A direct method for locating radiation sources

Abstract

This invention relates to a direct location method for radiation sources, belonging to the field of radiation source location technology, and solves the problem of low accuracy in radiation source location in existing technologies. The direct location method includes: constructing a correction cost function based on Bayes' theorem, using an observation station measurement position model and an external correction source measurement signal model; correcting the measurement positions of each observation station based on the external correction source measurement signals and the correction cost function; performing a first-order Taylor series expansion of the radiation source measurement signal model at the corrected position of each observation station to obtain the expanded observation station radiation source measurement signal model; constructing a location cost function for the radiation source position based on the radiation source measurement signals of each observation station, the corrected position radiation source signal model, and the corrected radiation source error model; and determining the location of the radiation source based on the location cost function. This achieves high-precision location of the radiation source.

Description

Technical Field

[0001] This invention relates to the field of radiation source location technology, and in particular to a direct location method for radiation sources. Background Art

[0002] In traditional two-step localization methods, it is necessary to extract signal parameters related to the location of the radiation source from the received electromagnetic signal, such as angle of arrival, time of arrival, time difference of arrival, and frequency difference of arrival, and then locate the radiation source based on the extracted signal parameters. Direct localization refers to the observation station directly estimating the location of the radiation source based on the received electromagnetic signal.

[0003] Traditional two-step localization methods are not optimal because they ignore the potential constraint that the extracted signal parameters correspond to a radiation source. Direct localization methods, on the other hand, can effectively utilize this potential constraint and improve the localization of the radiation source location.

[0004] In the existing technology, the direct positioning method for locating radiation sources cannot be adapted to the application environment, and it is difficult to meet the requirements when performing high-precision positioning tasks.

[0005] Therefore, there is an urgent need for a technical solution to locate radiation sources. Summary of the Invention

[0006] Based on the above analysis, the present invention aims to provide a direct location method for radiation sources, thereby solving the problem of low accuracy in radiation source location in the prior art.

[0007] This invention provides a method for directly locating the position of a radiation source, the method comprising:

[0008] Construct a station measurement location model that includes random location errors, a station radiation source measurement signal model that includes random signal errors, and a station external correction source measurement signal model that includes random signal errors;

[0009] Based on the observation station measurement location model and the external correction source measurement signal model, a correction cost function is constructed based on Bayes' theorem. The measurement location of each observation station is corrected according to the external correction source measurement signal and the correction cost function to obtain the corrected location of each observation station.

[0010] At the calibration position of each observation station, the radiation source measurement signal model of the observation station is expanded by a first-order Taylor series to obtain the expanded radiation source measurement signal model of the observation station; the expanded radiation source measurement signal model of the observation station includes the radiation source signal model at the calibration position and the radiation source error model at the calibration position.

[0011] The location cost function of the radiation source is constructed based on the radiation source measurement signals of each observation station, the radiation source signal model at the corrected location, and the radiation source error model at the corrected location.

[0012] The maximum eigenvalue corresponding to each possible location of the radiation source is determined based on the location cost function of the radiation source location, and the possible location corresponding to the largest maximum eigenvalue is taken as the location of the radiation source.

[0013] A further improvement to the above method, based on the observation station measurement location model and the external correction source measurement signal model, constructs a correction cost function based on Bayes' theorem, including:

[0014] Based on the observation station measurement location model and the observation station external correction source measurement signal model, the first posterior probability equation of each observation station is obtained based on Bayes' theorem;

[0015] The first posterior probability equation of each observation station is differentiated by the first order of the external correction source signal, and the derivative is set to zero to obtain the estimated value of the external correction source signal.

[0016] The estimated value of the externally corrected source signal is substituted into the first posterior probability equation of each observation station for derivation, and the derived second posterior probability equation of each observation station is obtained.

[0017] The second posterior probability equations for each observation station are simplified to obtain the third posterior probability equations for each observation station; based on the third posterior probability equations for each observation station, the correction cost function is obtained.

[0018] Based on a further improvement of the above method, the first posterior probability equation for each observation station is:

[0019]

[0020] in, P(z) represents the posterior probability of each observation station. c |s o ) represents the given location s of each observation station. o Measured z c The probability, P(s) o Let z represent the prior probability of each observation station, M represent the number of observation stations, i represent any single observation station, and z represent the probability of each observation station. ci η represents the measurement signal of the external correction source at the i-th observation station. ci Let Q represent the unknown path loss factor for the i-th observation station and the external correction source. ci Let r represent the discrete Fourier transform vector of the i-th observation station and the external correction source. c Indicates the external correction source signal. This represents the variance of the random signal error between the i-th observation station and the external correction source. This represents the variance of the random location error at each observation station. s represents the actual location of the i-th observation station. i This indicates the measurement location of the i-th observation station;

[0021] Estimated value of externally corrected source signal for:

[0022]

[0023] The second posterior probability equation for each observation station is:

[0024]

[0025] Among them, R c (s o Let be a matrix, and let the i-th row and a-th column be:

[0026]

[0027] The third posterior probability equation for each observation station is:

[0028]

[0029] Where, λ max {R c (s o )} is R c (s o The largest eigenvalue;

[0030] The correction cost function is:

[0031]

[0032] A further improvement to the above method, the step of correcting the measurement position of each observation station based on the external correction source measurement signal and correction cost function of each observation station to obtain the corrected position of each observation station, includes:

[0033] Substitute the external calibration source measurement signals of each observation station into the calibration cost function to obtain the updated calibration cost function;

[0034] The possible combinations of locations for each observation station are determined based on their measurement locations.

[0035] Substitute each possible location combination of each observation station into the correction cost function to obtain the correction cost value corresponding to each possible location combination. Select the possible location combination corresponding to the largest correction cost value as the correction location of each observation station.

[0036] Based on a further improvement of the above method, the expanded observation station radiation source measurement signal model is as follows:

[0037]

[0038] in, Indicates the correction position of each observation station, Δs o This represents the difference between the actual and corrected positions of each observation station, where w represents the random signal error of each observation station. denoted as the corrected position radiation source signal model, and w″ denotes the corrected radiation source error model.

[0039] Based on a further improvement to the above method, the step of constructing the location cost function for the radiation source based on the radiation source measurement signals of each observation station, the corrected location radiation source signal model, and the corrected radiation source error model includes:

[0040] Calculate the covariance matrix of the corrected radiation source error model;

[0041] Based on the covariance matrix of the corrected radiation source error model, the radiation source measurement signals of each observation station, and the radiation source signal model at the corrected location, a weighted least squares solution equation for the radiation source location is constructed.

[0042] The estimated value of the radiation source signal is obtained by solving the weighted least squares equation based on the location of the radiation source. Substituting the estimated value of the radiation source signal into the weighted least squares equation for the location of the radiation source, the location cost function of the radiation source is obtained.

[0043] Based on further improvements to the above method, the covariance matrix of the corrected radiation source error model is calculated, including:

[0044] At the calibration locations of each observation station, the measurement signal model of the calibration source outside the observation station is expanded using a first-order Taylor series. The expanded measurement signal model of the calibration source outside the calibration location is as follows:

[0045]

[0046]

[0047] Based on the measured signal model of the external correction source after the correction position is unfolded, the difference between the actual position and the correction position of each observation station is obtained;

[0048]

[0049] Among them, Λ c Indicates w c The covariance matrix;

[0050] Obtain the difference covariance matrix between the actual and corrected positions of each observation station, and determine the covariance matrix of the corrected radiation source error model based on the difference covariance matrix.

[0051] Based on the further improvement of the above method, the difference covariance matrix of the actual position and the corrected position of each observation station is obtained through the following steps:

[0052] An objective function is constructed based on the difference between the actual and corrected positions of each observation station. The objective function is:

[0053]

[0054] Since the gradient of the objective function is 0 at its maximum, then:

[0055]

[0056] Simplifying, we get:

[0057]

[0058] Substitute (2) into (1) to calculate the difference covariance matrix Δs. o (Δs o ) T get:

[0059]

[0060] A further improvement to the above method, the step of determining the covariance matrix of the corrected radiation source error model based on the difference covariance matrix, includes:

[0061] The covariance matrix of the radiation source error model is:

[0062]

[0063] Among them, Λ w″ This represents the covariance matrix of the model for correcting radiation source errors;

[0064] The difference covariance matrix Δs o (Δs o ) T Substituting the covariance matrix into the model for correcting radiation source errors, we get:

[0065]

[0066] n = [0, 1, ..., N-1] T ;

[0067] Where N represents the number of sampling points of each observation station for the radiation source, Δ represents the sampling time interval, b represents the speed of light, trace() represents the trace of the matrix, F represents the basis function matrix of the Fourier transform, diag{} represents the diagonal matrix, and H represents the conjugate transpose.

[0068] Furthermore, d is The largest element on the main diagonal, for The e-th element, e = 1, 2...3M, 1 1×3M It is a vector of all 1s with a size of 1×3M.

[0069] The covariance matrix of the simplified corrected radiation source error model is:

[0070]

[0071] Where blkdiag{} represents a block diagonal matrix.

[0072] Based on a further improvement of the above method, the location cost function for the radiation source is:

[0073]

[0074] Where, λ max {R(u o )} is R(u o The largest eigenvalue;

[0075] R(u o Let be an M×M matrix, with its i-th row and q-th column as follows:

[0076]

[0077] q = 1, 2...M.

