TDOA (time difference of arrival) rapid iteration positioning method and system based on space grid gradient

Abstract

The invention provides a TDOA (Time Difference of Arrival) rapid iteration positioning method and system based on a space grid gradient. The method comprises the following steps: dividing a positioning area into a plurality of grids with the same size; calculating a TDOA value corresponding to each space grid; constructing an iteration matrix of each space grid; acquiring a positioning initial value; calculating a grid corresponding to the positioning initial value to obtain a corresponding TDOA value; calculating the difference between the TDOA value corresponding to the initial value and the TDOA measurement value; obtaining a positioning compensation value according to the corresponding iteration matrix; and iterating until the difference of the TDOA is smaller than a set threshold, and outputting a positioning result. According to the scheme, the problem that an existing iterative positioning method is large in calculation amount is solved, and TDOA rapid iterative positioning is achieved in the mode of establishing the space grids and constructing the grid iterative matrix.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar, and particularly relates to a TDOA fast iterative positioning method and system based on spatial grid gradient. Background Art

[0002] The passive positioning technology has obvious advantages over the active positioning technology. Since it does not actively emit signals, the passive positioning system has higher concealment and anti-interference capabilities. The distributed passive positioning technology shows significant advantages in multiple aspects compared with the single-station passive positioning technology. First of all, through the collaborative work of multiple receiving stations, the distributed system can significantly improve the positioning accuracy and achieve a more accurate determination of the target position. Secondly, the system adopts a distributed structure, enhancing the robustness of the system. Even if a certain receiving station suffers from a fault or is interfered, other stations can still keep the system running. In addition, single-station positioning often needs to accumulate data for a period of time to output a positioning result, while the distributed passive positioning system can output a positioning result every time a signal is received.

[0003] The TDOA positioning technology is the most widely used distributed passive positioning technology at present. Multiple receiving stations observe the same radiation source target. Each receiving station is distributed at different positions, receives the signals of the target and obtains the received data. By processing these data, the time difference of arrival between different receiving stations is calculated, so as to achieve the precise positioning of the target radiation source.

[0004] Since the TDOA hyperbola equation is non-linear, it is difficult to directly solve. Therefore, many scholars have proposed various methods to solve this problem. For example, the least squares method, the maximum likelihood estimation method, and the method assisted by machine learning are used. Among them, the analytical iterative method, such as the Taylor iterative method, is often combined with other methods due to its high-precision characteristics to improve the overall positioning accuracy.

[0005] In 2023, Chen, J. et al. proposed a TDOA positioning method for achieving positioning with the minimum number of radars in the paper "A Two-Stage Aerial Target Localization Method Using Time-Difference-of-Arrival Measurements with the Minimum Number of Radars". This method first obtains the weighted least-squares solution of the positioning result and then substitutes it into the Taylor iteration method to obtain a positioning result with higher accuracy. In 2023, Dogancay, K. et al. proposed a three-dimensional TDOA positioning method that combines the iterative least-squares method and the Taylor iteration method in the paper "3D TDOA Emitter Localization Using Conic Approximation", thereby obtaining a positioning accuracy approaching the Cramer-Rao lower bound. Reference [4] uses the two-step weighted least-squares method to obtain the initial value of the positioning result and then uses the Taylor iteration method to obtain a high-precision positioning result.

[0006] In summary, analytical iterative methods are still widely used to improve the accuracy of TDOA positioning. However, since this type of method needs to calculate the first-order approximation relationship between the current position and the TDOA value in each iteration, the computational complexity is relatively large. This will lead to poor real-time performance of positioning and indirectly deteriorate the positioning accuracy, which is a major obstacle to the engineering application of TDOA positioning technology. Summary of the Invention

[0007] To solve the above technical problems, the present invention proposes a technical solution of a TDOA fast iterative positioning method based on spatial grid gradient to solve the above technical problems.

[0008] The first aspect of the present invention discloses a TDOA fast iterative positioning method based on spatial grid gradient, and the method includes:

[0009] Step S1: Divide the positioning area into a number of grids with the same size;

[0010] Step S2: Calculate the TDOA theoretical value of each spatial grid according to the coordinates of the grid center;

[0011] Step S3: Construct an iterative matrix for each spatial grid according to the TDOA theoretical value of the spatial grid;

[0012] Step S4: Obtain the positioning initial value by using the TDOA theoretical value of the spatial grid through the grid method;

[0013] Step S5: Calculate the grid index based on the initial positioning value; substitute the grid index into the TDOA theoretical value of the spatial grid to obtain the TDOA approximation value;

[0014] Step S6: Calculate the difference between the TDOA approximation value and the TDOA measurement value;

[0015] Step S7: If the difference is less than the set threshold, output the initial positioning value as the positioning result; if the difference is greater than the set threshold, calculate the coordinate compensation value according to the iteration matrix; apply the coordinate compensation value to add to the positioning result to obtain the initial positioning value for the next round of iteration, and repeat steps S5 to S7.

