A method for locating a radiation source based on continuously arriving signal strength

Abstract

The present application belongs to the technical field of radiation source positioning method, and particularly relates to a radiation source positioning method based on continuous arrival signal strength, comprising the following steps: S1, positioning the radiation source; S2, performing CSOA positioning; and S3, performing effectiveness determination. The present application can increase the number of observation points, reduce the position error of observation points or reduce the observation time error, and can improve the positioning success rate and positioning accuracy. Moreover, the random error generated when the observation points measure the signal strength has no obvious influence on the positioning success rate and accuracy. Furthermore, the present application can increase the scanning frequency or prolong the scanning time, so as to improve the positioning success rate and positioning accuracy.

Description

Technical Field

[0001] This invention belongs to the technical field of radiation source localization methods, specifically relating to a radiation source localization method based on the strength of continuously arriving signals. Background Technology

[0002] Radiation source localization is a crucial technique for acquiring the location information of electromagnetic signal sources. Distributed passive localization utilizes multiple distributed sensors to receive signals from target radiation sources for positioning. It offers advantages such as wide coverage, good concealment, high fault tolerance, and flexible and convenient network construction, and has been widely applied in various fields, including military and civilian sectors. Known distributed passive localization methods include those based on Angle of Arrival (AOA), Time of Arrival (TOA), Strength of Arrival (SOA), Time Difference of Arrival (TDOA), Frequency Difference of Arrival (FDOA), and joint localization methods based on TDOA and AOA, FDOA and AOA, and TDOA and FDOA.

[0003] These methods each have their own advantages and disadvantages. Among them, the SOA positioning method can discover frequencies that can be used for positioning through spectrum scanning and can simultaneously locate radiation sources at multiple frequencies. However, the SOA positioning method has high requirements for clock synchronization at each monitoring point; errors in the clocks at each measuring point will cause increased positioning errors or positioning failure. Summary of the Invention

[0004] To address the technical problem that the SOA positioning method mentioned above has high requirements for clock synchronization of each monitoring point, and that errors in the clocks of each measuring point will cause increased positioning errors or positioning failures, this invention provides a radiation source positioning method based on continuously arriving signal strength. This method can significantly improve the positioning success rate and accuracy without increasing hardware costs, at the cost of reduced real-time performance. It is applicable to electromagnetic radiation source positioning scenarios with low real-time requirements.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A radiation source localization method based on continuously arriving signal strength includes the following steps:

[0007] S1. Locate the radiation source;

[0008] S2. Perform CSOA positioning;

[0009] S3. Determine the validity of the results.

[0010] The method for locating the radiation source in S1 is as follows: Assume that within a certain time period, there is only one electromagnetic wave radiation source with a frequency of F (F < 10 GHz) radiating towards point O; the spatial coordinates of radiation source O are (x0, y0, h0), and the set of radiation signal intensities within a certain time period is... Where x0, y0, and h0 are the x-axis coordinate, y-axis coordinate, and z-axis coordinate, respectively; the x-axis is the east-west direction, with the x-axis positive from west to east; the y-axis is the north-south direction, with the y-axis positive from south to north; the z-axis is the height direction, with the z-axis positive from bottom to top; the units of the x-axis coordinate, y-axis coordinate, and z-axis coordinate are all in km; Let be the signal strength value of the radiation source at time j, in dBm; the signal strength value changes M times over a period of time, and the duration of the signal strength value before the j-th change is t. j j = 1, 2, ..., M;

[0011] Meanwhile, it is assumed that there are n observation points G on the ground. i (i = 1, 2, ..., n), represented by its spatial coordinates and observed signal strength as: G i =(x i ,y i ,h i E i ); where x i ,y i ,h i These are spatial coordinates; For G i The signal strength value observed at time j, in dBm.

[0012] The G i The following conditions must be met: the observation points are not on the same plane or the same straight line; there is no obstruction between each observation point and the radiation source; the intensity of electromagnetic wave signals with frequency F can be continuously measured at each observation point; n≥5;

[0013] Under these conditions, by continuously observing the intensity values ​​of the signals received at each observation point, the spatial coordinates (x0, y0, h0) of the radiation source O can be calculated using the CSOA positioning method.

