A positioning method based on a distributed sensor network

Abstract

The present application relates to the technical field of sensor and positioning, in particular to a positioning method based on distributed sensor network. The present application adopts distributed Newton iteration update, first carries out synchronous iteration transmission to the direction of arrival (DOA) measured by each connected and communicated direction finding station according to certain fusion weight, each direction finding station obtains the DOA information of other direction finding stations, and the process only needs to be iterated once, effectively reducing the pressure of large data transmission to one point. Then multiple iterations are carried out, the position measurement error generated in each iteration is calculated, the iteration amount is calculated, and the current target position is updated by using the iteration amount. The performance of the method of the present application is almost the same as that of the least square estimation, the pressure of data transmission amount is reduced, and the method has good robustness.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of sensor and positioning technology, in particular to a positioning method based on distributed sensor network. BACKGROUND

[0002] Electronic reconnaissance is the basis and premise of implementing electronic countermeasure, and direction finding positioning is a key link in electronic reconnaissance. At present, intersection positioning is widely used in direction finding positioning, which is usually implemented by two or more direction finding stations set at different positions to jointly direction find the target position. Since the direction finding station has measurement error, in order to improve the positioning accuracy, multiple direction finding stations are usually selected to estimate the direction of arrival (DOA) of the target, and then the data obtained by the direction finding stations is fused and processed to obtain the final target position estimation value. However, when the number of direction finding stations is large and the positions are far apart, the receiver has a large amount of data processing when collecting and processing the data, real-time performance is difficult to guarantee, and robustness is poor.

[0003] Compared with multi-sensor, distributed sensor network has the advantages of not depending on any network node, flexible addition and deletion of nodes, strong robustness, etc. In the distributed sensor network, each sensor generates a set of measurement information at each time and iteratively transmits and shares the information with its neighbor sensors. After reaching the maximum number of iterations, all sensors reach consensus, and the measurement information of each sensor no longer changes. SUMMARY

[0004] In view of the above problems, the present application provides a positioning method based on distributed sensor network. The present application uses distributed Newton iteration update, synchronously iteratively transmits the direction of arrival (DOA) measured by each connected and interconnected direction finding station according to a certain fusion weight, each direction finding station obtains the DOA information of other direction finding stations, and the process only needs to be iterated once, effectively reducing the pressure of large data transmission to one point. Then multiple iterations are performed, the position measurement error and iteration amount generated in each iteration are calculated, and the current target position is updated using the iteration amount.

[0005] The technical scheme of the present application is as follows:

[0006] A positioning method based on distributed sensor network, defining that the sensor network includes N direction finding stations, the position of the direction finding station is r i =[x i ,y i ] T , i = 1, 2,... N, the target with position p = [x, y] T is measured by the N direction finding stations to obtain DOA α i , i = 1, 2,... N; the positioning method comprises:

[0007] S1. Calculate the Hessian matrix H for each direction finding station. i :

[0008] H i =2*A i T *A i

[0009] Where A i =[-sinα] i cosα i ], i = 1, 2, ..., N; set H i Store the data column-wise to obtain H1;

[0010] For H i Perform synchronous iterations, setting a maximum number of iterations m and a measurement precision n, specifically as follows:

[0011] The transfer value H' of each direction finding station in each iteration is calculated using the Laplace matrix L:

[0012] H'=L*H1

[0013] Calculate the current measurement accuracy n':

[0014] n'=(H'-H1) / H1

[0015] in l i,j This represents the weight of the data transmitted and shared between the i-th and j-th direction-finding stations;

[0016] Once the measurement accuracy reaches the set value or the maximum number of iterations is reached, output H'. Rearrange H' to obtain H for each direction finding station. i , i = 1, 2, ..., N;

[0017] S2. Calculate the target location information obtained by each measurement station iteratively. Set the maximum number of target update iterations to z, and the initial target iteration value to X0. The initial target value is the same for each measurement station. Specifically:

[0018] Define the measurement error gradient as J, and calculate the measurement error gradient J in each iteration. t :

[0019] J t =A T *A*X t -A T *b

[0020] Where X is t Let z be the target position for each iteration, and t represent the iteration number, where t = 1, 2, ..., z. H is calculated using the method described in S1.The method of the application is as follows: i The method of the application is as follows: t Synchronous iteration is performed to obtain J t of each direction finding station.