[0016] According to the method of the first aspect of the present invention, in the step S2, the calculating the TDOA theoretical value of each spatial grid according to the coordinates of the grid center includes:

[0017] Divide the positioning range into a rectangular range of X sta ~X end 、Y sta ~Y end The number of grids is M*N, then the length, width of each spatial grid and the coordinates of the center of the spatial grid are:

[0018]

[0019] G (i,j) =(X sta +(i-1)*W x ,Y sta +(j-1)*W y )

[0020] Wherein, W x represents the grid length; W y represents the grid width; G (i,j) represents the coordinates of the center of the spatial grid in the i-th row and the j-th column;

[0021]

[0022] Wherein, TDOA G1_(i,j) and TDOA G2_(i,j) represent the TDOA theoretical value of the spatial grid; c represents the propagation speed of electromagnetic waves in space; S 1 represents the coordinates of slave station 1; S 2 represents the coordinates of slave station 2; M represents the coordinates of the master station.

[0023] According to the method of the first aspect of the present invention, in the step S3, the constructing the iteration matrix of each spatial grid according to the TDOA theoretical value of the spatial grid includes:

[0024] Calculate the gradient of the theoretical TDOA value of the spatial grid according to the theoretical TDOA value of the spatial grid; construct the iteration matrix of each spatial grid according to the gradient.

[0025] According to the method of the first aspect of the present invention, in the step S3, calculating the gradient of the theoretical TDOA value of the spatial grid according to the theoretical TDOA value of the spatial grid; constructing the iteration matrix of each spatial grid according to the gradient includes:

[0026] K x1_(i,j) =(TDOA G1_(i+1,j) -TDOA G1_(i-1,j) ) / 2W x

[0027] K y1_(i,j) =(TDOA G1_(i,j+1) -TDOA G1_(i,j-1) ) / 2W y

[0028] K x2_(i,j) =(TDOA G2_(i+1,j) -TDOA G2_(i-1,j) ) / 2W x

[0029] K y2_(i,j) =(TDOA G2_(i,j+1) -TDOA G2_(i,j-1) ) / 2W y

[0030]

[0031] Wherein, A (i,j) represents the iteration matrix of each spatial grid; K x1_(i,j) , K y1_(i,j) , K x2_(i,j) and K y2_(i,j) represent the gradient of the theoretical TDOA value of the spatial grid.

[0032] According to the method of the first aspect of the present invention, in the step S4, obtaining the positioning initial value by using the theoretical TDOA value of the spatial grid through the grid method includes:

[0033] Construct a cost function:

[0034]

[0035] Take the center of the spatial grid corresponding to the index of the minimum value of the cost function as the positioning initial value;

[0036] Wherein, TDOA e1 and TDOA e2 are TDOA measurement values.

[0037] For the method according to the first aspect of the present invention, in the step S5, calculating the grid index through the positioning initial value; substituting the grid index into the TDOA theoretical value of the spatial grid to obtain the TDOA approximation value includes:

[0038] I = [(x 0 - X sta ) / W x + 1

[0039] J = [(y 0 - Y sta ) / W y + 1

[0040]

[0041] wherein, P 0 (x 0 , y 0 ) is the initial value coordinate; I and J represent the grid index; TDOA 1_P0 and TDOA 2_P0 represent the TDOA approximation value.

[0042] For the method according to the first aspect of the present invention, in the step S7, calculating the coordinate compensation value according to the iteration matrix includes:

[0043] A 0 = A (I,J)

[0044]

[0045] wherein, A 0 represents the iteration matrix with the grid index substituted; D 1_0 and D 2_0 represent the difference between the TDOA approximation value and the TDOA measurement value; Δx 0 and Δy 0 represent the coordinate compensation value.

[0046] The second aspect of the present invention discloses a TDOA fast iterative positioning system based on spatial grid gradient, and the system includes:

[0047] A first processing module, configured to divide the positioning area into a number of grids with the same size;

[0048] A second processing module, configured to calculate the TDOA theoretical value of each spatial grid according to the coordinates of the grid center;

[0049] A third processing module, configured to construct the iteration matrix of each spatial grid according to the TDOA theoretical value of the spatial grid;

[0050] The fourth processing module is configured to obtain an initial positioning value by using the TDOA theoretical value of the spatial grid through a rasterization method;

[0051] The fifth processing module is configured to calculate a grid index based on the initial positioning value; substitute the grid index into the TDOA theoretical value of the spatial grid to obtain a TDOA approximation;

[0052] The sixth processing module is configured to calculate the difference between the TDOA approximation and the TDOA measurement value;

[0053] The seventh processing module is configured to, if the difference is less than a set threshold, output the initial positioning value as the positioning result; if the difference is greater than the set threshold, calculate a coordinate compensation value according to an iteration matrix; apply the coordinate compensation value to add to the positioning result to obtain the initial positioning value for the next round of iteration, and repeat the fifth processing module to the seventh processing module.

[0054] A third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, the steps in a TDOA fast iterative positioning method based on spatial grid gradient according to any one of the first aspects of the present disclosure are implemented.

[0055] A fourth aspect of the present invention discloses a computer-readable storage medium. A computer program is stored on the computer-readable storage medium. When the computer program is executed by a processor, the steps in a TDOA fast iterative positioning method based on spatial grid gradient according to any one of the first aspects of the present disclosure are implemented.