[0014] The method for CSOA positioning in S2 is as follows: Since there are no obstructions between the target and the observation point, and the propagation loss of electromagnetic waves in the air when the frequency is below 10GHz is negligible, it is assumed that the electromagnetic wave travels from the target O to the observation point G. i The loss between them is equal to the loss of electromagnetic waves propagating in free space; neglecting the time taken for electromagnetic waves to propagate through space, the formula is:

[0015]

[0016] Where F is the frequency, in MHz; D i For observation point G i The straight-line distance to target O, in km; i = 1, 2, ..., n, j = 1, 2, ..., M;

[0017]

[0018] Transform from equation (1) and multiply both sides of the equation by t. j achievable

[0019]

[0020] By summing the data from the M time points, we can obtain:

[0021]

[0022] make Then P i =Q-20lgD i ·T, transformed to:

[0023] lgD i =(QP i ) / (20T)

[0024]

[0025] Let B = 10 Q / (10T) , but:

[0026] D i 2 =B / K, KD i 2 =B, substituting equation (2) into it, we get:

[0027] K[(x-x0) 2 +(y-y0) 2 +(h-h0) 2 ]=B (5)

[0028] Equation (5) can be transformed to obtain:

[0029]

[0030] Let Y = K(x) 2 +y 2 +h 2 ), X0=2Kx, X1=2Ky, X2=2Kh,2 +y0 2 +h0 2 Substituting a4 = B into equation (6), we get:

[0031] a0X0+a1X1+a2X2+a3X3+a4=Y (7)

[0032] Equation (7) is a linear expression used to apply the expression to n sets of observations (X0, X1, X2, X3, Y) of the given set. 0i ,X 1i ,X 2i ,X 3i Y i Multiple linear regression analysis can be performed on (i = 0, 1, ..., n-1) to calculate the regression coefficients a0, a1, a2, a3, a4; where (X... 0i X 1i X 2i X 3i Y i )(i=0, 1,...,n-1) by G i n sets of observations (x i y i h i E i )Calculated;

[0033] Therefore, we can conclude that:

[0034] x0=a0, y0=a1, h0=a2.

[0035] The method for the multiple linear regression is as follows:

[0036] Let Y be a random variable and m independent variables X0, X1, ..., Xn. m-1 Given n sets of observation data (X) 0i X 1i , ......, X m-1i Y i (i = 0, 1, ..., n-1), expressed using a linear expression

[0037] Y = a0X0 + a1X1 + ... + a m-1 X m-1 +a m

[0038] Regression analysis based on least squares was performed on the observed data to obtain regression coefficients a0, a1, ..., a m The value of .

[0039] The regression analysis uses the following two variables to measure the regression effect:

[0040] Multiple correlation coefficient

[0041] in

[0042] When r is close to 1, it indicates that the relative error q / p is close to zero, and the linear regression effect is good.

[0043] Partial correlation coefficient

[0044] in

[0045] When v j The larger the value, the greater the value of X. j The more significant the effect of Y, the less likely x should be considered. j Remove.

[0046] The method for determining validity in S3 is as follows:

[0047] To determine the validity of the calculation results, the CSOA method uses the complex correlation coefficient r and defines two variables: the position deviation coefficient c and the signal strength variance d.

[0048] Position deviation coefficient:

[0049] c≥0, the smaller the value, the higher the accuracy of the calculation result;

[0050] Signal strength variance:

[0051]

[0052] d≥0, the smaller the value, the higher the accuracy of the calculation result;

[0053] The value is considered valid when r is close to 1 and c and d are close to 0.

[0054] Compared with the prior art, the beneficial effects of this invention are:

[0055] This invention improves positioning success rate and accuracy by increasing the number of observation points, reducing observation point location errors, or reducing observation time errors. Furthermore, random errors generated during signal strength measurement at observation points have little impact on positioning success rate and accuracy. Additionally, increasing the number of scans or extending the scan time further improves positioning success rate and accuracy. Attached Figure Description

[0056] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0057] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0058] Figure 1 This is a diagram showing the effect of the number of measuring points on positioning accuracy when the validity of this invention is not determined.

[0059] Figure 2 This is a statistical chart of the parameters for determining the effectiveness of the present invention;

[0060] Figure 3 This diagram illustrates the impact of the number of measurement points on positioning accuracy when determining the validity of this invention.

[0061] Figure 4 This is a diagram illustrating the impact of the position error on the positioning accuracy of this invention.

[0062] Figure 5 This is a diagram illustrating the impact of measurement error on positioning accuracy in this invention.

[0063] Figure 6 This is a diagram showing the impact of the initial time error on positioning accuracy in this invention.

[0064] Figure 7 This is a diagram showing the effect of the number of scans on the positioning accuracy in this invention; Detailed Implementation

[0065] 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. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. These descriptions are only for further illustrating the features and advantages of the present invention, and not for limiting the claims of the present invention. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0066] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0067] In this embodiment, the following steps are specifically included:

[0068] 1. Radiation source location problem

[0069] Suppose that for a certain period of time, there is one and only one electromagnetic wave radiation source with a frequency of F (F < 10 GHz) radiating towards point O. The spatial coordinates of the radiation source O are (x0, y0, h0), and the set of radiation signal intensities over a certain period of time is given by... Where x0, y0, and h0 are the coordinates of the x-axis (east-west direction, positive from west to east), y-axis (north-south direction, positive from south to north), and z-axis (height direction, positive from bottom to top), respectively, with units of km; Let be the signal strength value of the radiation source at time j, in dBm; the signal strength value changes M times over a period of time, and the duration of the signal strength value before the j-th change is t. j , j = 1, 2, ..., M.

