A direct positioning method with station location error

Abstract

The present invention relates to a direct positioning method under conditions of station address error, belonging to the field of radiation source positioning technology, and solves the problems of high positioning delay and poor accuracy of radiation source positions in the prior art. The direct positioning method comprises: based on the observation station measurement position model, performing a Taylor series first-order expansion of the observation station measurement signal model at the measurement position of each observation station to obtain the expanded observation station measurement signal model; constructing a cost function of the radiation source position based on the real-time error model, the measurement signals of each observation station, and the real-time position signal model; based on each possible position of the radiation source, using a grid search method to determine the maximum eigenvalue corresponding to each possible position in the cost function of the radiation source position, and using the possible position corresponding to the largest maximum eigenvalue as the positioning position of the radiation source. This achieves rapid and accurate positioning of the radiation source position.

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 station location error. Background Art

[0002] Traditional two-step positioning methods extract location-related signal parameters from the received electromagnetic signal of the radiation source, such as angle of arrival, time of arrival, time difference of arrival, and frequency difference of arrival. The radiation source is then located based on these extracted signal parameters. Direct positioning involves an observation station estimating the radiation source's position directly based on the received electromagnetic signal.

[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] Existing techniques use prior information about satellite orbits to construct a joint cost function for satellite position, velocity, and emitter location. These functions are then estimated simultaneously using an iterative optimization algorithm. This algorithm estimates both satellite position, velocity, and emitter location as deterministic position variables, resulting in high computational complexity. However, for scenarios requiring rapid emitter location, this algorithm can result in high positioning latency, making it difficult to meet timeliness requirements, resulting in slow positioning and poor 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 conditions where there is a station address 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 Represent the measured position vector, actual position vector, and random position error vector of the i-th observation station respectively;

[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, It represents the variance of the random position error of the observation station, I 3M Represents a 3M×3M matrix with diagonal elements set to 1 and the remaining elements set to 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 all diagonal elements set to 1 and all other elements set to 0, where N is the number of sampling points of the radiation source signal at 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 sequence 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 a 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 squares 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 all diagonal elements set to 1 and all other 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 squares solution equation of the radiation source position is:

[0049]

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

[0051] Based on a further improvement of the above method, the weighted least squares solution equation based on the radiation source position is used to obtain an estimated value of the radiation source signal, including:

[0052] The weighted least squares 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 the estimated value of the radiation source signal.

[0055] Based on a further improvement of the above method, the estimated value of the radiation source signal is substituted into the weighted least squares 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, a 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 )} means 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 utilizing 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. The computational complexity is low, and the radiation source can be quickly and accurately located to obtain the location of the radiation source;

[0065] 2. Using the measurement locations of each observation station, the Taylor series first-order expansion of the observation station measurement signal model is performed to construct a real-time position signal model and a real-time error model. This takes into account the uncertainty of each observation station's location and further improves the positioning accuracy of the radiation source.

[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 be combined with each other to achieve more preferred combinations. Other features and advantages of the present invention will be described in the following description, and some advantages will become apparent from the description or be learned through practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] The accompanying 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 parts 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 conditions of site error provided by an embodiment of the present invention;

[0071] Figure 3 A schematic diagram 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 will be 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, and 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, 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;

[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, such as Figure 2 As shown, in step S1, the observation station measurement position model containing random position errors is constructed, combined with Figure 1 , the constructed observation station measurement position 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 Represent the measured position vector, actual position vector, and random position error vector of the i-th observation station respectively;

[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, It represents the variance of the random position error of the observation station, I 3M Represents a 3M×3M matrix with diagonal elements set to 1 and the remaining elements set to 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 They are all 3×1 matrices, and each row of the matrix has the X-axis, Y-axis, and Z-axis coordinates; s, s o , Ψ are both 3M×1 matrices.

[0091] Specifically, such as Figure 2 As shown, the 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 all diagonal elements set to 1 and all other elements set to 0, where N is the number of sampling points of the radiation source signal at 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, M observation stations need to sample the signals emitted by the radiation source 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 sequence 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, such as Figure 2 As shown, in step S2, considering the influence of 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, 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, such as 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 squares 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 all diagonal elements set to 1 and all other 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 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.