[0078] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0079] 1. Using the external calibration source measurement signals of each observation station, a calibration cost function is constructed based on Bayes' theorem. The calibration cost function is used to quickly correct the position of each observation station. Based on the corrected position of each observation station, the radiation source is directly located. At the same time, the residual error of each observation station after calibration is considered, thus realizing the accurate location of the radiation source.

[0080] 2. Based on the observation station measurement location model and the external correction source measurement signal model, the first posterior probability equation for each observation station is obtained based on Bayes' theorem. The estimated value of the external correction source signal is obtained using the first posterior probability equation, and then the estimated value of the external correction source signal is substituted into the first posterior probability equation to obtain the second posterior probability equation. The second posterior probability equation is simplified to obtain the third posterior probability equation for each observation station, and then the correction cost function for each observation station is constructed. The correction position of each observation station is determined based on the correction cost function, and the position of the radiation source is located using the correction position of each observation station, thereby improving the positioning accuracy of the radiation source.

[0081] 3. Using the calibration position of each observation station and the measurement signal model of the calibration source outside the observation station, determine the difference between the actual position and the calibration position of each observation station, obtain the covariance matrix of the difference between the actual position and the calibration position of each observation station, determine the covariance matrix of the calibration radiation source error model based on the difference covariance matrix, and then construct the cost function of the radiation source position to improve the positioning accuracy of the radiation source position.

[0082] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0083] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0084] Figure 1 This invention provides a schematic diagram of a scenario in which M observation stations locate radiation source signals.

[0085] Figure 2 A flowchart illustrating a method for directly locating a radiation source according to an embodiment of the present invention;

[0086] Figure 3 This diagram illustrates the application effect comparison of a direct location method for radiation sources provided in an embodiment of the present invention. Detailed Implementation

[0087] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0088] like Figure 1 As shown, in the positioning scenario, the position of the external calibration source is c. o The location of the radiation source is It includes M observation stations, whose measurement locations are s1, s2, s3…s M The actual locations of the M observation stations are as follows: Where, τ c1 This indicates the time it takes for the external correction source signal to propagate from the external correction source to the first observation station.

[0089] One specific embodiment of the present invention discloses a method for directly locating the position of a radiation source, such as... Figure 2 As shown, the direct positioning method includes:

[0090] Step S1: Construct the observation station measurement location model containing random location errors, the observation station radiation source measurement signal model containing random signal errors, and the observation station external correction source measurement signal model containing random signal errors;

[0091] Step S2: Based on the observation station measurement position model and the external correction source measurement signal model, construct the correction cost function based on Bayes' theorem; correct the measurement position of each observation station according to the external correction source measurement signal and the correction cost function to obtain the corrected position of each observation station.

[0092] Step S3: Perform a first-order Taylor series expansion on the radiation source measurement signal model of each observation station at the calibration position to obtain the expanded radiation source measurement signal model of the observation station; the expanded radiation source measurement signal model of the observation station includes the radiation source signal model at the calibration position and the calibration radiation source error model.

[0093] Step S4: Construct the location cost function of the radiation source based on the radiation source measurement signals of each observation station, the radiation source signal model at the corrected location, and the radiation source error model at the corrected location;

[0094] Step S5: Determine the maximum eigenvalue corresponding to each possible location of the radiation source based on the location cost function of the radiation source location, and take the possible location corresponding to the largest maximum eigenvalue as the location of the radiation source.

[0095] Specifically, such as Figure 2 As shown, the observation station measurement location model constructed in step S1 is as follows:

[0096] s = s o +Ψ;

[0097]

[0098] Where M represents the number of observation stations, and s, s o Ψ represents the measured position vector, actual position vector, and random position error vector of the observation station; s i , Ψ i Let represent the measured position vector, actual position vector, and random position error vector of the i-th observation station, respectively;

[0099] The random position error vector Ψ has zero mean, and the covariance matrix of Ψ is:

[0100]

[0101] Among them, Q β Let Ψ be the covariance matrix. I represents the variance of the random location error of the observation station. 3M Represents a 3M×3M matrix with diagonal elements being 1 and all other elements being 0;

[0102] The measured position vector, actual position vector, and random position error vector of the i-th observation station are:

[0103] s i =[x i ,y i ,z i ] T ;

[0104]

[0105] Where, x i y i z i Let X, Y, and Z represent the measured coordinates of the i-th observation station, respectively. These represent the actual X-axis coordinates, actual Y-axis coordinates, and actual Z-axis coordinates of the i-th observation station, respectively. Let X, Y, and Z represent the random error values ​​of the i-th observation station, respectively.

[0106] It is worth noting that s i , Ψ i Both are 3×1 matrices, with each row containing the X, Y, and Z coordinates; s, s o Both Ψ and Ψ are 3M×1 matrices.