[0070] Meanwhile, it is assumed that there are n observation points G on the ground. i (i = 1, 2, ..., n), represented by its spatial coordinates and observed signal strength as: G i =(x i ,y i ,h i E i ), where x i ,y i ,h i These are spatial coordinates; For G i The signal strength value observed at time j, in dBm. G i The following conditions must be met:

[0071] 1) The observation points are not on the same plane or the same straight line;

[0072] 2) There is no obstruction between each observation point and the radiation source;

[0073] 3) The intensity of electromagnetic wave signals with frequency F can be continuously measured at each observation point;

[0074] 4) n≥5.

[0075] Under these conditions, by continuously observing the intensity values ​​of the signals received at each observation point, the spatial coordinates (x0, y0, h0) of the radiation source O can be calculated using the CSOA positioning method.

[0076] 2CSOA positioning method

[0077] Since there are no obstructions between the target and the observation point, and the propagation loss of electromagnetic waves in the air is negligible when the frequency is below 10 GHz, it can be assumed that the electromagnetic wave travels from the target O to the observation point G. i The loss between them is equal to the loss of the electromagnetic wave propagating in free space. Ignoring the time it takes for the electromagnetic wave to propagate through space, the formula is:

[0078]

[0079] Where F is the frequency, in MHz; D i For observation point G i The straight-line distance to target O, in km; i = 1, 2, ..., n, j = 1, 2, ..., M.

[0080]

[0081] Transform from equation (1) and multiply both sides of the equation by t. j achievable

[0082]

[0083] By summing the data from the M time points, we can obtain:

[0084]

[0085] make Then P i =Q-20lgD i ·T, by transformation, we can obtain:

[0086] lgD i =(QP i ) / (20T)

[0087]

[0088] Let B = 10 Q / (10T) , but:

[0089] D i 2 =B / K, KD i 2 =B, substituting equation (2) into it, we get:

[0090] K[(x-x0) 2 +(y-y0) 2 +(h-h0) 2 ]=B (5)

[0091] Equation (5) can be transformed to obtain:

[0092]

[0093] Let Y = K(x) 2 +y 2 +h 2 ), X0=2Kx, X1=2Ky, X2=2Kh, 2 +y0 2 +h0 2 Substituting a4 = B into equation (6), we get:

[0094] a0X0+a1X1+a2X2+a3X3+a4=Y (7)

[0095] Equation (7) is a linear expression used to apply the expression to n sets of observations (X0, X1, X2, X3, Y) of the given set. 0i ,X 1i ,X 2i ,X 3i Y i Multiple linear regression analysis was performed on the subsets (i = 0, 1, ..., n-1) to calculate the regression coefficients a0, a1, a2, a3, and a4. Where (X... 0i X 1i X 2i X 3i Y i (i = 0, 1, ..., n-1) can be derived from G i n sets of observations (x i y i h i E i ) was calculated.

[0096] Therefore, we can conclude that:

[0097] x0=a0, y0=a1, h0=a2.

[0098] 3 Implementation Methods

[0099] 3.1 Multiple Linear Regression

[0100] The key algorithm in the CSOA localization method is multiple linear regression. This paper presents a multiple linear regression method based on the least squares approach and its corresponding C language code implementation. The method is as follows.

[0101] Let Y be a random variable and m independent variables X0, X1, ..., Xn. m-1 Given n sets of observation data (X) 0i X 1i, ......, X m-1i Y i (i = 0, 1, ..., n-1), expressed using a linear expression

[0102] Y = a0X0 + a1X1 + ... + a m-1 X m-1 +a m

[0103] Regression analysis based on least squares was performed on the observed data to obtain regression coefficients a0, a1, ..., a m The value of .

[0104] This method can use the following two variables to measure the regression effect.

[0105] 1) Multiple correlation coefficient

[0106] in

[0107] When r is close to 1, it indicates that the relative error q / p is close to zero, and the linear regression effect is good.

[0108] 2) Partial correlation coefficient

[0109] in

[0110] When v j The larger the value, the greater the value of X. j The more significant the effect of Y, the less likely x should be considered. j Remove.

[0111] 3.2 Validity determination

[0112] To determine the validity of the calculation results, the CSOA method uses the multiple correlation coefficient r and defines two variables: the position deviation coefficient c and the signal strength variance d.

[0113] Position deviation coefficient:

[0114] c≥0, the smaller the value, the higher the accuracy of the calculation result.

[0115] Signal strength variance:

[0116]

[0117] d≥0, the smaller the value, the higher the accuracy of the calculation result.