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

[0124]

[0125] Where 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 step of solving the equation based on the weighted least squares method of the radiation source position to obtain an estimated value of the radiation source signal comprises:

[0128] The weighted least squares 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 the 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, a 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 )} means 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, such as Figure 2 As shown, in step S4, each possible position of the predetermined radiation source is substituted into the constructed cost function of the 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 noting that in scenarios where higher positioning accuracy is required, 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 demonstrating the technical effect of a direct positioning method provided by an embodiment of the present invention under conditions of site error.

[0144] Consider a scenario consisting of a 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 modulation mode of the radiation source signal waveform is BPSK, with a bandwidth of 25kHz. The carrier frequency is set to 303MHz and the sampling frequency is 100kHz. 2000 points of signal data are collected at each station for radiation source positioning. The direct positioning method provided by the embodiment of the present invention is denoted as DPD. NCUFor comparison, the direct positioning algorithm that ignores the site error is recorded as DPD NCNU , the positioning error Cramer-Lao bound CRLB under each signal-to-noise ratio scenario.

[0145] 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.

[0146] 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 root mean square 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.

[0147] 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 random position error of the station site 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 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.

[0148] Those skilled in the art will appreciate that all or part of the process steps of the above-described embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, such as a magnetic disk, an optical disk, a read-only memory, or a random access memory.

[0149] The above description is only a preferred specific 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 thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A direct positioning method under the condition of station location error, characterized in that: The direct positioning method includes: 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; Substitute 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, including: Substitute the estimated value of the radiation source signal into the weighted least squares solution equation of the radiation source position to obtain the transfer equation of the cost function, which is: ； in, for The matrix in which Rank The column elements are: ， ； ； because Unknown, replace it with its maximum likelihood estimate, which corresponds to The eigenvector of the maximum eigenvalue is used to obtain the cost function of the radiation source position. The cost function of the radiation source position is: ； in, express The maximum eigenvalue of .

2. The direct positioning method according to claim 1, characterized in that: The observation station measurement position model is: ； ； ； ； Among them, it means represents the number of observation stations, 、 、 Represents the measured position vector, actual position vector, and random position error vector of the observation station; 、 、 Respectively represent The measured position vector, actual position vector, and random position error vector of each observation station; Random position error vector has zero mean, and The covariance matrix of is: ； in, express The covariance matrix of represents the variance of the random position error of the observation station, Indicates that the diagonal elements are 1 and the rest of the elements are 0 Matrix of No. The measured position vector, actual position vector, and random position error vector of each observation station are: ； ； ； in, 、 、 Respectively represent The X-axis measurement coordinates, Y-axis measurement coordinates, and Z-axis measurement coordinates of each observation station; 、 、 Respectively represent The actual X-axis coordinate, Y-axis coordinate, and Z-axis coordinate of each observation station; 、 、 Respectively represent The X-axis random error, Y-axis random error, and Z-axis random error of each observation station.

3. The direct positioning method according to claim 2, characterized in that: The observation station measurement signal model is: ； ； ； ； ； in, Indicates the The signal vector of the sampling point of each observation station, Indicates the The unknown path loss factor of each observation station, and ; Indicates the Random signal error vector of each observation station; represents the radiation source signal vector, and ; Indicates the The discrete Fourier transform vector of each observation station; Indicates that the diagonal elements are 1 and the rest of the elements are 0 N is the number of sampling points of the radiation source signal at each observation station, Represents matrix transpose; ； ； 。 4. The direct positioning method according to claim 3, characterized in that: No. The discrete Fourier transform vector of each observation station is: ； ； ； ； ； ； in, represents the imaginary unit, represents the signal sampling interval of each observation station, Indicates the actual location of the radiation source, represents the speed of light, Indicates the The actual location of the observation station, represents the basis function matrix of Fourier transform, represents the sampling point number matrix, Indicates that the radiation source signal propagates to the The time of each observation station, Represents the distance between 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, represents the real-time error model, represents a diagonal matrix, 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 squares 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: ； ； in, represents the covariance matrix of the real-time error model, Indicates that the diagonal elements are 1 and the rest of the elements are 0 Matrix of 、 、 Respectively represent the first observation station, Observation stations, The variance of the random signal error at each observation station.

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

9. The direct positioning method according to claim 8, characterized in that: The weighted least squares solution equation based on the radiation source position is used to obtain an estimated value of the radiation source signal, including: The weighted least squares 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 the estimated value of the radiation source signal.

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