Radiation source positioning method based on arrival signal intensity difference
By switching nonlinear optimization and linear regression methods under different number of monitoring points, combined with the customized SDOA residual function, the problem of degradation of positioning accuracy caused by insufficient number of monitoring points or complex environment is solved, and efficient and robust radiation source positioning is achieved.
Patent Information
- Application Number
- CN202510488504.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-18
- Publication Date
- 2025-07-11
AI Technical Summary
When the existing radiation source positioning method is insufficient in the number of monitoring points or the environment is complex, the positioning accuracy is reduced and the robustness is insufficient, making it difficult to balance the calculation efficiency and accuracy.
When the number of monitoring points is 4 is used to solve the problem that the number of monitoring points is 4, the BFGS algorithm is used to optimize the SDOA residual function; when the number of monitoring points is greater than or equal to 5, nonlinear optimization is used first, and if the residual is less than the threshold, it is used directly. Otherwise, switch to the linear regression method and combine the customized SDOA residual function and multivariate linear expression for solution.
When the number of monitoring points changes, ensure unique solutions and improve robustness, reduce multipath effect errors, improve positioning accuracy and anti-interference ability, especially in multi-monitoring point scenarios to effectively utilize data redundancy.
Smart Images
Figure CN120294673A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of positioning methods, and particularly relates to a radiation source positioning method based on the difference in received signal strength. Background Art
[0002] Radiation source positioning technology has important applications in fields such as wireless communication, electronic reconnaissance, and environmental monitoring. Traditional positioning methods are mainly based on principles such as time difference of arrival (TDOA), angle of arrival (AOA), or received signal strength (RSS). However, these methods have significant limitations: TDOA technology relies on precise time synchronization, and multipath effects and clock biases in complex environments can lead to increased positioning errors; AOA technology requires high-precision directional antennas, which are costly and have strict requirements for the deployment environment; RSS-based positioning does not require complex hardware, but the signal strength is easily affected by factors such as environmental attenuation and multipath interference. Especially when the number of monitoring points is insufficient, traditional single algorithms (such as nonlinear optimization) are prone to falling into local optima or having unstable solutions, resulting in a decrease in positioning accuracy.
[0003] In the prior art, positioning methods for signal strength differences usually adopt fixed algorithms (such as only nonlinear optimization or only linear models), lacking the ability to dynamically adapt to the number of monitoring points and data quality. For example, when the number of monitoring points is small (such as 4), the linear method may fail due to an underdetermined equation; when the number of monitoring points is large, nonlinear optimization may result in divergent results due to sensitivity to initial values or excessive residuals. In addition, existing methods have insufficient robustness in dealing with complex environmental interference and are difficult to balance computational efficiency and positioning accuracy. Summary of the Invention
[0004] In view of the above technical problems existing in the prior positioning methods, the present invention provides a radiation source positioning method based on the difference in received signal strength.
[0005] To solve the above technical problems, the technical solution adopted by the present invention is as follows:
[0006] A radiation source positioning method based on the difference in received signal strength, comprising the following steps:
[0007] S1. Set at least 4 monitoring points, and calculate the difference between the signal strength monitored at each observation point and the signal strength of the first monitoring point;
[0008] S2. When the number of measurement points is 4, only use the nonlinear optimization method for solution;
[0009] S3. When the number of measurement points is greater than or equal to 5, first use the nonlinear optimization method for solution. If a result can be obtained and the residual value is less than a certain threshold, directly adopt it; otherwise, use the linear regression method to solve the result.
[0010] The non - linear optimization method is as follows: It includes the following steps:
[0011] S2.1. Define the SDOA residual function according to the SDOA principle of the radiation source location method based on the difference in received signal strength. Let O be the position of the radiation source; there are N monitoring points, and the distance between each monitoring point and the radiation source position is denoted as D i (O), and the signal strength of the same signal observed at the same moment at each monitoring point is denoted as E i , i = 1, 2... N;
[0012] S2.2. Use the non - linear optimization algorithm (such as the BFGS algorithm) to complete the optimization with f(O) as the SDOA residual function, so that the SDOA residual function f(O) is minimized.
[0013] The SDOA residual function is as follows:
[0014]
[0015] Where: E j is the signal strength of the same signal observed at the same moment at each monitoring point, D j (O) is the distance between each monitoring point and the radiation source position, and N is the number of monitoring points.