[0107] Specifically, such as Figure 2 As shown, the observation station radiation source measurement signal model constructed in step S1 is as follows:

[0108] z = ηQr + w;

[0109]

[0110]

[0111] Among them, z i η represents the sampling point signal vector of the i-th observation station. i Let represent the unknown path loss factor of the i-th observation station, and ||η i ||=1;w i Let the random signal error vector of the i-th observation station satisfy the following conditions: zero-mean statistical independent circular Gaussian error. r represents the radiation source signal vector, and ||r|| = 1; Q i I represents the discrete Fourier transform vector of the i-th observation station;N This represents an N×N matrix with diagonal elements of 1 and all other elements of 0, where N is the number of sampling points for the radiation source signal at each observation station.

[0112] Specifically, T represents matrix transpose.

[0113] z i =[z i [0],z i [1],...,z i [N-1] T ;

[0114] w i =[w i [0],w i [1],...,w i [N-1] T ;

[0115] r = [r[0], r[1], ..., r[N-1]] T .

[0116] It is worth noting that, in Figure 1 In this scenario, when M observation stations sample the signal emitted by the radiation source, they need to sample synchronously, and each observation station samples N points to obtain N signals from the radiation source signal.

[0117] Specifically, the radiation source signal in this invention is r, and there is only one, taking into account the potential constraint that there is only one radiation source signal.

[0118] Specifically, diag{} represents a diagonal matrix.

[0119] It is understandable that z and w are both MN×1 matrices, representing the radiation source signals and random signal errors collected by M observation stations.

[0120] Specifically, the discrete Fourier transform vector of the i-th observation station is:

[0121]

[0122] n = [0, 1, ..., N-1] T ;

[0123]

[0124] Where j represents the imaginary unit, Δ represents the signal sampling interval of each observation station, and u o Indicates the actual location of the radiation source. This represents the actual location of the i-th observation station.

[0125] Specifically, b represents the speed of light, F represents the basis function matrix of the Fourier transform, n represents the sampling point index matrix, and τ i Let || represent the time it takes for the radiation source signal to travel to the i-th observation station, and || represent the distance between the two locations.

[0126] It is worth noting that the external calibration source measurement signal model constructed in step S1 has the same structure as the above-mentioned observation station radiation source measurement signal model. They are observation models of the external calibration source and radiation source of each observation station, respectively. The difference is that the radiation source location data in the observation station radiation source measurement signal model is unknown, while the external calibration source location data in the observation station external calibration source measurement signal model is known.

[0127] That is, such as Figure 2 As shown, the measurement signal model of the external correction source constructed in step S1 is as follows:

[0128] z c =η c Q c r c +w c ;

[0129]

[0130]

[0131] Among them, z ci η represents the sampling point signal vector of the i-th observation station and the external correction source. ci Let |η| represent the unknown path loss factor for the i-th observation station and the external correction source, and |η| represent the unknown path loss factor for the i-th observation station and the external correction source. ci ||=1;w ci Let the random signal error vector of the i-th observation station and the external correction source satisfy the following conditions: zero-mean statistically independent circular Gaussian error. r c Let |r| represent the externally corrected source signal vector, and |r| represent the externally corrected source signal vector. c || = 1; Q ci Represents the discrete Fourier transform vector of the i-th observation station and the external correction source; N represents a diagonal element that is 1 and the rest are 0. c ×N c The matrix, N c N represents the number of sampling points for radiation source signals at each observation station. c N represents the number of sampling points for each observation station and the external correction source signal. c It can be the same as or different from N; no specific restrictions are made here.

[0132] Specifically, T represents matrix transpose.

[0133] zci =[z ci [0],z ci [1],...,z ci [N-1] T ;

[0134] w ci =[w ci [0],w ci [1],...,w ci [N-1] T ;

[0135] r c =[r c [0],r c [1],...,r c [N-1] T .

[0136] It is worth noting that, in Figure 1 In this process, when M observation stations sample the signal emitted by the external correction source, they need to sample synchronously, and each observation station samples N. c The N points yield the signal from the radiation source. c One signal.

[0137] Specifically, the radiation source signal in this invention is r c There is only one.

[0138] Specifically, diag{} represents a diagonal matrix.

[0139] Understandably, z c w c All are MN c A 1×1 matrix represents the radiation source signals and random signal errors collected by M observation stations.

[0140] Specifically, the discrete Fourier transform vectors of the i-th observation station and the external correction source are:

[0141]

[0142] n c =[0,1,...,N c -1] T ;

[0143]

[0144] Where j represents the imaginary unit, Δ represents the signal sampling interval of each observation station and the external correction source, and c o Indicates the actual location of the external calibration source. This represents the actual location of the i-th observation station.

[0145] Specifically, b represents the speed of light, and F... c The basis function matrix represents the Fourier transform of the external correction source, n. c τ represents the sampling point index matrix of the external correction source. ci Let || represent the time it takes for the external correction source to propagate to the i-th observation station, and || represent the distance between the two locations.