[0118] The value is considered valid when r is close to 1 and c and d are close to 0.

[0119] To verify the correctness and adaptability of the CSOA method, simulation verification was performed. For ease of comparison, the experiment used the same hardware and software environment and simulation environment as existing technologies. The experimental hardware and software environment was: Windows 7 64-bit Ultimate Edition, 8GB RAM, Intel(R) Core(TM) i7-6700 CPU@3.40GHz. The development environment was: Visual Studio 2013, C# language. The simulation environment was: assuming a simulation space with length, width, and height of 100m, 100m, and 20m respectively, the coordinates of the lowest vertex in the southwest direction of this space were taken as the origin (0, 0, 0). In this space, the radiation source was located at (10, 10, 10), continuously radiating an electromagnetic wave signal with a frequency of 30MHz, and the signal strength varied randomly.

[0120] 4. Simulation Analysis

[0121] 4.1 Simulation Methods and Procedures

[0122] 4.1.1 Signal Source Simulation

[0123] A simulated signal source, denoted as ET0, is constructed using a circular queue of length 50 million. Adjacent elements in the queue represent the signal strength at adjacent times, and the values ​​are random real numbers within the interval (-40, 0), expressed in dBm. The following assumptions are made regarding this simulated signal source:

[0124] 1) The radiation intensity of the signal source remains unchanged until the next moment;

[0125] 2) The time difference between two consecutive elements in the queue is 100 μs, meaning that the radiation intensity of the signal source changes every 100 μs.

[0126] 4.1.2 Simulation of Observation Points

[0127] The simulation method for the observation points is as follows.

[0128] 1) Assume a start measurement time, denoted as tick, corresponding to a certain position in the circular queue ET0. All observation points start measurement simultaneously at this time.

[0129] 2) Assume that the observation point measures data through spectrum scanning, and a set of measurement values ​​is obtained after M consecutive scans. The time taken for each scan is called the dwell time, denoted as sweeptime; there is a certain time interval between each scan, during which the signal strength is not measured, denoted as droptime. The dwell time and droptime each correspond to a subset of ET0, and the subsets corresponding to the two are adjacent.

[0130] 3) The dwell time corresponds to a subset of ET0, consisting of multiple elements. The measurement value of each scan is calculated by simulation of multiple elements of this subset. The simulation calculation method of the measurement value is as follows: 1) Calculate the value corresponding to the current observation point for each element using formula (1), with the unit being dBm; 2) Convert the unit from dBm to Vpp; 3) After calculating the corresponding values ​​of all elements to the current observation point, calculate the average value in Vpp; 4) Convert the unit of the average value to dBm, which is the simulation measurement value of this scan. In this process, dBm and Vpp are converted to each other with an impedance of 50 ohms, and the formula is:

[0131] dBm=10+20lg(0.5Vpp) (8)

[0132]

[0133] 4) Ideally, the start time and dwell time of each measuring point are exactly the same, and the discard time is 0. However, in actual measurements, the start time and dwell time of each measuring point may have some random error, and the discard time is also a random data point greater than 0. The error in the start time only occurs during the first scan, and this value remains unchanged in subsequent scans; the error in the dwell time and the discard time may change with each scan. These errors are collectively referred to as observation time errors, and can all be simulated using random numbers.

[0134] 5) When simulating and calculating the measured values ​​of the observation points, the error of the observation point location and the measured values ​​should be taken into account. Random numbers can also be used for simulation.

[0135] 4.2 Experimental Procedure

[0136] The first step is to construct a circular queue for the simulated signal source.

[0137] The second step involves randomly generating n (n≥5) measurement points within the simulation space, and setting the start time tick, the number of continuous measurements M, the dwell time sweeptime for each scan, and the error range for each parameter.

[0138] The third step is to generate a sequence of simulated measurement values ​​for each observation point according to the given conditions. The method is as follows.

[0139] From equation (1), we can know that the observation point G i The signal strength at any given time is:

[0140] e i =e0-32.44-20lgF-20lgD (10)

[0141] Where e0 is the intensity of the radiation source at that moment. From equation (10), the observation point G corresponding to any element in ET0 can be calculated. ；The monitored signal strength, plus the random errors of the measurement values ​​and the observation point locations, can then be used to calculate simulation data. The formula is:

[0142] e i =e0-32.44-20lgF-20lgD′+N E ·Rnd(-0.5, 0.5) (11)

[0143] Where NE is the magnitude of the random error generated during the measurement at the observation point; the function Rnd(-0.5, 0.5) generates random numbers within the interval (-0.5, 0.5); D′ is the distance from the observation point to the radiation source after adding the random error of the position. x N y N h N These are the coordinates of the observation point in the x, y, and z axes after adding random errors; x N =x+N x ·Rnd(-0.5, 0.5), y N =y+N y ·Rnd(-0.5, 0.5), h N =h+H h ·Rnd(-0.5, 0.5); N x N y H h These represent the magnitudes of the random errors at the observation points along the x, y, and z axes, respectively.