[0016] Taking the BFGS algorithm as an example, the steps of the non - linear optimization algorithm are as follows:
[0017] S2.2.1. Initialization: Select the initial point O0 and initialize B0 as the identity matrix I;
[0018] S2.2.2. Calculate the gradient: Calculate the gradient at the current point
[0019] S2.2.3. Search direction: Calculate the search direction
[0020] S2.2.4. Line search: Perform a line search to determine the step size a k , such that f(O k + a k p k ) is small enough;
[0021] S2.2.5. Update the point: Update the point O k+1 = O k + a k p k ;
[0022] S2.2.6. Update B k : Update the inverse matrix B of the approximate Hessian matrix using the BFGS formula k ;
[0023] S2.2.7. Check the convergence: Check whether the convergence condition is satisfied. The convergence condition is that the gradient is small enough. If it is satisfied, output O k+1 as the approximate optimal solution; if not, return to S2.2.2 to continue the iteration.
[0024] The method of using the BFGS formula to update the inverse matrix B of the approximate Hessian matrix in S2.2.6 k is as follows:
[0025]
[0026] where s k = O k+1 − O k is the vector of the step size or search direction, is the gradient difference, and I is the identity matrix.
[0027] The linear regression method is as follows: It includes the following steps:
[0028] S3.1. Define a multiple linear expression:
[0029] a0X0 + a1X1 + a2X2 + a3 = Y
[0030] S3.2. Assume that O is the position of the radiation source and there are N monitoring points. According to the signal strength difference of the same signal received at the same moment by each monitoring point and the first monitoring point, multiple groups of observed values of (X0, X1, X2, Y) are formed; where:
[0031] X0 = 2(Kx j − x1) / (K − 1)
[0032] X1 = 2(Ky j − y1) / (K − 1)
[0033] X2 = 2(Kh j − h1) / (K − 1)
[0034]
[0035] where, (x j , y j , h j ) and (x1, y1, h1) are the coordinates of monitoring point j and monitoring point 1, in units of Km; E j and E1 are the signal strength values of the same signal observed at the same moment by monitoring point j and monitoring point 1, in units of dBm; j = 2, 3... N;
[0036] S3.3. Use the multiple linear expression in S3.1 to perform multiple linear regression analysis on N - 1 groups of observed values (X 0k , X 1k , X 2k , Y k )(k = 0, 1, …, N - 2), and calculate the regression coefficients a0, a1, a2, a3; where (a0, a1, a2) are the position coordinates (x0, y0, h0) of the radiation source.
[0037] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0038] 1. When there are 4 monitoring points in the present invention, nonlinear optimization is directly adopted to avoid the underdetermined problem of the linear model and ensure a unique solution; when the number of monitoring points ≥ 5, the BFGS algorithm is preferentially used for rapid solution. If the residual exceeds the threshold (indicating environmental interference or model mismatch), the linear regression method is switched to, and redundant data is used to suppress noise and improve robustness. And compared with the existing radiation source location methods based on the received signal strength, the present invention can more effectively calculate the location data; and when using the linear regression method, since only the data in four dimensions of a0, a1, a2, and a3 are calculated, its computational complexity is less than that of the radiation source location method based on the received signal strength.
[0039] 2. The present invention combines a custom SDOA residual function to significantly reduce the error caused by the multipath effect; converts the nonlinear distance relationship into a linear model, and reduces the risk of local optimum through least squares fitting. Especially in the scenario of multiple monitoring points, data redundancy is effectively utilized to improve the anti-interference ability. BRIEF DESCRIPTION OF THE DRAWINGS
[0040] In order to more clearly illustrate the 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 embodiments or the prior art. Obviously, the drawings in the following description are only exemplary, and for those of ordinary skill in the art, without creative efforts, other implementation drawings can also be obtained according to the provided drawings.
[0041] The structures, ratios, sizes, etc. illustrated in this specification are only used to cooperate with the content disclosed in the specification for those familiar with this technology to understand and read, and are not used to limit the limiting conditions for the implementation of the present invention. Therefore, they do not have technical essence. Any modification of the structure, change of the ratio relationship, or adjustment of the size should still fall within the scope covered by the technical content disclosed in the present invention without affecting the effects that the present invention can produce and the purposes that can be achieved.
[0042] Figure 1 It is the flowchart of the steps of the present invention. Detailed implementation manners
[0043] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Apparently, the described embodiments are only a part rather than all of the embodiments of the present application. These descriptions are only for further illustrating the features and advantages of the present invention rather than limiting the claims of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the scope of protection of the present application.
[0044] The following further describes in detail the specific implementation manners of the present invention in conjunction with the accompanying drawings and embodiments. The following embodiments are used to illustrate the present invention but are not intended to limit the scope of the present invention.
[0045] This embodiment provides a radiation source positioning method based on the strength difference of arrival (SDOA), as Figure 1 shown, including the following steps:
[0046] Step 1: Set at least 4 monitoring points, and calculate the difference between the signal strength monitored at each observation point and the signal strength at the first monitoring point.
[0047] Step 2: When the number of measurement points is 4, only use the non-linear optimization method for solution.