[0056] In summary, the solution proposed by the present invention can fully expand the information provided by spatial rasterization, combine the traditional rasterization method with the iterative method, take the advantages of both methods and avoid their respective defects. Design a TDOA fast iterative positioning method based on spatial grid gradient to solve the problem of excessive computational complexity in the prior art. By dividing the positioning area into several grids, calculating the change gradient of the TDOA value between these grids, constructing a grid iteration matrix, and pre-calculating the relationship between the positioning compensation value and the current TDOA difference before positioning. In each iteration process, only the pre-calculated iteration matrix needs to be called, avoiding a large amount of calculations. Without sacrificing the positioning accuracy, the computational complexity is significantly reduced, the TDOA positioning efficiency for the radiation source target is improved, and it has significant practical application value. Description of the Drawings

[0057] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0058] Figure 1 It is a flowchart of a TDOA fast iterative positioning method based on spatial grid gradient according to an embodiment of the present invention;

[0059] Figure 2 It is the positioning result of 2000 Monte Carlo simulations of the radiation source target according to an embodiment of the present invention;

[0060] Figure 3 It is the comparison between the method of the present invention and the classical spatial grid method according to an embodiment of the present invention;

[0061] Figure 4 It is a comparison chart of the calculation time and positioning accuracy of the method of the present invention and the Taylor iterative method under the same scenario, target parameters, and different TDOA estimation error levels according to an embodiment of the present invention;

[0062] Figure 5 It is a structural diagram of a TDOA fast iterative positioning system based on spatial grid gradient according to an embodiment of the present invention;

[0063] Figure 6 It is a structural diagram of an electronic device according to an embodiment of the present invention. Specific Embodiments

[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, rather than all, embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0065] The first aspect of the present invention discloses a TDOA fast iterative positioning method based on spatial grid gradient. Figure 1 It is a flowchart of a TDOA fast iterative positioning method based on spatial grid gradient according to an embodiment of the present invention. As Figure 1 shown, the method includes:

[0066] Step S1: Divide the positioning area into a number of grids of the same size;

[0067] Step S2: Calculate the TDOA theoretical value of each spatial grid according to the coordinates of the grid center;

[0068] Step S3: Construct an iterative matrix for each spatial grid according to the TDOA theoretical value of the spatial grid;

[0069] Step S4: Obtain the initial positioning value by using the TDOA theoretical value of the spatial grid through a rasterization method;

[0070] Step S5: Calculate the grid index through the initial positioning value; Substitute the grid index into the TDOA theoretical value of the spatial grid to obtain the TDOA approximation;

[0071] Step S6: Calculate the difference between the TDOA approximation and the TDOA measurement value;

[0072] Step S7: If the difference is less than the set threshold, output the initial positioning value as the positioning result; If the difference is greater than the set threshold, calculate the coordinate compensation value according to the iterative matrix; Apply the coordinate compensation value and add it to the positioning result to obtain the initial positioning value for the next round of iteration, and repeat steps S5 to S7.

[0073] In step S1, divide the positioning area into several grids of the same size.

[0074] Specifically, when dividing the positioning area, the geometric configuration of the receiving stations should be fully considered to avoid multi-value problems due to the geometric relationship between the target and the receiving stations.

[0075] The number of divided spatial grids does not affect the computational complexity of the method, but the size of the spatial grid affects the positioning accuracy. The smaller the spatial grid, the higher the positioning accuracy. Therefore, as many and small spatial grids as possible should be divided according to the positioning scenario.

[0076] In step S2, calculate the TDOA theoretical value of each spatial grid according to the coordinates of the grid center.

[0077] In some embodiments, in step S2, the calculating the TDOA theoretical value of each spatial grid according to the coordinates of the grid center includes:

[0078] Divide the positioning range into a rectangular range of X sta ~X end 、Y sta ~Y end If the number of grids is M*N, then the length, width of each spatial grid and the coordinates of the center of the spatial grid are:

[0079]

[0080] G (i,j) =(X sta +(i-1)*Wx , Y sta +(j - 1)*W y )

[0081] Among them, W x represents the grid length; W y represents the grid width; G (i,j) represents the coordinates of the center of the spatial grid at the i-th row and the j-th column;

[0082]

[0083] Among them, TDOA G1_(i,j) and TDOA G2_(i,j) represent the theoretical TDOA values of the spatial grid; c represents the propagation speed of electromagnetic waves in space; S 1 represents the coordinates of slave station 1; S 2 represents the coordinates of slave station 2; M represents the coordinates of the master station.

[0084] In step S3, an iterative matrix for each spatial grid is constructed according to the theoretical TDOA values of the spatial grid.

[0085] In some embodiments, in the said step S3, the constructing an iterative matrix for each spatial grid according to the theoretical TDOA values of the spatial grid includes:

[0086] Calculating the gradient of the theoretical TDOA values of the spatial grid according to the theoretical TDOA values of the spatial grid; constructing an iterative matrix for each spatial grid according to the gradient.

