Direct positioning method under condition of station address error

Abstract

The invention relates to a direct positioning method in the presence of a site error, belongs to the technical field of radiation source positioning, and solves the problems of high positioning delay and poor precision of a radiation source position in the prior art. The direct positioning method comprises the following steps: based on an observation station measurement position model, performing Taylor series first-order expansion on an observation station measurement signal model at the measurement position of each observation station to obtain an expanded observation station measurement signal model; constructing a cost function of a radiation source position according to the real-time error model, the measurement signal of each observation station and the real-time position signal model; and according to each possible position of the radiation source, determining the maximum characteristic value corresponding to each possible position in the cost function of the radiation source position by adopting a grid search method, and taking the possible position corresponding to the maximum characteristic value as the positioning position of the radiation source. And rapid and accurate positioning of the position of the radiation source is realized.

Description

Technical Field

[0001] The present invention relates to the field of radiation source positioning technology, and in particular to a direct positioning method under the condition of site error. Background Art

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

[0003] The traditional two-step positioning method ignores the potential constraint that the extracted signal parameters correspond to a radiation source, resulting in suboptimal positioning. The direct positioning method can effectively utilize this potential constraint and improve the positioning of the radiation source.

[0004] In the prior art, the prior information of satellite orbits is used to construct a joint cost function of satellite position velocity and radiation source position, and the satellite position velocity and radiation source position are estimated simultaneously based on an alternating iterative optimization algorithm. This algorithm estimates both the satellite position velocity and the radiation source position as deterministic position quantities, and the computational complexity is very high. However, for some scenarios that require rapid positioning of radiation sources, the use of this algorithm will result in high positioning delays, making it difficult to meet timeliness requirements, resulting in slow positioning speed and poor positioning accuracy. Summary of the invention

[0005] In view of the above analysis, an embodiment of the present invention aims to provide a direct positioning method under the condition of site error, so as to solve the problems of high positioning delay and poor accuracy of the radiation source position in the prior art.

[0006] An embodiment of the present invention provides a direct positioning method under the condition of site error, the direct positioning method comprising:

[0007] Constructing an observation station measurement position model including random position errors and an observation station measurement signal model including random signal errors;

[0008] Based on the observation station measurement position model, performing a Taylor series first-order expansion on the observation station measurement signal model at the measurement position of each observation station to obtain an expanded observation station measurement signal model; the expanded observation station measurement signal model includes a real-time position signal model and a real-time error model;

[0009] Constructing a cost function of the radiation source position according to the real-time error model, the measurement signals of each observation station and the real-time position signal model;

[0010] According to each possible position of the radiation source, a grid search method is used to determine the maximum eigenvalue corresponding to each possible position in the cost function of the radiation source position, and the possible position corresponding to the largest maximum eigenvalue is used as the positioning position of the radiation source.

[0011] Based on the further improvement of the above method, the observation station measurement position model is:

[0012] s=s o +Ψ;

[0013]

[0014] Where M represents the number of observation stations, 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 Respectively represent the measured position vector, actual position vector, and random position error vector of the i-th observation station;

[0015] The random position error vector Ψ has zero mean, and the covariance matrix of Ψ is:

[0016]

[0017] Among them, Q β represents the covariance matrix of Ψ, represents the variance of the random position error of the observation station, I 3M Represents a 3M×3M matrix with diagonal elements of 1 and the remaining elements of 0;

[0018] The measured position vector, actual position vector, and random position error vector of the i-th observation station are:

[0019] s i =[x i ,y i ,z i ] T ;

[0020]

[0021] Among them, x i ,y i 、z i They represent the X-axis measurement coordinate, Y-axis measurement coordinate, and Z-axis measurement coordinate of the i-th observation station respectively; They represent the actual X-axis coordinate, Y-axis coordinate, and Z-axis coordinate of the i-th observation station respectively; They represent the X-axis random error, Y-axis random error, and Z-axis random error of the i-th observation station respectively.