[0144] In the subset corresponding to the dwell time ET0, there are multiple elements, which will generate multiple ei. Following the simulation calculation method for observation values ​​in the observation point simulation, the observation value of the j-th scan can be obtained. During the calculation, the set of elements used should be a subset of ET0 after taking into account the observation time error.

[0145] After M scans are completed, the observation sequence can be formed using equations (4) to (7), where t j The value is sweeptime.

[0146] Below is a set of simulation data from 10 randomly distributed observation points, with M set to 1000 and sweep time set to 1000 microseconds. The units of x, y, and h are in meters (m). The unit is dBm·μs.

[0147] Table 1. Simulation data for ten observation points

[0148] Serial Number x y h P 1 56.76 69.581 0.83243 -5.3095E+08 2 6.3855 21.552 2.1682 -3.8585E+08 3 96.603 77.508 2.4321 -5.6264E+08 4 22.872 1.6045 10.183 -3.9207E+08 5 13.018 96.125 10.149 -5.4125E+08 6 53.786 75.621 12.053 -5.3375E+08 7 20.299 80.744 12.972 -5.2524E+08 8 14.803 75.725 19.895 -5.1906E+08 9 89.905 22.355 7.5915 -5.3587E+08 10 83.143 97.518 16.882 -5.6593E+08

[0149] The fourth step involves using the simulated observation point locations and observation sequence to deduce the location of radiation source O using the CSOA method. If the deduction is successful, the distance is calculated by comparing it with a given radiation source location. An example of this method is as follows:

[0150] Based on the above conditions, according to equations (5) to (7), let Y = K(x) 2 +y 2 +h 2 X0 = 2Kx, X1 = 2Ky, X2 = 2Kh, X3 = -K. The 10 sets of observations (X0, X1, X2, X3, Y) required for linear regression can be calculated from the 10 sets of data in Table 2, as shown in Table 2.

[0151] Table 2 (X0, X1, X2, X3, Y) contains 10 sets of observations.

[0152] Serial Number <![CDATA[X0]]> <![CDATA[X1]]> <![CDATA[X2]]> <![CDATA[X3]]> Y 1 5.5660E-07 6.8232E-07 5.5660E-07 6.8232E-07 5.5660E-07 2 1.7691E-06 5.9709E-06 1.7691E-06 5.9709E-06 1.7691E-06 3 4.5671E-07 3.6643E-07 4.5671E-07 3.6643E-07 4.5671E-07 4 5.4913E-06 3.8521E-07 5.4913E-06 3.8521E-07 5.4913E-06 5 1.0070E-07 7.4356E-07 1.0070E-07 7.4356E-07 1.0070E-07 6 4.9452E-07 6.9526E-07 4.9452E-07 6.9526E-07 4.9452E-07 7 2.2706E-07 9.0318E-07 2.2706E-07 9.0318E-07 2.2706E-07 8 1.9087E-07 9.7641E-07 1.9087E-07 9.7641E-07 1.9087E-07 9 7.8725E-07 1.9575E-07 7.8725E-07 1.9575E-07 7.8725E-07 10 3.6438E-07 4.2738E-07 3.6438E-07 4.2738E-07 3.6438E-07

[0153] Multiple linear regression yielded a multiple correlation coefficient r = 1, a positional deviation coefficient c = 0.0027, and a signal strength variance d = 46.5864.

[0154] Using the CSOA positioning method described above, the target's position coordinates obtained from the above 10 sets of observation data are: (9.6802, 9.7863, 9.8968).

[0155] The validity criteria are as follows:

[0156] 1) r>0.8;

[0157] 2) c < 4.

[0158] 3)d<49.

[0159] The calculation result is valid after validity assessment.

[0160] Finally, given different simulation conditions, steps two through four were repeated multiple times to analyze the impact of each parameter on positioning accuracy.

[0161] 4.3 Simulation Experiment

[0162] Various simulation experiments were used to verify the impact of the number of observation points, position error, measurement error, observation time error, and number of scans on the positioning success rate and accuracy.

[0163] Each simulation experiment sets multiple different conditions, and each experiment is repeated at least 10,000 times according to the simulation experiment steps described in 4.2. The result of each calculation is recorded as (x0, y0, h0), and then the distance to the true position of the target O is calculated, which is the positioning error, denoted as s.

[0164]

[0165] Finally, by using the cumulative distribution function, the distribution of positioning error s under different parameters is compared, and the influence of each parameter on the positioning result is summarized.