[0087] Calculating the gradient of the theoretical TDOA values of the spatial grid according to the theoretical TDOA values of the spatial grid; constructing an iterative matrix for each spatial grid according to the gradient includes:

[0088] K x1_(i,j) =(TDOA G1_(i+1,j) - TDOA G1_(i-1,j) ) / 2W x

[0089] K y1_(i,j) =(TDOA G1_(i,j+1) - TDOA G1_(i,j-1) ) / 2W y

[0090] K x2_(i,j) =(TDOA G2_(i+1,j) - TDOA G2_(i-1,j) ) / 2W x

[0091] K y2_(i,j) =(TDOA G2_(i,j+1) - TDOA G2_(i,j-1)) / 2W y

[0092]

[0093] Among them, A (i,j) represents the iteration matrix of each spatial grid; K x1_(i,j) , K y1_(i,j) , K x2_(i,j) and K y2_(i,j) represent the gradients of the TDOA theoretical values of the spatial grid.

[0094] Specifically, since the grid width is much smaller than the distance from the target to the receiving station, within the range of a single spatial grid, the relationship between the TDOA theoretical value and the target position is a first-order linear relationship:

[0095]

[0096] where Δx and Δy are the differences between the target to be measured and the center of the grid where it is located in the x and y directions, respectively, and D 1 , D 2 is the difference between the TDOA estimated value and the TDOA value corresponding to the grid.

[0097] In step S4, through the grid method, the initial positioning value is obtained by using the TDOA theoretical value of the spatial grid.

[0098] In some embodiments, in step S4, the obtaining of the initial positioning value by using the TDOA theoretical value of the spatial grid through the grid method includes:

[0099] Construct a cost function:

[0100]

[0101] Take the center of the spatial grid corresponding to the index of the minimum value of the cost function as the initial positioning value;

[0102] where TDOA e1 and TDOA e2 are TDOA measurement values.

[0103] Specifically, the initial positioning value does not need to be calculated every time for positioning. According to the application scenario, it can be updated every once in a while, or the previous positioning result can be used as the initial value for the next time.

[0104] In step S5, calculate the grid index through the initial positioning value; substitute the grid index into the TDOA theoretical value of the spatial grid to obtain the TDOA approximate value.

[0105] In some embodiments, in step S5, calculating the grid index through the positioning initial value; substituting the grid index into the TDOA theoretical value of the spatial grid to obtain the TDOA approximation value includes:

[0106] I = [(x 0 - X sta ) / W x + 1

[0107] J = [(y 0 - Y sta ) / W y + 1

[0108]

[0109] where P 0 (x 0 , y 0 ) is the initial value coordinate; I and J represent the grid index; TDOA 1_P0 and TDOA 2_P0 represent the TDOA approximation value.

[0110] In step S6, calculate the difference between the TDOA approximation value and the TDOA measured value.

[0111] Specifically,

[0112]

[0113] In step S7, if the difference is less than the set threshold, output the positioning initial value as the positioning result; if the difference is greater than the set threshold, calculate the coordinate compensation value according to the iteration matrix; apply the coordinate compensation value added to the positioning result to obtain the positioning initial value for the next round of iteration, and repeat steps S5 to S7.

[0114] In some embodiments, in step S7, calculating the coordinate compensation value according to the iteration matrix includes:

[0115] A 0 = A (I,J)

[0116]

[0117] where A 0 represents the iteration matrix with the grid index substituted; D 1_0 and D 2_0 represent the difference between the TDOA approximation value and the TDOA measured value; Δx 0 and Δy 0 represent the coordinate compensation value.

[0118] Embodiment 1

[0119] Taking the two-dimensional three-station TDOA positioning as an example, a geometric model is established.

[0120] Let the positions of the three receiving stations be: the main station M(x m ,y m ), the slave station 1 S 1 (x s1 ,y s1 ), the slave station 2 S 2 (x s2 ,y s2 ), and the position of the target be T(x, y). The TDOA values corresponding to S 1 , S 2 obtained by the TDOA estimation method are TDOA 1 , TDOA 2 .

[0121] The distances from the target to the three receiving stations are respectively:

[0122]

[0123] It can be obtained that

[0124]

[0125] where c is the propagation speed of electromagnetic waves in space.

[0126] According to the TDOA estimation method, the TDOA estimated values TDOA e1 , TDOA e2 are substituted into the hyperbola equation (2) and solved to obtain the target position.

[0127] The classical spatial grid method divides the positioning range into several grids. First, it calculates the TDOA value of the center point of each grid, and then matches it with the TDOA value of the target radiation source to obtain the closest result. Finally, the center point of the obtained grid is used as the positioning result. This method has the advantage of being simple and easy to implement, facilitating implementation in engineering practice; however, its disadvantage is that the positioning accuracy is restricted by the grid width, and reducing the grid width will lead to a sharp increase in the calculation amount.

[0128] To solve the contradiction between the positioning accuracy and the calculation amount of the spatial grid method and make full use of the advantages of the grid method, the positioning range is divided into a rectangular range of X sta ~X end , Y sta ~Y end . If the number of grids is M*N, then the width of each grid and the grid center are:

[0129]

[0130] G(i,j) = (X sta + (i - 1) * W x , Y sta + (j - 1) * W y ), i = 1, 2, 3....M, j = 1, 2, 3...N (4)

[0131] Wherein, W x and W y are the widths of the grid in the x - dimension and y - dimension respectively, and G (i,j) is the coordinate of the center of each grid.