[0022] Based on the further improvement of the above method, the observation station measurement signal model is:

[0023] z=ηQr+w;

[0024]

[0025]

[0026] Among them, z i represents the sampling point signal vector of the i-th observation station, η i represents the unknown path loss factor of the i-th observation station, and ||η i ||=1;w i represents the random signal error vector of the i-th observation station; 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 represents an N×N matrix with diagonal elements of 1 and other elements of 0, N is the number of sampling points of the radiation source signal of each observation station, and T represents the matrix transpose;

[0027] z i =[z i [0],z i [1],...,z i [N-1]] T ;

[0028] w i =[w i [0],w i [1],...,w i [N-1]] T ;

[0029] r=[r[0],r[1],...,r[N-1]] T .

[0030] Based on the further improvement of the above method, the discrete Fourier transform vector of the i-th observation station is:

[0031]

[0032]

[0033] n=[0,1,...,N-1] T ;

[0034]

[0035] Where j represents the imaginary unit, Δ represents the signal sampling interval of each observation station, and uo represents the actual position of the radiation source, c represents the speed of light, represents the actual position of the i-th observation station, F represents the basis function matrix of Fourier transform, n represents the sampling point number matrix, τ i represents the time it takes for the radiation source signal to propagate to the i-th observation station, and || || represents the distance between the two locations.

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

[0037]

[0038]

[0039] in, represents the real-time position signal model, w′ represents the real-time error model, diag{} represents a diagonal matrix, and blkdiag{} represents a block diagonal matrix.

[0040] Based on the further improvement of the above method, the cost function of the radiation source position is constructed according to the real-time error model, the measurement signals of each observation station and the real-time position signal model, including:

[0041] Calculating a covariance matrix of the real-time error model;

[0042] Constructing a weighted least square solution equation for the radiation source position based on the covariance matrix of the real-time error model, the measurement signals of each observation station and the real-time position signal model;

[0043] The estimated value of the radiation source signal is obtained by solving the equation based on the weighted least squares of the radiation source position;

[0044] Substituting the estimated value of the radiation source signal into the weighted least squares solution equation of the radiation source position, a cost function of the radiation source position is obtained.

[0045] Based on the further improvement of the above method, the covariance matrix of the real-time error model is:

[0046]

[0047] Among them, Λ w′ represents the covariance matrix of the real-time error model, I M represents an M×M matrix with diagonal elements set to 1 and the remaining elements set to 0; They represent the variance of the random signal errors of the 1st observation station, the i-th observation station, and the M-th observation station respectively.

[0048] Based on the further improvement of the above method, the weighted least square solution equation of the radiation source position is:

[0049]

[0050] Wherein, z represents the measurement signal vector of each observation station.

[0051] Based on the further improvement of the above method, the weighted least square solution equation based on the radiation source position obtains the estimated value of the radiation source signal, including:

[0052] The weighted least square solution equation of the radiation source position is used to perform a first-order derivative on the radiation source signal, and the derivative is set to zero to obtain an estimated value of the radiation source signal:

[0053]

[0054] in, represents an estimated value of the radiation source signal.

[0055] Based on the further improvement of the above method, the estimated value of the radiation source signal is substituted into the weighted least square solution equation of the radiation source position to obtain the cost function of the radiation source position, including:

[0056] Substituting the estimated value of the radiation source signal into the weighted least squares solution equation of the radiation source position, the transfer equation of the cost function is obtained. The transfer equation of the cost function is:

[0057]

[0058] Among them, R(u o ) is an M×M matrix, and the element in the i-th row and q-th column of the matrix is:

[0059]

[0060] Since [η1,...η i ,...,η M ] is unknown, replace it with its maximum likelihood estimate, which corresponds to R(u o )The eigenvector of the maximum eigenvalue is obtained, and the cost function of the radiation source position is obtained. The cost function of the radiation source position is:

[0061]

[0062] Among them, λ max {R(u o )} represents R(u o )’s maximum eigenvalue.

[0063] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0064] 1. By using the measurement position of each observation station, the uncertainty of the random position error of each observation station is taken into account, and the cost function of the constructed radiation source position is only a function of the radiation source position, with low computational complexity, and the radiation source can be quickly and accurately located to obtain the location of the radiation source;

[0065] 2. The measurement positions of each observation station are used to perform the first-order Taylor series expansion of the observation station measurement signal model to construct the real-time position signal model and real-time error model. The uncertainty of the site of each observation station is taken into account to further improve the positioning accuracy of the radiation source position;

[0066] 3. The grid search method is used to calculate the maximum eigenvalue of the cost function of the radiation source position corresponding to each possible position of the radiation source, which can improve the positioning efficiency and quickly locate the position of the radiation source.