[0146] Specifically, such as Figure 2 As shown, in step S2, the measurement position of each observation station is corrected based on the observation station measurement position model and the external correction source measurement signal of each observation station.

[0147] When acquiring the external calibration source measurement signals at each observation station, synchronous sampling is required. The number of sampling points can be the same as or different from the number of sampling points at the radiation source. The measurement position of each observation station is the position obtained by measuring its own location.

[0148] Preferably, the step of constructing a correction cost function based on Bayes' theorem, according to the observation station measurement location model and the external correction source measurement signal model, includes:

[0149] Based on the observation station measurement location model and the observation station external correction source measurement signal model, the first posterior probability equation of each observation station is obtained based on Bayes' theorem;

[0150] The first posterior probability equation of each observation station is differentiated by the first order of the external correction source signal, and the derivative is set to zero to obtain the estimated value of the external correction source signal.

[0151] The estimated value of the externally corrected source signal is substituted into the first posterior probability equation of each observation station for derivation, and the derived second posterior probability equation of each observation station is obtained.

[0152] The second posterior probability equations for each observation station are simplified to obtain the third posterior probability equations for each observation station; based on the third posterior probability equations for each observation station, the correction cost function is obtained.

[0153] Specifically, based on the aforementioned observation station measurement location model and observation station external correction source measurement signal model, the first posterior probability equation for each observation station, obtained based on Bayes' theorem, is as follows:

[0154]

[0155] in, P(z) represents the posterior probability of each observation station. c |s o ) represents the given location s of each observation station. o Measured z c The probability, P(s) o) represents the prior probability of each observation station; This represents the variance of the random signal error between the i-th observation station and the external correction source. and same.

[0156] make External calibration source signal r c Taking the first derivative and setting it to zero, we get r. c The maximum likelihood estimate, i.e., the estimate of the externally corrected source signal. for:

[0157]

[0158] The estimated value of the externally corrected source signal Substituting into the first posterior probability equation, the second posterior probability equation is obtained as follows:

[0159]

[0160] Among them, R c (s o Let be a matrix, and let the i-th row and a-th column be:

[0161]

[0162] The simplified second posterior probability equation is the third posterior probability equation, that is:

[0163]

[0164] Where, λ max {R c (s o )} is R c (s o The largest eigenvalue of ).

[0165] Based on the third posterior probability equation, the corrected cost function is:

[0166]

[0167] Specifically, such as Figure 2 As shown, in step S2, preferably, the step of correcting the measurement position of each observation station based on the external correction source measurement signal and correction cost function of each observation station to obtain the corrected position of each observation station includes:

[0168] Substitute the external calibration source measurement signals of each observation station into the calibration cost function to obtain the updated calibration cost function;

[0169] The possible combinations of locations for each observation station are determined based on their measurement locations.

[0170] Substitute each possible location combination of each observation station into the correction cost function to obtain the correction cost value corresponding to each possible location combination. Select the possible location combination corresponding to the largest correction cost value as the correction location of each observation station.

[0171] Specifically, the measurement signals from the external correction sources of each observation station are substituted into the correction cost function, and the correction cost function is updated, that is, r in the correction cost function is updated. c Replace with the external calibration source measurement signals of each observation station.

[0172] It is worth noting that the possible location combinations of each observation station can be reasonably determined based on the positioning accuracy; that is, the higher the accuracy, the more possible location combinations can be obtained. After substituting each possible location combination into the correction cost function, the corresponding correction cost value is obtained. The possible location combination corresponding to the maximum correction cost value is taken as the corrected position of each observation station, i.e., the corrected position of each observation station.

[0173] Specifically, such as Figure 2 As shown, in step S3, the radiation source measurement signal model of each observation station is expanded using a first-order Taylor series at the calibration position of each observation station. The expanded radiation source measurement signal model of the observation station is as follows:

[0174]

[0175] in, Indicates the correction position of each observation station, Δs o This represents the difference between the actual and corrected positions of each observation station, where w represents the random signal error of each observation station. denoted as the corrected position radiation source signal model, and w″ denotes the corrected radiation source error model.

[0176] Preferably, such as Figure 2 As shown, in step S4, the step of constructing the location cost function for the radiation source based on the radiation source measurement signals of each observation station, the corrected location radiation source signal model, and the corrected radiation source error model includes:

[0177] Calculate the covariance matrix of the corrected radiation source error model;

[0178] Based on the covariance matrix of the corrected radiation source error model, the radiation source measurement signals of each observation station, and the radiation source signal model at the corrected location, a weighted least squares solution equation for the radiation source location is constructed.

[0179] The estimated value of the radiation source signal is obtained by solving the weighted least squares equation based on the location of the radiation source. Substituting the estimated value of the radiation source signal into the weighted least squares equation for the location of the radiation source, the location cost function of the radiation source is obtained.

