) of each particle is calculated; The current fitness value of the particle is used as the individual optimal fitness value pb, and the optimal fitness value gb of the particle swarm is updated. The expressions are: pb k =max(Fit(X k )); gb k =max(Fit(p)); Among them, Fit(p) represents the fitness value of particle swarm p; At the preset number of iterations iter max In the process, the particle with the largest fitness value is calculated, and the positions of the central station and each positioning station corresponding to the particle are taken as the optimal positions.

8. The high-precision passive positioning method based on optimized position according to claim 7, characterized in that: The expression of the initial fitness value Fit(X) of the particle is: Where X=[x1,y1,...,x n ,y n ] represents the position coordinates of the central station and each positioning station, D represents the area where the target is located, s represents the set of lateral line intersection points in the cluster set of the positioning fuzzy area, M represents the number of discrete points, GDOP(s) represents the geometric precision factor at s, m represents the number of radiation source targets, e x and e y represents the coordinates of the center point of the area where the target is located, n represents the number of central stations and positioning stations, and G represents the connectivity between the central station and the positioning station or any two positioning stations.

9. The high-precision passive positioning method based on optimized position according to claim 7, characterized in that: The particle with the largest fitness value obtained by the calculation includes: Calculate the dynamic inertia weight coefficient w(i), which is expressed as: Among them, w max Indicates the maximum value of the inertia weight coefficient, w min Indicates the minimum value of the inertia weight coefficient; Update the current particle's velocity v according to the dynamic inertia weight coefficient i+1 and position X i+1 , whose expression is: v i+1 =ω×v i +c1×rand()×(pb i -X i )+c2×rand()×(gb-X i ); X i+1 =X i +v i+1 ; Among them, ω represents the inertia factor, c1 represents the individual learning factor, c2 represents the group learning factor, rand() represents the random number, X i represents the position of the particle at the last moment, v i represents the velocity of the particle at the previous moment; Update the particle's fitness value Fit(X); According to the updated fitness value of the particle, the individual optimal fitness value pb of the particle and the optimal fitness value gb of the particle swarm are updated.

Images