[0067] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.

[0069] Figure 1 A schematic diagram of a scenario in which M observation stations locate radiation source signals is provided for an embodiment of the present invention;

[0070] Figure 2 A schematic flow chart of a direct positioning method under the condition of site error provided by an embodiment of the present invention;

[0071] Figure 3 A schematic diagram for comparing the application effects of a direct positioning method under the condition of site error provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0072] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a 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 used to limit the scope of the present invention.

[0073] like Figure 1 As shown, the positioning scenario includes M observation stations, and the measurement positions of the M observation stations are s1, s2, s3, ..., s M , the actual locations of the M observation stations are The actual position of the radiation source is u o .

[0074] A specific embodiment of the present invention discloses a direct positioning method under the condition of station location error, such as Figure 2 As shown, the direct positioning method includes:

[0075] Step S1: constructing an observation station measurement position model including random position errors and an observation station measurement signal model including random signal errors;

[0076] Step S2: Based on the observation station measurement position model, the observation station measurement signal model is subjected to Taylor series first-order expansion at the measurement position of each observation station to obtain an expanded observation station measurement signal model; the expanded observation station measurement signal model includes a real-time position signal model and a real-time error model;

[0077] Step S3: constructing a cost function of the radiation source position according to the real-time error model, the measurement signals of each observation station and the real-time position signal model;

[0078] Step S4: According to each possible position of the radiation source, a grid search method is used to determine the maximum eigenvalue corresponding to each possible position in the cost function of the radiation source position, and the possible position corresponding to the largest maximum eigenvalue is used as the positioning position of the radiation source.

[0079] Specifically, Figure 2 As shown, in step S1, a station measurement position model including random position errors is constructed, combined with Figure 1 , the constructed observation station measurement location model is:

[0080] s=s o +Ψ;

[0081]

[0082] Where M represents the number of observation stations, 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 Respectively represent the measured position vector, actual position vector, and random position error vector of the i-th observation station;

[0083] The random position error vector Ψ has zero mean, and the covariance matrix of Ψ is:

[0084]

[0085] Among them, Q β represents the covariance matrix of Ψ, represents the variance of the random position error of the observation station, I 3M Represents a 3M×3M matrix with diagonal elements of 1 and the remaining elements of 0;

[0086] The measured position vector, actual position vector, and random position error vector of the i-th observation station are:

[0087] s i =[x i ,y i ,z i ] T ;

[0088]

[0089] Among them, x i ,y i 、z i They represent the X-axis measurement coordinate, Y-axis measurement coordinate, and Z-axis measurement coordinate of the i-th observation station respectively; They represent the actual X-axis coordinate, Y-axis coordinate, and Z-axis coordinate of the i-th observation station respectively; They represent the X-axis random error, Y-axis random error, and Z-axis random error of the i-th observation station respectively.

[0090] It is worth noting that s i , Ψ i are all 3×1 matrices, and each row of the matrix contains the X-axis, Y-axis, and Z-axis coordinates; s, s o , Ψ are both 3M×1 matrices.

[0091] Specifically, Figure 2 As shown, an observation station measurement signal model containing random signal errors is constructed. The observation station measurement signal model is:

[0092] z=ηQr+w;

[0093]

[0094] Among them, z i represents the sampling point signal vector of the i-th observation station, η i represents the unknown path loss factor of the i-th observation station, and ||η i ||=1;w i represents the random signal error vector of the i-th observation station; 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; Nrepresents an N×N matrix with diagonal elements of 1 and other elements of 0, N is the number of sampling points of the radiation source signal of each observation station, and T represents the matrix transpose;

[0095] z i =[z i [0],z i [1],...,z i [N-1]] T ;

[0096] w i =[w i [0],w i [1],...,w i [N-1]] T ;

[0097] r=[r[0],r[1],...,r[N-1]] T .

[0098] It is worth noting that in Figure 1 In the method, when the M observation stations sample the signals emitted by the radiation source, they need to sample synchronously, and each observation station samples N points to obtain N signals of the radiation source signal.

[0099] Specifically, the radiation source signal in the present invention is r, which is only one, taking into account the potential constraint that there is only one radiation source signal.