[0166] 4.3.1 The impact of the number of measurement points on the results and the determination of their validity

[0167] This embodiment tests the effect of the number of measurement points (n) on the positioning results. It consists of 11 groups, with the number of measurement points (n) ranging from 5 to 15. Other parameters are as follows:

[0168] Based on the performance specifications achievable by a typical spectrum analyzer and a standard computer, the dwell time (sweeptime) is set to 10ms, the initial error (tickerr) to 1s, the dwell time error (sweeptimeerr) to 1ms, the dropout time error (droperr) to 1ms, and the measurement error (N) to be set. e Set to 0.2 dBm, the magnitude N of the observation point position error x N y N h The depth was set to 0.4m, and the number of scans M was set to 1000.

[0169] Each experiment was repeated 50,000 times. Without considering validity criteria (as long as the result can be obtained through the aforementioned multiple linear regression, the localization success rate is considered successful):

[0170] Table 3. Number of measuring points and positioning success rate without considering validity assessment.

[0171]

[0172]

[0173] Based on this condition, the cumulative distribution of positioning error is calculated, see... Figure 1 .

[0174] Depend on Figure 1 It can be seen that as n increases, the cumulative distribution function tends to 1 at lower positioning errors, meaning the positioning error becomes increasingly concentrated at lower values, and the positioning accuracy becomes higher. However, as n increases further, the improvement becomes smaller. For example, with a positioning error of 10... 0.6Taking the cumulative distribution value at approximately 3.98 meters as an example: when n=5, the cumulative distribution value is 0.559; when n=6, the value is 0.805, with a cumulative distribution increase of 44.0%; when n=10, the value is 0.993; when n=11, the value is 0.997, with a cumulative distribution increase of only 0.4%. Comparing this with existing experimental results, it can be found that, similar to the SOA method, when n is less than 10, increasing the number of measurement points can significantly improve positioning accuracy; when n is greater than 10, increasing the number of measurement points can continue to improve positioning accuracy, but the effect becomes significantly slower; when n is greater than 15, increasing the number of measurement points has little impact on positioning accuracy.

[0175] To determine the validity, the complex correlation coefficient r, the positional deviation coefficient c, and the signal strength variance d were verified. Figure 2 The graphs show the statistics for r, c, and d, where r is the minimum value when n=6 (because in the experiment, r is 1 for all values ​​when n=5), and c and d are the mean values ​​when n=5. The graphs show that the positioning error is 10. 2 Within 100 meters, the value of r will not be less than 0.8; the positioning error is within 10. 0.8 At approximately 6.31 meters, the value of c increases significantly, exceeding 4; the positioning error is within 10. 1.8 At a distance of approximately 63.10 meters, the value of d increases dramatically, exceeding 48.

[0176] Based on this result, an validity check was added, and the data from this experiment were re-analyzed. The results are shown in Table 4 and... Figure 3 .based on Figure 2 Based on some empirical data summarized in the experiment, the conditions for determining the validity of this simulation environment are: r>0.8, c<4, and d<49.

[0177] Table 4. Number of measuring points and positioning success rate after validity assessment

[0178]

[0179]

[0180] Compared to the case where validity is not considered, the positioning success rate decreased, but the positioning accuracy improved. Taking n=5 as an example, the positioning success rate decreased from 98.94% to 89.74%, a drop of 9.2 percentage points; in n=10... 0.6 The cumulative distribution value at (approximately 3.98 meters) is derived from... Figure 1 The value of 0.556 was increased to Figure 3 The value was 0.610, an increase of 9.71%. This demonstrates that the validity determination can, to some extent, eliminate results with inaccurate positioning.

[0181] Based on the results of this experiment, in the following experiments, the number of measurement points was set to 5 for all, and all results were evaluated for validity using the same criteria as in this embodiment.

[0182] 4.3.2 Influence of measuring point location error on the results

[0183] This embodiment is used to test the impact of measurement point position error on positioning results. It is divided into 6 groups, and the amplitude N of the position error in each group is... xyh (N x N y N h Set all to N xyh The values ​​are 0.2m, 0.4m, 0.6m, 1.2m, 1.6m, and 2.0m respectively. Other parameters are set as follows: n = 5, sweeptime = 10ms, ticker = 1s, sweeptimeerr = 1ms, droperr = 1ms, N e =0.2dBm, M=1000.

[0184] Each experiment was repeated 100,000 times. After validity assessment, the localization success rate is shown in Table 5.

[0185] Table 5. Measurement Point Location Error and Positioning Success Rate

[0186]

[0187]

[0188] Based on this condition, the cumulative distribution of positioning error is calculated, see... Figure 4 .

[0189] As shown in Table 5, an increase in position error will reduce the positioning success rate. Figure 4 In the case where the position error amplitude is less than or equal to 0.4, the positioning error is less than 10. 0.4 The convergence is reached at approximately 2.51m; when the value is less than or equal to 1.2, it converges at 10. 0.6 The convergence is reached at approximately 3.98m; when the value is less than or equal to 2, the convergence is reached at 10. 0.8 The positions tend to be consistent at approximately 6.31m. This indicates that positional errors have a significant impact on positioning accuracy within a certain range, but a smaller impact beyond that range.