[0132] Calculate the TDOA value corresponding to the grid center according to the coordinates of the three receiving stations and the grid center coordinates:

[0133]

[0134] Wherein, i = 1, 2, 3....M, j = 1, 2, 3...N.

[0135] The traditional spatial grid - based method is to construct a cost function with the TDOA value of the grid center obtained from Equation (5) and the obtained TDOA estimated value, and find the optimal grid according to the cost function, and output the center point of the grid as the positioning result.

[0136] The following is a way to construct the cost function:

[0137]

[0138] Wherein, i = 1, 2, 3....M, j = 1, 2, 3...N.

[0139] Find the minimum value of P (i,j) , and the corresponding grid center is the positioning result.

[0140] This method will cause the positioning accuracy to be strictly restricted by the grid width. Reducing the grid width will cause the number of grids to increase geometrically. Since the TDOA estimated value is different each time of positioning, and for each different TDOA estimated value, it is necessary to calculate its cost function with each grid, the computational amount of positioning will also increase sharply with the increase of the number of grids. To solve this problem, this embodiment proposes a new method that uses grid gradient instead of cost function for positioning.

[0141] Calculate the growth rate of the TDOA value of each grid with respect to the increments in the x - and y - dimensions according to adjacent grids, that is, the grid gradient of this grid:

[0142]

[0143] Let Δx and Δy be the differences between the target to be measured and the center of the obtained grid in the x and y directions respectively, D 1 , D 2 is the difference between the TDOA estimate value and the TDOA value corresponding to the previous positioning result. Since the grid width is much smaller than the distance from the target to the receiving station, within a single spatial grid range, the relationship between the TDOA value and the target position can be considered as a first-order linear relationship:

[0144]

[0145] Let

[0146]

[0147] Then

[0148]

[0149] A (i,j) is the iterative matrix required in the positioning process. Among them, i = 1, 2, 3....M, j = 1, 2, 3...N.

[0150] Before the positioning starts, construct the grids required for positioning according to Equations (3), (4) and (5) and calculate the TDOA values TDOA G1_(i,j) , TDOA G2_(i,j) , and calculate the grid gradient according to Equation (7) and construct all grid iterative matrices A (i,j) .

[0151] At the start of positioning, the initial positioning value can be obtained using the classical grid positioning method, or it can be obtained by other means. Let's assume the obtained initial value is P 0 (x 0 , y 0 ).

[0152] Calculate the TDOA value corresponding to the initial value:

[0153]

[0154] Among them, c is the propagation speed of electromagnetic waves in a vacuum, and TDOA 1_p0 is the TDOA value corresponding to the current initial positioning value and the master station M and slave station 1S 1 , and TDOA 2_p0 is the TDOA value corresponding to the current initial positioning value and the master station M and slave station 2S 2 .

[0155] Calculate the difference between the TDOA value corresponding to the initial value and the TDOA measurement value:

[0156]

[0157] In all iterative matrices A (i,j) (i = 1, 2, 3....M, j = 1, 2, 3...N), according to P 0 's coordinates, obtain the iterative matrix A of its corresponding grid 0 .

[0158] According to Equation (10), it can be obtained that:

[0159]

[0160] Obtain the positioning result after one iteration: P 1 (x 0 + Δx 0 , y 0 + Δy 0 ). Then calculate the difference between the TDOA value corresponding to P 1 and the TDOA measured value according to Equation (11) and Equation (12). If it is less than the set threshold, then output P 1 as the positioning result. If it is less than the set threshold, repeat the above process.

[0161] From the calculation processes of Equation (11), Equation (12), and Equation (13) in the iterative process, it can be found that the computational complexity of the method is independent of the number of grids, and the part that occupies the largest computational complexity in the entire iterative process is the square root calculation in Equation (11). Therefore, the grids used in the proposed method can be separated from the grids of the traditional grid method that provides the initial value. Set the grid width of the proposed method to be small enough, use the grid center closest to the original initial value as the new initial value, and directly obtain the corresponding TDOA value.

[0162]

[0163] Among them, I and J are the indices of the grid center closest to P 0 .

[0164]

[0165] The iterative process of the method becomes Equation (14), Equation (15), Equation (12), and Equation (13), and a total of 14 simple arithmetic operations are performed, with small computational complexity.

[0166] The following further illustrates the effect of the present invention in combination with simulation experiments. The simulation parameters are shown in Table 1,

[0167] Table 1

[0168]

[0169]

[0170] According to the proposed method and processing steps, 2000 Monte Carlo simulations are carried out, and the distribution of the positioning results is as Figure 2 shown, and the CEP positioning accuracy is 7.13m.