[0180] Preferably, calculating the covariance matrix of the corrected radiation source error model includes:

[0181] At the calibration locations of each observation station, the measurement signal model of the calibration source outside the observation station is expanded using a first-order Taylor series. The expanded measurement signal model of the calibration source outside the calibration location is as follows:

[0182]

[0183] Based on the expanded external correction source measurement signal model, the difference Δs between the actual position and the corrected position of each observation station is obtained. o ;

[0184]

[0185] Among them, Λ c Indicates w c The covariance matrix;

[0186] Obtain the difference covariance matrix between the actual and corrected positions of each observation station, and determine the covariance matrix of the corrected radiation source error model based on the difference covariance matrix.

[0187] Preferably, the difference covariance matrix between the actual and corrected positions of each observation station is obtained through the following steps:

[0188] An objective function is constructed based on the difference between the actual and corrected positions of each observation station. The objective function is:

[0189]

[0190] Since the gradient of the objective function is 0 at its maximum, then:

[0191]

[0192] Simplifying, we get:

[0193]

[0194] Substitute (2) into (1) to calculate the difference covariance matrix Δs. o (Δs o ) T get:

[0195]

[0196] Preferably, determining the covariance matrix of the corrected radiation source error model based on the difference covariance matrix includes: the covariance matrix of the corrected radiation source error model is:

[0197]

[0198] Among them, Λ w″ This represents the covariance matrix of the model for correcting radiation source errors;

[0199] The difference covariance matrix Δs o (Δs o ) T Substituting the covariance matrix into the model for correcting radiation source errors, we get:

[0200]

[0201] n = [0, 1, ..., N-1] T ;

[0202] Here, trace() represents the trace of the matrix, and conjugate transpose represents the transpose of the matrix.

[0203] Furthermore, d is The largest element on the main diagonal, for The e-th element, e = 1, 2...3M, 1 1×3M It is a vector of all 1s with a size of 1×3M.

[0204] The covariance matrix of the simplified corrected radiation source error model is:

[0205]

[0206] Where blkdiag{} represents a block diagonal matrix.

[0207] Specifically, based on the covariance matrix of the calibrated radiation source error model, the radiation source measurement signals from each observation station, and the calibrated location radiation source signal model, a weighted least squares solution equation for the radiation source location is constructed. The weighted least squares solution equation for the radiation source location is as follows:

[0208]

[0209] Where z represents the radiation source measurement signal vector of each observation station.

[0210] Specifically, argmin{} represents the location of the radiation source that minimizes {}, and this location is used as the positioning location of the radiation source.

[0211] Specifically, the estimated value of the radiation source signal is obtained by solving the weighted least squares equation based on the location of the radiation source, including:

[0212] Get Taking the first derivative of the radiation source signal r and setting it to zero, we can calculate the estimated value of the radiation source signal, i.e.:

[0213]

[0214] Specifically, the estimated value of the radiation source signal is substituted into the weighted least squares solution equation for the radiation source location.

[0215] The transfer equation for the location cost function is obtained, namely:

[0216]

[0217] Among them, R(u o Let be an M×M matrix, and the element in the i-th row and q-th column of this matrix is:

[0218]

[0219] Since [η1,...η i ,...,η M [Unknown] is replaced with its maximum likelihood estimate, which corresponds to R(u) o The eigenvector with the largest eigenvalue yields the location cost function for the radiation source. The location cost function for the radiation source is:

[0220]

[0221] Where, λ max {R(u o )} is R(u o The largest eigenvalue;

[0222] R(u o Let be an M×M matrix, with its i-th row and q-th column as follows:

[0223]

[0224] q = 1, 2...M.

[0225] Specifically, the location cost function for the radiation source location only includes the location of the radiation source as a variable.

[0226] Specifically, such as Figure 2 As shown, in step S5, each possible location of the pre-determined radiation source is substituted into the constructed radiation source location cost function to obtain the maximum eigenvalue corresponding to each possible location. The maximum eigenvalues ​​corresponding to each possible location are compared, and the possible location corresponding to the largest maximum eigenvalue is taken as the location of the radiation source.

[0227] It is worth noting that in scenarios where high positioning accuracy is required, a hierarchical grid search method can be used. That is, in the area near the radiation source location determined by the previous level grid search method, the grid search is repeated with smaller grid steps until the grid step reaches the desired search accuracy.

[0228] The following specific embodiment demonstrates the technical effect of a direct location method for radiation sources provided by this invention.

[0229] Consider a scenario involving one stationary radiation source and four stationary observation stations. The radiation source is located at u... o =[-1,70,10] T (km). The location of the observation station is and The location of the external calibration source is c o =[10,90,10] T The radiation source signal waveform modulation style is BPSK, bandwidth is 25kHz, carrier frequency is set to 303MHz, sampling frequency is 100kHz, and 2000 signal data points are collected at each station for radiation source localization.