[0190] 4.3.3 The Influence of Measurement Error on Results

[0191] This embodiment is used to test the impact of measurement errors at observation points on positioning results. It is divided into 6 groups, with the amplitude N of the measurement error at each observation point being... eThe values ​​are 0.2dBm, 0.4dBm, 0.6dBm, 0.8dBm, 1.0dBm, and 1.2dBm, respectively. Other parameters are set as follows: n = 5, sweeptime = 10ms, ticker = 1s, sweeptimeerr = 1ms, droperr = 1ms, N x =N y =N h =0.4m, M=1000.

[0192] Each experiment was repeated 100,000 times. After validity assessment, the localization success rate is shown in Table 6.

[0193] Table 6. Measurement Point Location Error and Positioning Success Rate

[0194] <![CDATA[N e (dBm)]]> Number of successful location attempts Location success rate (%) 0.2 96190 96.19 0.4 96111 96.11 0.6 96179 96.18 0.8 96252 96.25 1.0 96197 96.20 1.2 96063 96.06

[0195] Based on this condition, the cumulative distribution of positioning error is calculated, see... Figure 5 .

[0196] From Table 6 and Figure 5 It can be seen that the magnitude of the measurement error has no significant relationship with the positioning success rate, and the impact on positioning accuracy is also negligible. The reason for this is that the measurement process is actually a process of integrating signal strength over time. During the integration process, the random errors generated by the measurement will cancel each other out, ultimately reducing the impact on positioning accuracy.

[0197] 4.3.4 The impact of observation time error on the results

[0198] This embodiment is used to test the impact of observation time error on positioning results. In general practical applications, the start time error of each measuring point is relatively large, while the dwell time error and drop time error are relatively small. Therefore, in this implementation, sweeptimeerr and droperr are fixed, and only sweeptime and tickerr are changed. The experiment is divided into 14 groups: the first 7 groups have sweeptime = 10ms, and tickerr is 10ms, 20ms, 50ms, 100ms, 200ms, 500ms, and 1s respectively; the last 7 groups have sweeptime = 100ms, and tickerr is 100ms, 200ms, 500ms, 1s, 2s, 5s, and 10s respectively. Other parameters are set as follows: n = 5, sweeptimeerr = 1ms, droperr = 1ms, N e =0.2dBm, N x =N y =N h =0.4m, M=1000.

[0199] Each experiment was repeated 10,000 times. After validity assessment, the localization success rate is shown in Table 7. Here, rate represents the error time percentage, i.e., the proportion of the error at the start time in the total continuous scanning time, calculated as rate = tickerr / (sweeptime·M)·100, in percentages.

[0200] Table 7. Start Time Error and Positioning Success Rate

[0201]

[0202]

[0203] Based on this condition, the cumulative distribution of positioning error is calculated, see... Figure 6 .

[0204] From Table 7 and Figure 6 Comparing series 1 to 7, or series 8 to 14, it can be observed that the initial time error has a significant impact on both the positioning success rate and positioning accuracy. With other parameters remaining constant, a larger proportion of the error time results in a lower positioning success rate and lower positioning accuracy. Taking series 1 and 7 as examples, the positioning success rate decreased from 96.47% to 89.66%, a drop of 6.81 percentage points; with a positioning error of 10... 0.6 At a distance of approximately 3.98 meters, the cumulative distribution value decreased from 0.852 to 0.541, a decrease of 36.5%.

[0205] With the same percentage of error time, a larger sweep time per scan results in a higher positioning success rate and higher positioning accuracy. For example, Series 1 has an error time percentage of 0.1%, but its positioning success rate falls between Series 11 (1% error time percentage) and Series 12 (1% error time percentage), and its positioning accuracy curve almost overlaps with that of Series 12. Compared to Series 8, which also has an error time percentage of 0.1%, the positioning success rate increases from 96.47% to 99.15%, an improvement of 2.68 percentage points, with a positioning error of 10... 0.6 At approximately 3.98 meters, the cumulative distribution value increased from 0.852 to 0.962, an increase of 12.9%. The reason for this is that in addition to the error in the start time, the dwell time error and the discard time also affect the results in the observation time error. Increasing the dwell time can reduce the proportion of the latter two in the dwell time, and thus reduce their impact, thereby improving the positioning success rate and accuracy.

[0206] 4.3.5 The impact of the number of scans on the results

[0207] This embodiment tests the impact of the number of scans on the localization results. It is divided into 7 groups, with the number of scans M for each group being 1000, 2000, 5000, 10000, 20000, 50000, and 100000 respectively. Other parameters are set as follows: n = 5, sweeptime = 10ms, ticker = 1s, sweeptimeerr = 1ms, droperr = 1ms, N e =0.2dBm, N x =N y =N h =0.4m.