[0171] When other parameters remain the same and the grid width is changed, the Monte Carlo simulations are respectively carried out using the method proposed in the present invention and the classical spatial grid method, and the obtained positioning accuracy curve and the comparison chart of the calculation time are as Figure 3 shown. It can be seen from the simulation results that the positioning accuracy and calculation time of the traditional grid method are related to the grid width, while the influence of the proposed method on the grid width is much smaller than that of the traditional grid method. The proposed method can achieve good positioning accuracy when the grid width is 16m, while the traditional grid method needs to have a grid width of 2m to achieve comparable positioning accuracy, which will also lead to a large increase in the amount of calculation.

[0172] When other parameters remain the same and the TDOA estimation error exists, the Monte Carlo simulations are respectively carried out using the method proposed in the present invention and the Taylor iteration method, and the obtained positioning accuracy curve and the comparison chart of the calculation time are as Figure 4 shown. It can be known from the simulation results that in the same scenario, the positioning accuracy of the proposed method is slightly better than that of the Taylor iteration method, but the calculation time is 76% less than that of the Taylor iteration method.

[0173] In summary, the solution proposed in the present invention can fully expand the information provided by spatial gridification, combine the traditional gridification method with the iterative method, take the advantages of both methods and avoid their respective defects. A fast iterative TDOA positioning method based on spatial grid gradient is designed to solve the problem of excessive calculation amount in the prior art. By dividing the positioning area into several grids, calculating the change gradient of the TDOA values between these grids, constructing a grid iteration matrix, and pre-calculating the relationship between the positioning compensation value and the current TDOA difference before positioning. In each iteration process, only the pre-calculated iteration matrix needs to be called, avoiding a large amount of calculation. On the premise of ensuring that the positioning accuracy does not decrease, the calculation amount is greatly reduced, the TDOA positioning efficiency of the radiation source target is improved, and it has significant practical application value.

[0174] The second aspect of the present invention discloses a fast iterative TDOA positioning system based on spatial grid gradient. Figure 5 It is a structural diagram of a fast iterative TDOA positioning system based on the embodiments of the present invention; as Figure 5 shown, the system 100 includes:

[0175] A first processing module 101, configured to divide the positioning area into several grids of the same size;

[0176] The second processing module 102 is configured to calculate the theoretical TDOA value of each spatial grid according to the coordinates of the grid center;

[0177] The third processing module 103 is configured to construct an iterative matrix for each spatial grid according to the theoretical TDOA value of the spatial grid;

[0178] The fourth processing module 104 is configured to obtain an initial positioning value by using the theoretical TDOA value of the spatial grid through a rasterization method;

[0179] The fifth processing module 105 is configured to calculate a grid index through the initial positioning value; substitute the grid index into the theoretical TDOA value of the spatial grid to obtain an approximate TDOA value;

[0180] The sixth processing module 106 is configured to calculate the difference between the approximate TDOA value and the measured TDOA value;

[0181] The seventh processing module 107 is configured to, if the difference is less than a set threshold, output the initial positioning value as the positioning result; if the difference is greater than the set threshold, calculate a coordinate compensation value according to the iterative matrix; apply the coordinate compensation value to add to the positioning result to obtain the initial positioning value for the next round of iteration, and repeat the fifth processing module to the seventh processing module

[0182] According to the system of the second aspect of the present invention, the first processing module 101 is specifically configured that the positioning area division should fully consider the geometric configuration of the receiving stations to avoid multi-value problems due to the geometric relationship between the target and the receiving stations.

[0183] The number of divided spatial grids does not affect the computational amount of the method, but the size of the spatial grid affects the positioning accuracy. The smaller the spatial grid, the higher the positioning accuracy. Therefore, as many and small spatial grids as possible should be divided according to the positioning scenario.

[0184] According to the system of the second aspect of the present invention, the second processing module 102 is specifically configured that the calculating the theoretical TDOA value of each spatial grid according to the coordinates of the grid center includes:

[0185] Divide the positioning range into a rectangular range of X sta ~X end 、Y sta ~Y end If the number of grids is M*N, then the length, width of each spatial grid and the coordinates of the center of the spatial grid are:

[0186]

[0187] G (i,j) =(X sta +(i-1)*Wx , Y sta +(j - 1)*W y )

[0188] Wherein, W x represents the grid length; W y represents the grid width; G (i,j) represents the coordinates of the center of the spatial grid at the i-th row and the j-th column;

[0189]

[0190] Wherein, TDOA G1_(i,j) and TDOA G2_(i,j) represent the theoretical TDOA values of the spatial grid; c represents the propagation speed of electromagnetic waves in space; S 1 represents the coordinates of slave station 1; S 2 represents the coordinates of slave station 2; M represents the coordinates of the master station.

[0191] For the system according to the second aspect of the present invention, the third processing module 103 is specifically configured that constructing the iteration matrix for each spatial grid according to the theoretical TDOA value of the spatial grid includes:

[0192] Calculating the gradient of the theoretical TDOA value of the spatial grid according to the theoretical TDOA value of the spatial grid; constructing the iteration matrix for each spatial grid according to the gradient.