[0021] The iteration amount h is defined as:

[0022] h = H -1 * J

[0023] The target position is updated by using the iteration amount h in each iteration:

[0024] X t+1 = X t -h

[0025] When the iteration number reaches the set maximum value, the target coordinate position X z of each measurement station is output, and X z is the final positioning result. After the iteration is completed, the last target position obtained by each direction finding station is approximately the same, and consensus is achieved.

[0026] The application has the following beneficial effects: the application takes the DOA measured by the direction finding station as the starting point, and transmits the DOA information of each direction finding station to the other direction finding stations by using synchronous interactive iteration. According to the Newton method, the Hessian matrix H and the measurement error gradient J are interacted in the same way, the iteration amount h is calculated, and the target position is updated. The performance of the method of the application is approximately the same as that of the least square estimation, the pressure of data transmission is reduced, and the method has good robustness. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is a relationship diagram of distributed direction finding stations

[0028] Figure 2 is a synchronous iteration flowchart.

[0029] Figure 3 is a target updating flowchart.

[0030] Figure 4 is a direction finding station target position iteration diagram.

[0031] Figure 5 is a curve diagram of the measurement error standard deviation and the two calculation methods MESE.

[0032] Figure 6 is a final target coordinate diagram of ten direction finding stations. DETAILED DESCRIPTION

[0033] The application will be further described below in combination with the drawings and examples.

[0034] The present application is based on a distributed sensor, i.e. a distributed direction finding station, as shown in Figure 1 The adjacent sensors are connected to each other, and the direct communication relationship of the direction finding stations can be represented by a matrix G:

[0035]

[0036] wherein g i,j =1 represents that the ith and jth direction finding stations are connected; and g i,j =0 represents that the ith and jth direction finding stations are not connected.

[0037] The method of the present application synchronously iterates the direction of arrival (DOA) angles measured by each connected and communicated direction finding station according to a certain fusion weight, so that each direction finding station obtains the DOA information of other direction finding stations, and the specific method is as follows:

[0038] The position r of the measuring station and the direction of arrival angle α i The position p of the target is modeled as:

[0039] A*X = b

[0040] wherein,

[0041] The fusion weight of the direction finding station is set as a Laplace matrix L:

[0042]

[0043] wherein l i,j represents the weight of data transmission and sharing between the ith and jth direction finding stations. The Laplace matrix is defined as L = D-B, wherein D is a degree matrix of the graph, and B is an adjacency matrix of the graph. The degree matrix is a diagonal matrix, and the elements on the diagonal are the degrees of the points, i.e. the number of points connected to the point. The adjacency matrix is a symmetric matrix, and represents the relationship between the points. If two points are connected, the corresponding position is 1.

[0044] Unlike the centralized Newton method, the present application synchronously iterates H using the fusion weight L, and gives an error precision. After the iteration reaches the set precision, the H of each observation station is output, and the iteration only needs to be performed once. The iteration flow chart is as shown in Figure 2 .

[0045] The Hessian matrix H i of each direction finding station is calculated:

[0046] H i = 2*A i T *A i

[0047] wherein A i =[-sinαi cosα i ], i = 1, 2, ..., N; H i Store the data column-wise to obtain H1;

[0048] For H i Perform synchronous iterations, setting a maximum number of iterations m and a measurement precision n, specifically as follows:

[0049] The transfer value H' of each direction finding station in each iteration is calculated using the Laplace matrix L:

[0050] H'=L*H1

[0051] Calculate the current measurement accuracy n':

[0052] n'=(H'-H1) / H1

[0053] in l i,j This represents the weight of the data transmitted and shared between the i-th and j-th direction-finding stations;

[0054] Once the measurement accuracy reaches the set value or the maximum number of iterations is reached, the H value for each direction finding station is output. i i = 1, 2, ..., N

[0055] H was obtained for each direction finding station i Then, multiple iterations are performed, calculating the position measurement error and iteration amount generated in each iteration, and using the iteration amount to update the current target position. The specific process is as follows: Figure 3 As shown:

[0056] Let z be the maximum number of iterations for the target update, and J be the gradient of the measurement error. Calculate the gradient of the measurement error J in each iteration. t :