[0230] For the sake of simplicity, the direct location method for a radiation source provided in this embodiment of the invention will be referred to as DPD. 2CU For comparison, the direct positioning algorithm that ignores site errors is denoted as DPD. NCNU Other direct positioning algorithms that take into account site errors are denoted as DPD. NCU and DPD 1CU .

[0231] like Figure 3 As shown, the DPD calculated based on 100 independent samples is presented as the signal-to-noise ratio (SNR) of the received signal at observation station 1 changes from -10dB to 15dB. 2CU DPD 1CU DPD NCU and DPD NCNU The root mean square error. In this embodiment, for each signal-to-noise ratio scenario, it is assumed that the covariance matrix of the site error is equal to the covariance matrix of the measurement error of the distance difference between observation station 1 and observation station 2 under that signal-to-noise ratio condition, where the distance difference is defined as the product of the time difference and the wave speed.

[0232] Depend on Figure 3 It can be seen that under various signal-to-noise ratio scenarios, DPD 2CU The root mean square positioning error is always lower than that of DPD. 1CU DPD NCU and DPD NCNU This demonstrates the effectiveness of the direct location method for radiation sources provided in this embodiment of the invention.

[0233] Compared with existing technologies, the direct location method for radiation sources provided in this invention utilizes the external calibration source measurement signals from each observation station to construct a calibration cost function based on Bayes' theorem. This calibration cost function is used to quickly correct the positions of each observation station, and the radiation source is directly located based on the corrected positions of each observation station. Simultaneously, the residual errors of the corrected observation station sites are considered, achieving precise location of the radiation source. Furthermore, based on the observation station measurement position model and the external calibration source measurement signal model, a first posterior probability equation for each observation station is obtained using Bayes' theorem. The estimated value of the external calibration source signal is obtained using the first posterior probability equation, and then substituted into the first posterior probability equation... The process yields the second posterior probability equation; simplifies the second posterior probability equation to obtain the third posterior probability equation for each observation station, and then constructs the correction cost function for each observation station; based on the correction cost function, the correction position of each observation station is determined, and the location of the radiation source is located using the correction position of each observation station, improving the positioning accuracy of the radiation source; furthermore, the difference between the actual position and the correction position of each observation station is determined using the correction position of each observation station and the external correction source measurement signal model, and the covariance matrix of the difference between the actual position and the correction position of each observation station is obtained. Based on the difference covariance matrix, the covariance matrix of the correction radiation source error model is determined, and then the cost function for the radiation source position is constructed, improving the positioning accuracy of the radiation source position.

[0234] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0235] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for directly locating the position of a radiation source, characterized in that, The direct positioning method includes: Construct a station measurement location model that includes random location errors, a station radiation source measurement signal model that includes random signal errors, and a station external correction source measurement signal model that includes random signal errors; Based on the observation station measurement location model and the external correction source measurement signal model, a correction cost function is constructed based on Bayes' theorem. The measurement location of each observation station is corrected according to the external correction source measurement signal and the correction cost function to obtain the corrected location of each observation station. At the calibration position of each observation station, the radiation source measurement signal model of the observation station is expanded by a first-order Taylor series to obtain the expanded radiation source measurement signal model of the observation station; the expanded radiation source measurement signal model of the observation station includes the radiation source signal model at the calibration position and the radiation source error model at the calibration position. The location cost function of the radiation source is constructed based on the radiation source measurement signals of each observation station, the radiation source signal model at the corrected location, and the radiation source error model at the corrected location. The maximum eigenvalue corresponding to each possible location of the radiation source is determined based on the location cost function of the radiation source location, and the possible location corresponding to the largest maximum eigenvalue is taken as the location of the radiation source.

2. The direct positioning method according to claim 1, characterized in that, The step involves constructing a correction cost function based on Bayes' theorem, using the observation station's measurement location model and the external correction source measurement signal model. This includes: Based on the observation station measurement location model and the observation station external correction source measurement signal model, the first posterior probability equation of each observation station is obtained based on Bayes' theorem; The first posterior probability equation of each observation station is differentiated by the first order of the external correction source signal, and the derivative is set to zero to obtain the estimated value of the external correction source signal. The estimated value of the externally corrected source signal is substituted into the first posterior probability equation of each observation station for derivation, and the derived second posterior probability equation of each observation station is obtained. The second posterior probability equations for each observation station are simplified to obtain the third posterior probability equations for each observation station; based on the third posterior probability equations for each observation station, the correction cost function is obtained.