[0048] Step 2.1: Define the SDOA residual function according to the SDOA principle. Let O be the position of the radiation source. There are N monitoring points, and the distance between each monitoring point and the radiation source position is denoted as D i (O), and the signal strength of the same signal observed at the same moment at each monitoring point is denoted as E i , i = 1, 2... N.
[0049] Step 2.2: Use the BFGS algorithm to complete the optimization with f(O) as the SDOA residual function to minimize the SDOA residual function f(O).
[0050] The SDOA residual function is:
[0051]
[0052] where: E j is the signal strength of the same signal observed at the same moment at each monitoring point, D j (O) is the distance between each monitoring point and the radiation source position, and N is the number of monitoring points.
[0053] The BFGS algorithm is:
[0054] Step 2.2.1, Initialization: Select the initial point O0, and initialize B0 as the identity matrix I.
[0055] Step 2.2.2, Calculate the gradient: Calculate the gradient of the current point
[0056] Step 2.2.3, Search direction: Calculate the search direction
[0057] Step 2.2.4, Line search: Perform a line search to determine the step size a k , such that f(O k +a k p k ) is small enough.
[0058] Step 2.2.5, Update the point: Update the point O k+1 =O k +a k p k .
[0059] Step 2.2.6, Update B k : Update the inverse matrix B of the approximate Hessian matrix using the BFGS formula k .
[0060]
[0061] where s k =O k+1 ―O k is the vector of the step size or the search direction, is the gradient difference, and I is the identity matrix.
[0062] Step 2.2.7, Check for convergence: Check if the convergence condition is satisfied. The convergence condition is that the gradient is small enough. If it is satisfied, output O k+1 as the approximate optimal solution. If not, return to Step 2.2.2 to continue the iteration.
[0063] Step 3, When the number of measurement points is greater than or equal to 5, first use the nonlinear optimization method for calculation. If a result can be obtained and the residual value is less than a certain threshold, directly adopt it. Otherwise, use the linear regression method to calculate the result.
[0064] The nonlinear optimization method is as follows: It includes the following steps:
[0065] Step 3.1, Define a multivariate linear expression:
[0066] a0X0 + a1X1 + a2X2 + a3 = Y
[0067] Step 3.2: Assume that O is the position of the radiation source and there are N monitoring points. Based on the signal strength differences at the same moment of the same signal received by each monitoring point and the first monitoring point, multiple sets of observed values of (X0, X1, X2, Y) are formed. Among them:
[0068] X0 = 2(Kx j ―x1) / (K―1)
[0069] X1 = 2(Ky j ―y1) / (K―1)
[0070] X2 = 2(Kh j ―h1) / (K―1)
[0071]
[0072] Among them, (x j ,y j ,h j ) and (x1, y1, h1) are the coordinates of monitoring point j and monitoring point 1 respectively, with the unit of Km. E j and E1 are the signal strength values of the same signal observed at monitoring point j and monitoring point 1 at the same moment respectively, with the unit of dBm. j = 2, 3... N.
[0073] Step 3.3: Use the multiple linear expression in Step 3.1 to perform multiple linear regression analysis on N - 1 groups of observed values (X 0k ,X 1k ,X 2k ,Y k )(k = 0, 1,... N - 2) to calculate the regression coefficients a0, a1, a2, a3. Among them, (a0, a1, a2) are the position coordinates (x0, y0, h0) of the radiation source.
[0074] The non - linear optimization solution method in this embodiment can be developed using programming languages such as Python, JAVA, C#, C++. The following gives the main code implemented based on Python. Its core is to use the minimize function of scipy.optimize and set method = 'BFGS' to call the BFGS algorithm.
[0075] def SDOA_residual(x, sensors_positions, observed_E):
[0076]
[0077]
[0078] deflocate_source(sensors_positions, observed_E, initial_guess=None):
[0079]
[0080]
[0081] The linear regression solution method in this embodiment can be developed using programming languages such as Python, JAVA, C#, and C++. The main code implemented based on C# is given below.
[0082]
[0083]
[0084]
[0085] Simulation results
[0086] The method of the present invention is tested by simulation. The radiation source position coordinates (unit: m) are set to (100, 200, 300). Five measurement points are randomly distributed in the space of (0 - 1000, 0 - 1000, 0 - 1000). The time for the signal to travel from the radiation source to each measurement point is simulated and calculated, and a certain amount of random noise is added as the measurement error. The residual value threshold is set to 0.001.