[0193] Calculating the gradient of the theoretical TDOA value of the spatial grid according to the theoretical TDOA value of the spatial grid; constructing the iteration matrix for each spatial grid according to the gradient includes:

[0194] K x1_(i,j) =(TDOA G1_(i+1,j) - TDOA G1_(i-1,j) ) / 2W x

[0195] K y1_(i,j) =(TDOA G1_(i,j+1) - TDOA G1_(i,j-1) ) / 2W y

[0196] K x2_(i,j) =(TDOA G2_(i+1,j) - TDOA G2_(i-1,j) ) / 2W x

[0197] K y2_(i,j) =(TDOA G2_(i,j+1) - TDOA G2_(i,j-1) ) / 2W y

[0198]

[0199] Among them, A (i,j) represents the iterative matrix of each spatial grid; K x1_(i,j) , K y1_(i,j) , K x2_(i,j) and K y2_(i,j) represent the gradients of the TDOA theoretical values of the spatial grid.

[0200] Specifically, since the grid width is much smaller than the distance from the target to the receiving station, within the range of a single spatial grid, the relationship between the TDOA theoretical value and the target position is a first-order linear relationship:

[0201]

[0202] Among them, Δx and Δy are the differences between the target to be measured and the center of the grid where it is located in the x and y directions respectively, and D 1 , D 2 is the difference between the TDOA estimated value and the TDOA value corresponding to the grid.

[0203] According to the system of the second aspect of the present invention, the fourth processing module 104 is specifically configured that the obtaining of the positioning initial value by using the TDOA theoretical value of the spatial grid through the grid method includes:

[0204] Construct a cost function:

[0205]

[0206] Take the center of the spatial grid corresponding to the index of the minimum value of the cost function as the positioning initial value;

[0207] Among them, TDOA e1 and TDOA e2 are TDOA measurement values.

[0208] Specifically, the positioning initial value does not need to be calculated every time for positioning. According to the application scenario, it can be updated every once in a while, or the previous positioning result can be taken as the initial value for the next time.

[0209] According to the system of the second aspect of the present invention, the fifth processing module 105 is specifically configured that the calculating the grid index by using the positioning initial value; bringing the grid index into the TDOA theoretical value of the spatial grid to obtain the TDOA approximation value includes:

[0210] I = [(x 0 - X sta ) / W x + 1

[0211] J = [(y 0 - Y sta) / W y +1

[0212]

[0213] Among them, P 0 (x 0 ,y 0 ) is the initial coordinate; I and J represent grid indices; TDOA 1_P0 and TDOA 2_P0 represent TDOA approximations.

[0214] For the system according to the second aspect of the present invention, the sixth processing module 106 is specifically configured to,

[0215]

[0216] For the system according to the second aspect of the present invention, the seventh processing module 107 is specifically configured to, the calculating the coordinate compensation value according to the iterative matrix includes:

[0217] A 0 = A (I,J)

[0218]

[0219] Among them, A 0 represents the iterative matrix with grid indices substituted; D 1_0 and D 2_0 represent the difference between the TDOA approximation and the TDOA measurement; Δx 0 and Δy 0 represent the coordinate compensation values.

[0220] The third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor. When the processor executes the computer program, the steps in any one of the first aspects of the present invention for a fast iterative positioning method based on spatial grid gradient are implemented.

[0221] Figure 6 is a structural diagram of an electronic device according to an embodiment of the present invention, as Figure 6As shown, the electronic device includes a processor, a memory, a communication interface, a display screen, and an input device connected via a system bus. Among them, the processor of the electronic device is used to provide computing and control capabilities. The memory of the electronic device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The communication interface of the electronic device is used to communicate with external terminals in a wired or wireless manner, and the wireless manner can be implemented through WIFI, carrier networks, near-field communication (NFC), or other technologies. The display screen of the electronic device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the electronic device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads provided on the housing of the electronic device, or an external keyboard, touchpad, or mouse, etc.

[0222] Those skilled in the art can understand that Figure 6 the structure shown in is only the structure diagram of the part related to the technical solution of the present disclosure, and does not constitute a limitation on the electronic device to which the solution of the present application is applied. The specific electronic device may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0223] The fourth aspect of the present invention discloses a computer-readable storage medium. A computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the steps in a TDOA fast iterative positioning method based on spatial grid gradient in any one of the first aspects disclosed by the present invention are implemented.

[0224] Please note that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combinations of these technical features do not conflict, they should all be considered as within the scope described in this specification. The above embodiments only represent several implementation manners of the present application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be pointed out that for those of ordinary skill in the art, without departing from the concept of the present application, several deformations and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A TDOA fast iterative positioning method based on spatial grid gradient, characterized in that: The method comprises: Step S1, dividing the positioning area into a number of grids of the same size; Step S2, calculating the TDOA theoretical value of each spatial grid according to the coordinates of the grid center; Step S3, constructing an iteration matrix of each spatial grid according to the TDOA theoretical value of the spatial grid; Step S4, obtaining an initial positioning value by using the TDOA theoretical value of the spatial grid through a rasterization method; Step S5, calculating a grid index using the initial positioning value; substituting the grid index into the TDOA theoretical value of the spatial grid to obtain a TDOA approximate value; Step S6, calculating the difference between the TDOA approximate value and the TDOA measured value; Step S7: if the difference is less than the set threshold, the initial positioning value is output as the positioning result; if the difference is greater than the set threshold, the coordinate compensation value is calculated according to the iteration matrix; the coordinate compensation value is added to the positioning result to obtain the initial positioning value for the next iteration, and steps S5 to S7 are repeated.