[0100] Specifically, diag{} represents a diagonal matrix.

[0101] It can be understood that z and w are both MN×1 matrices, representing the radiation source signals and random signal errors collected by M observation stations.

[0102] Preferably, the discrete Fourier transform vector of the i-th observation station is:

[0103]

[0104] n=[0,1,...,N-1] T ;

[0105]

[0106] Where j represents the imaginary unit, Δ represents the signal sampling interval of each observation station, and u o represents the actual position of the radiation source, c represents the speed of light, represents the actual position of the i-th observation station, F represents the basis function matrix of Fourier transform, n represents the sampling point number matrix, τ i represents the time it takes for the radiation source signal to propagate to the i-th observation station, and || || represents the distance between the two locations.

[0107] Specifically, Figure 2 As shown, in step S2, considering the influence of the uncertainty of the observation station location, the observation station measurement signal model is expanded by Taylor series at the measurement location of each observation station. From the observation station measurement location model, it can be obtained that Ψ = s o -s, and the expanded observation station measurement signal model is obtained as follows:

[0108]

[0109] Specifically, the expanded observation station measurement signal model is:

[0110]

[0111] in, represents the real-time position signal model, w′ represents the real-time error model, diag{} represents a diagonal matrix, and blkdiag{} represents a block diagonal matrix.

[0112] Specifically, Figure 2 As shown, in step S3, preferably, the cost function of the radiation source position is constructed according to the real-time error model, the measurement signals of each observation station and the real-time position signal model, including:

[0113] Calculating a covariance matrix of the real-time error model;

[0114] Constructing a weighted least square solution equation for the radiation source position based on the covariance matrix of the real-time error model, the measurement signals of each observation station and the real-time position signal model;

[0115] The estimated value of the radiation source signal is obtained by solving the equation based on the weighted least squares of the radiation source position;

[0116] Substituting the estimated value of the radiation source signal into the weighted least squares solution equation of the radiation source position, a cost function of the radiation source position is obtained.

[0117] Specifically, the real-time error model is w′, which is The real-time position signal model is

[0118] Calculating the covariance matrix of the real-time error model yields:

[0119]

[0120] Among them, Λ w′ represents the covariance matrix of the real-time error model, I M represents an M×M matrix with diagonal elements set to 1 and the remaining elements set to 0; They represent the variance of the random signal errors of the 1st observation station, the i-th observation station, and the M-th observation station respectively.

[0121] It is worth noting that the variance of the random signal error at each observation station is is the known observation station parameter, and the variance of the random position error of the observation station Also known parameters of the observation station.

[0122] Specifically, a weighted least square solution equation for the radiation source position is constructed according to the covariance matrix of the real-time error model, the measurement signals of each observation station and the real-time position signal model.

[0123] Specifically, the weighted least squares solution equation for the radiation source position is:

[0124]

[0125] Wherein, z represents the measurement signal vector of each observation station.

[0126] Specifically, argmin{} represents the radiation source position when {} takes the minimum value, and the radiation source position is used as the positioning position of the radiation source.

[0127] Preferably, the weighted least squares solution equation based on the radiation source position to obtain an estimated value of the radiation source signal includes:

[0128] The weighted least square solution equation of the radiation source position is used to perform a first-order derivative on the radiation source signal, and the derivative is set to zero to obtain an estimated value of the radiation source signal:

[0129]

[0130] in, represents an estimated value of the radiation source signal.

[0131] Specifically, yes By taking the first-order derivative and setting the derivative to zero, we can get an estimate of the radiation source signal.

[0132] Preferably, substituting the estimated value of the radiation source signal into the weighted least squares solution equation of the radiation source position to obtain the cost function of the radiation source position includes:

[0133] Substituting the estimated value of the radiation source signal into the weighted least squares solution equation of the radiation source position, the transfer equation of the cost function is obtained. The transfer equation of the cost function is:

[0134]

[0135] Among them, R(u o) is an M×M matrix, and the element in the i-th row and q-th column of the matrix is:

[0136]

[0137] Since [η1,...η i ,...,η M ] is unknown, replace it with its maximum likelihood estimate, which corresponds to R(u o )The eigenvector of the maximum eigenvalue is obtained, and the cost function of the radiation source position is obtained. The cost function of the radiation source position is:

[0138]

[0139] Among them, λ max {R(u o )} represents R(u o )’s maximum eigenvalue.