[0208] Each experiment was repeated 10,000 times. After validity assessment, the positioning success rate is shown in Table 8, where rate is the percentage of error time, in units of %.

[0209] Table 8. Number of Scans and Positioning Success Rate

[0210]

[0211] Based on this condition, the cumulative distribution of positioning error is calculated, see... Figure 7 .

[0212] From Table 8 and Figure 7 It can be seen that as the number of scans M increases, the positioning success rate and positioning accuracy are significantly improved. When M increases from 1000 to 10000, the positioning success rate increases from 89.46% to 99.52%, an increase of 10.6 percentage points; the positioning error is within 10... 0.6 The cumulative distribution value at approximately 3.98 meters increased from 0.590 to 0.985, an improvement of 66.9%. This demonstrates that increasing the number of scans can significantly improve the success rate and accuracy of positioning.

[0213] The above description only illustrates 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 skilled in the art, various changes can be made without departing from the spirit of the present invention, and all such changes should be included within the protection scope of the present invention.

Claims

1. A method of emitter location based on the strength of continuously arriving signals, characterized in that: Comprising the following steps: S1, positioning the radiation source; assuming that in a period of time, there is only one electromagnetic wave radiation source with a frequency of to O, ; the spatial coordinates of the radiation source O , the set of radiation signal intensity in a certain period of time is ; wherein x-axis coordinate, y-axis coordinate, z-axis coordinate; the x-axis is east-west direction, the x-axis is positive from west to east; the y-axis is south-north direction, the y-axis is positive from south to north; the z-axis is height direction, the z-axis is positive from down to up; the unit of x-axis coordinate, y-axis coordinate, z-axis coordinate is Km; is the signal intensity value of the radiation source at the jth moment, the unit is dBm; the signal intensity value has M changes in a period of time, the signal intensity value before the jth change lasts for t j , ; Meanwhile, it is assumed that there are observation points on the ground, which are represented by their spatial coordinates and observed signal strengths as follows: ; where, is the spatial coordinate; , is the observed signal strength value at the jth time instant, in dBm; S2, CSOA positioning is performed; since there is no obstruction from the target to the observation point, and the electromagnetic wave frequency is lower than the loss of electromagnetic wave propagation in air at this time can be ignored, so it is considered that the loss of electromagnetic wave from the target O to the observation point G i between the loss of electromagnetic wave transmission in free space; without considering the time spent by electromagnetic wave in space transmission, its formula is: （1） Wherein, F is frequency, unit is MHz; D i The straight line distance from observation point G i to target O, unit is Km; ; （2） Transformed from equation (1) and multiplied by t on both sides j Yield （3） Add the data of M time points, and the following equation can be obtained: (4) Let , , , then , transforming gives: Let , then: , Substituting equation (2) gives: (5) Equation (5) is transformed as follows: (6) Let , , , , , , , , , , substituting equation (6), we have: (7) Equation (7) is a linear expression, and it is used to... n sets of observations By performing multiple linear regression analysis, the regression coefficients can be calculated. ;in By G i n sets of observations Calculated; Thus, the final equation is obtained as follows: ， ， ； S3, validity determination.

2. The method of claim 1, wherein: The G i The following conditions are met: each observation point is not on the same plane or the same straight line; each observation point is not blocked from the radiation source; each observation point can continuously measure the intensity of the electromagnetic wave signal with a frequency of ; ; Under this condition, by continuously observing the intensity value of the signal received by each observation point, the spatial coordinates of the radiation source O are calculated using the CSOA positioning method .

3. The method of claim 1, wherein: The method of the multiple linear regression is: Let Y be a random variable and m independent variables ; given n sets of observation data , in a linear expression Regression analysis based on least square method is performed on the observation data to obtain the value of regression coefficient .

4. The method of claim 3, wherein: The regression analysis uses the following two variables to measure the regression effect: multiple correlation coefficient wherein , , ; When Close to 1, the relative error Close to zero, linear regression works well; Partial correlation coefficient wherein The greater the difference between the two values, the more significant the effect of the the greater the difference between the two values, the more significant the effect of the the greater the difference between the two values, the more significant the effect of the the greater the difference between the two values, the more significant the effect of the the greater 5. The method of claim 1, wherein: The method of the validity determination in S3 is: In order to determine the validity of the calculation result, the CSOA method uses the complex correlation coefficient r, and defines two variables of the position deviation coefficient c and the signal intensity variance d; Position deviation coefficient: ; The smaller the value, the higher the accuracy of the calculation result. Signal intensity variance: The smaller the value, the higher the accuracy of the calculation result. When r is close to 1, c and d are close to 0, and the value is considered valid.

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