[0057] J t =A T *A*X t -A T *b

[0058] Where X is t Let z be the target position for each iteration, and t represent the iteration number, where t = 1, 2, ..., z. Adopting such Figure 2 Iterative methods for J t Perform synchronous iterations to obtain J for each direction finding station. t ;

[0059] Define the iteration quantity as h:

[0060] h = H -1 *J

[0061] In each iteration, the target position is updated using the iteration amount h:

[0062] X t+1 =X t -h

[0063] When the number of iterations reaches the set maximum value, the target coordinate position X of each measurement station is output. z X z This is the final positioning result. After iteration, each direction finding station can obtain a nearly identical target position, reaching a consensus.

[0064] Example

[0065] To more intuitively demonstrate the effects of this invention, this example is a simulation example combined with actual parameters. It is assumed that the locations of ten direction finding stations are randomly distributed within [1,1], and a random graph depicting the communication relationships between the direction finding stations (without isolated points) is drawn, such as... Figure 4 As shown. The Laplacian matrix L = DB, where D is the degree matrix of the graph, and B is the adjacency matrix. The degree matrix is ​​a diagonal matrix, and the elements on the diagonal are the degrees of each vertex, that is, the number of vertices connected to that vertex. The adjacency matrix is ​​a symmetric matrix representing the relationships between vertices; if two vertices are connected, their corresponding positions are set to 1. Given the target position p = [10, 12] T The initial value of the target position during iteration is X. b =[9,8] T The initial target position is set to be the same for each direction finding station. Noise is added to the DOA measured by each station, with a given angular standard deviation of [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7]. The synchronous iteration accuracy of H is given as 1e-15, the synchronous iteration accuracy of the measurement error gradient J is given as 1e-10, the maximum number of synchronous iterations is 200, and the number of target update iterations is 100. The target position iteration diagram for each direction finding station with an angular standard deviation of 0.1 is shown below. Figure Four As shown, the root mean square error (MESE) of the two calculation methods varies with the standard deviation of the angle measurement as follows: Figure 5 As shown, the final target position determined by the direction finding station is as follows: Figure 6 As shown.

[0066] Simulation results show that the target position measurement by the direction finding station converges quickly, almost reaching convergence by the tenth iteration. The converged value is nearly identical to the target position estimated by least squares, indicating high estimation accuracy. The root mean square error (MESE) increases with the standard deviation of the angle measurement. In summary, the method proposed in this invention effectively reduces data transmission pressure, achieves fast convergence, and enables information exchange between stations. In information warfare, it can also effectively prevent the enemy from detecting and destroying the data transmission hub, protecting the normal operation of our communications, and exhibits good stability.

Claims

1. A localization method based on a distributed sensor network, wherein the sensor network includes... There are 1 direction finding station, and the location of the direction finding station is... , ,pass The location of each direction finding station is The target was measured to obtain the DOA. , Its characteristics are, The positioning method includes: S1. Calculate the Hessian matrix for each direction finding station. : ， in , ;Will Stored in columns, resulting in ; right Perform synchronous iterations, setting a maximum number of iterations m and a measurement precision n, specifically as follows: The Laplace matrix L is used to calculate the transfer value of each direction finding station in each iteration. : ， Calculate the current measurement accuracy : ， in , Indicates the first and the Weights that are transmitted and shared among direction finding stations; When the measurement accuracy reaches the set value or the maximum number of iterations is reached, output... ,Will After rearranging, we get the values ​​of each direction finding station. , ; S2. Calculate the target location information obtained by each measurement station iteratively, setting the maximum number of target update iterations to z, and the initial target iteration value to be z. Furthermore, the initial target value is the same for each measurement station, specifically: Define the measurement error gradient as Calculate the measurement error gradient in each iteration. : ， in Let t represent the target position for each iteration, and t represent the number of iterations. , , ; Calculations are performed as in S1 The method for Synchronous iteration is performed to obtain the values ​​of each direction finding station. ; Define the iteration quantity as : ， Utilize the iteration amount in each iteration Update the target location: ， When the number of iterations reaches the set maximum value, the target coordinate position of each measurement station is output. , This is the final positioning result.

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