[0140] Specifically, the cost function of the radiation source position only includes the position of the radiation source.

[0141] Specifically, Figure 2 As shown, in step S4, each possible position of the predetermined radiation source is substituted into the cost function of the constructed radiation source, and the maximum eigenvalue corresponding to each possible position can be obtained. The maximum eigenvalue corresponding to each possible position is compared, and the possible position corresponding to the largest maximum eigenvalue is used as the positioning position of the radiation source.

[0142] It is worth mentioning that in scenarios with high requirements for positioning accuracy, a hierarchical grid search method can be used, that is, in the area near the estimated radiation source position determined by the previous level grid search method, a grid search is repeated with a smaller grid step until the grid step reaches the desired search accuracy.

[0143] The following is a specific example to demonstrate the technical effect of a direct positioning method under the condition of site error provided by an embodiment of the present invention.

[0144] Consider a scenario consisting of a stationary radiation source and four stationary observation stations. o =[-1,70,10] T (km). The location of the observation station is

[0145] and The modulation style of the radiation source signal waveform is BPSK, and the bandwidth is 25kHz. The carrier frequency is set to 303MHz, and the sampling frequency is 100kHz. Each station collects 2000 points of signal data for radiation source positioning. The direct positioning method provided in the embodiment of the present invention is denoted as DPDNCU For comparison, the direct positioning algorithm that ignores the site error is denoted as DPD NCNU , the positioning error Cramer-Lao bound CRLB under each signal-to-noise ratio scenario.

[0146] like Figure 3 As shown in the figure, the DPD calculated based on 100 independent samples when the signal-to-noise ratio of the received signal at observation station 1 changes from -10dB to 15dB is given. NCU and DPD NCNU The root mean square error.

[0147] Depend on Figure 3 It can be seen that when the signal-to-noise ratio gradually increases, DPD NCU The root mean square positioning error tends to CRLB. In addition, Figure 3 The results show that DPD NCU The RMS positioning error is always lower than DPD NCNU , which proves that the direct positioning method provided by the embodiment of the present invention has better positioning accuracy.

[0148] Compared with the prior art, an embodiment of the present invention provides a direct positioning method under the condition of station site error. By utilizing the measurement position of each observation station, the uncertainty of the station site of each observation station containing random position errors is taken into account, and the cost function of the constructed radiation source position is only a function of the radiation source position, with low calculation complexity, and the radiation source can be quickly and accurately positioned to obtain the positioning position of the radiation source; at the same time, the measurement position of each observation station is used to perform a Taylor series first-order expansion of the observation station measurement signal model to construct a real-time position signal model and a real-time error model, taking into account the uncertainty of the station site of each observation station, and further improving the positioning accuracy of the radiation source position; and a grid search method is used to calculate the maximum eigenvalue of the cost function of the radiation source position corresponding to each possible position of the radiation source, which can improve the positioning efficiency and quickly locate the position of the radiation source.

[0149] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0150] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A direct positioning method under the condition of station location error, characterized in that: The direct positioning method comprises: Constructing an observation station measurement position model including random position errors and an observation station measurement signal model including random signal errors; Based on the observation station measurement position model, performing a Taylor series first-order expansion on the observation station measurement signal model at the measurement position of each observation station to obtain an expanded observation station measurement signal model; the expanded observation station measurement signal model includes a real-time position signal model and a real-time error model; Constructing a cost function of the radiation source position according to the real-time error model, the measurement signals of each observation station and the real-time position signal model; According to each possible position of the radiation source, a grid search method is used to determine the maximum eigenvalue corresponding to each possible position in the cost function of the radiation source position, and the possible position corresponding to the largest maximum eigenvalue is used as the positioning position of the radiation source.

2. The direct positioning method according to claim 1, characterized in that: The observation station measurement position model is: s=s o +Ψ; Where M represents the number of observation stations, 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 They represent the measured position vector, actual position vector, and random position error vector of the i-th observation station respectively; The random position error vector Ψ has zero mean, and the covariance matrix of Ψ is: Among them, Q β represents the covariance matrix of Ψ, represents the variance of the random position error of the observation station, I 3M Represents a 3M×3M matrix with diagonal elements of 1 and the remaining elements of 0; The measured position vector, actual position vector, and random position error vector of the i-th observation station are: s i =[x i ,y i ,z i ] T ; Among them, x i ,y i 、z i They represent the X-axis measurement coordinate, Y-axis measurement coordinate, and Z-axis measurement coordinate of the i-th observation station respectively; They represent the actual X-axis coordinate, Y-axis coordinate, and Z-axis coordinate of the i-th observation station respectively; They represent the X-axis random error, Y-axis random error, and Z-axis random error of the i-th observation station respectively.