2. The TDOA fast iterative positioning method based on spatial grid gradient according to claim 1, characterized in that: In step S2, calculating the TDOA theoretical value of each spatial grid according to the coordinates of the grid center includes: Divide the positioning range into X sta ~X end , Y sta ~Y end The rectangular range is M*N, and the number of grids is M*N. Then the length, width and coordinates of the center of each spatial grid are: G (i,j) =(X sta +(i-1)*W x ,Y sta +(j-1)*W y ) Among them, W x Indicates the grid length; W y Indicates the grid width; G (i,j) Represents the coordinates of the center of the spatial grid at row i and column j; Among them, TDOA G1_(i,j) and TDOA G2_(i,j) represents the TDOA theoretical value of the space grid; c represents the speed of electromagnetic wave propagation in space; S1 represents the coordinates of slave station 1; S2 represents the coordinates of slave station 2; M represents the coordinates of the master station.

3. The TDOA fast iterative positioning method based on spatial grid gradient according to claim 2, characterized in that: In step S3, constructing an iterative matrix of each spatial grid according to the TDOA theoretical value of the spatial grid includes: According to the TDOA theoretical value of the spatial grid, the gradient of the TDOA theoretical value of the spatial grid is calculated; according to the gradient, an iteration matrix of each spatial grid is constructed.

4. The TDOA fast iterative positioning method based on spatial grid gradient according to claim 3, characterized in that: In step S3, the gradient of the TDOA theoretical value of the spatial grid is calculated according to the TDOA theoretical value of the spatial grid; and an iteration matrix of each spatial grid is constructed according to the gradient. include: K x1_(i,j) =(TDOA G1_(i+1,j) -TDOA G1_(i-1,j) ) / 2W x K y1_(i,j) =(TDOA G1_(i,j+1) -TDOA G1_(i,j-1) ) / 2W y K x2_(i,j) =(TDOA G2_(i+1,j) -TDOA G2_(i-1,j) ) / 2W x K y2_(i,j) =(TDOA G2_(i,j+1) -TDOA G2_(i,j-1) ) / 2W y Among them, A (i,j) Represents the iteration matrix of each spatial grid; K x1_(i,j) , K y1_(i,j) , K x2_(i,j) and K y2_(i,j) Represents the gradient of the theoretical TDOA value of the spatial grid.

5. The TDOA fast iterative positioning method based on spatial grid gradient according to claim 4, characterized in that: In step S4, the method of obtaining the initial positioning value by using the TDOA theoretical value of the space grid through the rasterization method includes: Construct the cost function: Taking the center of the spatial grid corresponding to the index of the minimum value of the cost function as the initial positioning value; Among them, TDOA e1 and TDOA e2 is the TDOA measurement value.

6. The TDOA fast iterative positioning method based on spatial grid gradient according to claim 5, characterized in that: In the step S5, the grid index is calculated by the initial positioning value; the grid index is brought into the TDOA theoretical value of the spatial grid to obtain the TDOA approximate value, including: I=[(x0-X sta ) / W x ]+1 J=[(y0-Y sta ) / W y ]+1 Among them, P0(x0,y0) is the initial value coordinate; I,J represents the grid index; TDOA 1_P0 and TDOA 2_P0 Represents the TDOA approximation.

7. The TDOA fast iterative positioning method based on spatial grid gradient according to claim 6, characterized in that: In step S7, calculating the coordinate compensation value according to the iterative matrix includes: A0=A (I,J) Among them, A0 represents the iteration matrix brought into the grid index; D 1_0 and D 2_0 It represents the difference between the TDOA approximate value and the TDOA measured value; Δx0 and Δy0 represent the coordinate compensation values.

8. A TDOA fast iterative positioning system based on spatial grid gradient, characterized in that: The system comprises: A first processing module is configured to divide the positioning area into a plurality of grids of uniform size; The second processing module is configured to calculate the TDOA theoretical value of each spatial grid according to the coordinates of the grid center; A third processing module is configured to construct an iteration matrix of each spatial grid according to the TDOA theoretical value of the spatial grid; The fourth processing module is configured to obtain an initial positioning value by using the TDOA theoretical value of the spatial grid through a rasterization method; A fifth processing module is configured to calculate a grid index using the initial positioning value; bring the grid index into the TDOA theoretical value of the spatial grid to obtain a TDOA approximate value; A sixth processing module is configured to calculate a difference between the TDOA approximation value and the TDOA measurement value; The seventh processing module is configured to output the initial positioning value as the positioning result if the difference is less than the set threshold; calculate the coordinate compensation value according to the iteration matrix if the difference is greater than the set threshold; apply the coordinate compensation value and the positioning result to obtain the initial positioning value for the next round of iteration, and repeat the fifth processing module to the seventh processing module.

9. An electronic device, characterized in that: The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the steps of a TDOA fast iterative positioning method based on spatial grid gradient described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, the steps of the TDOA fast iterative positioning method based on spatial grid gradient described in any one of claims 1 to 7 are implemented.

Images