3. The direct positioning method according to claim 2, characterized in that, The first posterior probability equation for each observation station is: in, P(z) represents the posterior probability of each observation station. c |s o ) represents the given location s of each observation station. o Measured z c The probability, P(s) o Let z represent the prior probability of each observation station, M represent the number of observation stations, i represent any single observation station, and z represent the probability of each observation station. ci η represents the measurement signal of the external correction source at the i-th observation station. ci Let Q represent the unknown path loss factor for the i-th observation station and the external correction source. ci Let r represent the discrete Fourier transform vector of the i-th observation station and the external correction source. c Indicates the external correction source signal. This represents the variance of the random signal error between the i-th observation station and the external correction source. This represents the variance of the random location error at each observation station. s represents the actual location of the i-th observation station. i This indicates the measurement location of the i-th observation station; Estimated value of externally corrected source signal for: The second posterior probability equation for each observation station is: Among them, R c (s o Let be a matrix, and let the i-th row and a-th column be: The third posterior probability equation for each observation station is: Where, λ max {R c (s o )} is R c (s o The largest eigenvalue; The correction cost function is:

4. The direct positioning method according to claim 2, characterized in that, The process of correcting the measurement positions of each observation station based on the external correction source measurement signals and correction cost functions to obtain the corrected positions of each observation station includes: Substitute the external calibration source measurement signals of each observation station into the calibration cost function to obtain the updated calibration cost function; The possible combinations of locations for each observation station are determined based on their measurement locations. Substitute each possible location combination of each observation station into the correction cost function to obtain the correction cost value corresponding to each possible location combination. Select the possible location combination corresponding to the largest correction cost value as the correction location of each observation station.

5. The direct positioning method according to claim 1, characterized in that, The radiation source measurement signal model of the expanded observation station is as follows: in, Indicates the correction position of each observation station, Δs o This represents the difference between the actual and corrected positions of each observation station, where w represents the random signal error of each observation station. denoted as the corrected position radiation source signal model, and w″ denotes the corrected radiation source error model.

6. The direct positioning method according to claim 5, characterized in that, The location cost function for constructing the radiation source location based on the radiation source measurement signals of each observation station, the corrected location radiation source signal model, and the corrected radiation source error model includes: Calculate the covariance matrix of the corrected radiation source error model; Based on the covariance matrix of the corrected radiation source error model, the radiation source measurement signals of each observation station, and the radiation source signal model at the corrected location, a weighted least squares solution equation for the radiation source location is constructed. The estimated value of the radiation source signal is obtained by solving the weighted least squares equation based on the location of the radiation source. Substituting the estimated value of the radiation source signal into the weighted least squares equation for the location of the radiation source, the location cost function of the radiation source is obtained.

7. The direct positioning method according to claim 6, characterized in that, Calculate the covariance matrix of the corrected radiation source error model, including: At the calibration locations of each observation station, the measurement signal model of the calibration source outside the observation station is expanded using a first-order Taylor series. The expanded measurement signal model of the calibration source outside the calibration location is as follows: Based on the measured signal model of the external correction source after the correction position is unfolded, the difference between the actual position and the correction position of each observation station is obtained; Among them, Λ c Indicates w c The covariance matrix; Obtain the difference covariance matrix between the actual and corrected positions of each observation station, and determine the covariance matrix of the corrected radiation source error model based on the difference covariance matrix.

8. The direct positioning method according to claim 7, characterized in that, The covariance matrix of the difference between the actual and corrected positions of each observation station is obtained through the following steps: An objective function is constructed based on the difference between the actual and corrected positions of each observation station. The objective function is: Since the gradient of the objective function is 0 at its maximum, then: Simplifying, we get: Substitute (2) into (1) to calculate the difference covariance matrix Δs. o (Δs o ) T get:

9. The direct positioning method according to claim 8, characterized in that, The step of determining the covariance matrix of the corrected radiation source error model based on the difference covariance matrix includes: The covariance matrix of the radiation source error model is: Among them, Λ w″ This represents the covariance matrix of the model for correcting radiation source errors; The difference covariance matrix Δs o (Δs o ) T Substituting the covariance matrix into the model for correcting radiation source errors, we get: Where N represents the number of sampling points of each observation station for the radiation source, Δ represents the sampling time interval, b represents the speed of light, trace() represents the trace of the matrix, F represents the basis function matrix of the Fourier transform, diag{} represents the diagonal matrix, and H represents the conjugate transpose. Furthermore, d is The largest element on the main diagonal, for The e-th element, e = 1, 2...3M, 1 1×3M It is a vector of all 1s with a size of 1×3M. The covariance matrix of the simplified corrected radiation source error model is: Where blkdiag{} represents a block diagonal matrix.

10. The direct positioning method according to claim 9, characterized in that, The location cost function for the radiation source is: Where, λ max {R(u o )} is R(u o The largest eigenvalue; R(u o Let be an M×M matrix, with its i-th row and q-th column as follows:

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