3. The direct positioning method according to claim 2, characterized in that: The observation station measurement signal model is: z=ηQr+w; Among them, z i represents the sampling point signal vector of the i-th observation station, η i represents the unknown path loss factor of the i-th observation station, and ||η i ||=1;w i represents the random signal error vector of the i-th observation station; 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 represents an N×N matrix with diagonal elements of 1 and other elements of 0, N is the number of sampling points of the radiation source signal of each observation station, and T represents the matrix transpose; With i =[of i [0],from i [1],...,of i [N-1]] T ; w i =[w i [0],w i [1],...,w i [N-1]] T ; r＝[r[0],r[1],...,r[N-1]] T 。 4. The direct positioning method according to claim 3, characterized in that: The discrete Fourier transform vector of the i-th observation station is: Q i =F H Dτ i F; n=[0,1,...,N-1] T ; Where j represents the imaginary unit, Δ represents the signal sampling interval of each observation station, and u o represents the actual position of the radiation source, c represents the speed of light, represents the actual position of the i-th observation station, F represents the basis function matrix of Fourier transform, n represents the sampling point number matrix, τ i represents the time it takes for the radiation source signal to propagate to the i-th observation station, and || || represents the distance between the two locations.

5. The direct positioning method according to claim 4, characterized in that: The expanded observation station measurement signal model is: in, represents the real-time position signal model, w′ represents the real-time error model, diag{} represents a diagonal matrix, and blkdiag{} represents a block diagonal matrix.

6. The direct positioning method according to claim 5, characterized in that: The cost function of the radiation source position is constructed according to the real-time error model, the measurement signals of each observation station and the real-time position signal model, including: Calculating a covariance matrix of the real-time error model; Constructing a weighted least square solution equation for the radiation source position based on the covariance matrix of the real-time error model, the measurement signals of each observation station and the real-time position signal model; The estimated value of the radiation source signal is obtained by solving the equation based on the weighted least squares of the radiation source position; Substituting the estimated value of the radiation source signal into the weighted least squares solution equation of the radiation source position, a cost function of the radiation source position is obtained.

7. The direct positioning method according to claim 6, characterized in that: The covariance matrix of the real-time error model is: Among them, Λ w′ represents the covariance matrix of the real-time error model, I M represents an M×M matrix with diagonal elements set to 1 and the remaining elements set to 0; They represent the variance of the random signal errors of the 1st observation station, the i-th observation station, and the M-th observation station respectively.

8. The direct positioning method according to claim 7, characterized in that: The weighted least squares solution equation for the radiation source position is: Wherein, z represents the measurement signal vector of each observation station.

9. The direct positioning method according to claim 8, characterized in that: The weighted least square solution equation based on the radiation source position obtains an estimated value of the radiation source signal, including: The weighted least square solution equation of the radiation source position is used to perform a first-order derivative on the radiation source signal, and the derivative is set to zero to obtain an estimated value of the radiation source signal: in, represents an estimated value of the radiation source signal.

10. The direct positioning method according to claim 9, characterized in that: Substituting the estimated value of the radiation source signal into the weighted least squares solution equation of the radiation source position, a cost function of the radiation source position is obtained, including: Substituting the estimated value of the radiation source signal into the weighted least squares solution equation of the radiation source position, the transfer equation of the cost function is obtained. The transfer equation of the cost function is: Among them, R(u o ) is an M×M matrix, and the element in the i-th row and q-th column of the matrix is: Since [η1,...η i ,...,η M ] is unknown, replace it with its maximum likelihood estimate, which corresponds to R(u o )The eigenvector of the maximum eigenvalue is obtained, and the cost function of the radiation source position is obtained. The cost function of the radiation source position is: Among them, λ max {R(u o )} represents R(u o )’s maximum eigenvalue.

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