[0087] Example 1: The coordinates (unit: m) of the five measurement points are respectively:
[0088] (799.9787376075977, 576.0336384138672, 560.6183571840007)
[0089] (596.6654859931198, 221.55414305226884, 30.224017604237098)
[0090] (705.3903813006197, 458.6011283122173, 532.6309850870184)
[0091] (34.409583886576556, 446.4331713706854, 420.7393361586646)
[0092] (820.8076811332301, 460.98949992316926, 288.4406922893045)
[0093] The signal strengths (unit: dBm) monitored at 5 measurement points are:
[0094] (-90.42851288530055, -87.03318874894957, -88.86145821303167, -80.99197422884822, -89.67575694357771)
[0095] Using the nonlinear programming method, the calculated position of the radiation source is:
[0096] (99.88411411514114, 199.83544634685344, 300.1282770905816)
[0097] At this time, the corresponding residual value is 1.059970632663819e-06, which is less than the threshold value of 0.001, and no further linear regression is performed.
[0098] Example 2: The coordinates (unit: m) of 5 measurement points are respectively:
[0099] (445.26137131299606, 699.402903196089, 775.974256602719)
[0100] (804.2018193362528, 536.0104486983802, 285.65361507035425)
[0101] (584.45480339633, 899.196388032822, 434.4666116365867)
[0102] (137.7837158828722, 515.9453550793752, 95.1488871685734)
[0103] (280.50776769432326, 271.27780385177505, 220.08570893334655)
[0104] The signal strengths (unit: dBm) monitored at 5 measurement points are:
[0105] (-89.72797379841417, -89.82841804350039, -90.68354712145573, -83.54159663235906, -78.42095674970636)
[0106] Using the nonlinear programming method, the calculated result is
[0107] (217.43461383919566, 366.33938947256166, 335.3638026850767), and the corresponding residual value is 0.04196740748672127. Since the residual value is greater than the threshold value of 0.001, the linear regression method needs to be used to recalculate the radiation source position, and the calculation result is:
[0108] (100.323691531409, 200.494495231739, 300.132680398129)
[0109] The above only elaborates in detail on the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those of ordinary skill in the art, various changes can be made without departing from the gist of the present invention, and all such changes should be included within the protection scope of the present invention.
Claims
1. A method for locating a radiation source based on the difference in received signal strength, characterized in that, Including the following steps: S1. Set at least 4 monitoring points, and calculate the difference between the signal strength monitored at each observation point and the signal strength at the first monitoring point; S2. When the number of measurement points is 4, only use the non-linear optimization method for solution; S3. When the number of measurement points is greater than or equal to 5, first use the non-linear optimization method for solution. If a result can be obtained and the residual value is less than a certain threshold, directly adopt it. Otherwise, use the linear regression method to calculate the result.
2. The method for radiating source location based on difference in received signal strength according to claim 1, wherein The non-linear optimization method is as follows: including the following steps: S2.
1. Define the SDOA residual function according to the principle of the SDOA (Source Location based on Difference in Signal Strength) radiation source location method. Let O be the location of the radiation source; there are N monitoring points, and the distance between each monitoring point and the radiation source location is denoted as D i (O), and the signal strength of the same signal observed at the same moment at each monitoring point is denoted as E i , i = 1, 2... N; S2.
2. Take f(O) as the SDOA residual function, and use the non-linear optimization algorithm to complete the optimization to minimize the SDOA residual function f(O).
3. The method for radiating source location based on difference in received signal strength according to claim 2, wherein The SDOA residual function is: Where: E j is the signal strength of the same signal observed at the same moment at each monitoring point, D j (O) is the distance between each monitoring point and the position of the radiation source, and N is the number of monitoring points.
4. The method for radiating source positioning based on the difference in received signal strength according to claim 2, wherein, The non-linear optimization algorithm adopts the BFGS algorithm.
5. A method for radiating source location based on difference in received signal strength according to claim 1, characterized in that The linear regression method is as follows: including the following steps: S3.
1. Define a multiple linear expression: a0X0 + a1X1 + a2X2 + a3 = Y S3.
2. Assume that O is the position of the radiation source and there are N monitoring points. According to the signal strength difference of the same signal received at the same moment by each monitoring point and the first monitoring point, multiple groups of observed values of (X0, X1, X2, Y) are formed; where: X0 = 2(Kx j ―x1) / (K―1) X1 = 2(Ky j ― y1) / (K ― 1) X2 = 2(Kh j ― h1) / (K ― 1) Among them, (x j ,y j ,h j ) and (x1, y1, h1) are the coordinates of monitoring point j and monitoring point 1 respectively, with the unit of Km; E j and E1 are the signal strength values of the same signal observed at the same moment at monitoring point j and monitoring point 1 respectively, with the unit of dBm; j = 2, 3... N; S3.
3. Use the multiple linear expression in S3.1 to perform multiple linear regression analysis on N - 1 groups of observed values (X 0k , X 1k , X 2k , Y k )(k = 0, 1, … N - 2), and calculate the regression coefficients a0, a1, a2, a3; where (a0, a1, a2) are the position coordinates (x0, y0, h0) of the radiation source.