Passive location method of ground motion radiation source

Abstract

The application provides a passive positioning method for a ground moving radiation source, and the implementation steps are as follows: a positioning scene based on time-frequency difference measurement is constructed, an estimated value of an intermediate variable vector is calculated through measurement information, then two sets of rough estimated values of a moving radiation source position and a velocity vector are calculated by using the result, a set of estimated values of a moving radiation source position and a velocity error vector is screened out for re-estimation, finally, the initial estimated values of the moving radiation source position and the velocity are corrected by using the re-estimated result, and the passive positioning result of the moving radiation source is obtained. The application selects the parameter of the moving radiation source with the minimum height in the rough estimation as the initial value, improves the reliability of the positioning result, and directly obtains two sets of intermediate variable estimated vectors by considering the sign information of the parameters in the calculation, and effectively improves the positioning efficiency by screening out an initial estimated vector of the moving radiation source position and the velocity, calculating a weighted matrix and performing re-estimation.

Description

Technical Field

[0001] This invention belongs to the field of passive positioning technology and relates to a multi-station passive sensor target positioning method, specifically a passive positioning method for ground motion radiation sources, which can be applied to disaster relief or commanding drones to spray pesticides. Background Technology

[0002] Ground-based moving radiation sources are moving targets that actively radiate electromagnetic wave signals. Their altitude changes according to the ground elevation during movement. Localization of moving radiation sources involves using sensors to measure their position and velocity, making it a crucial area of ​​research in signal processing. Based on sensor type, moving radiation source localization methods can be categorized into active and passive localization techniques. Passive localization does not actively radiate electromagnetic waves into the radiation source but extracts various measurement information from the emitted signal to estimate its location. Compared to passive localization systems based on angle of arrival, received signal strength, and arrival signal gain ratio, localization systems based on time difference of arrival (TDOA) and rate of change of TDOA require only a single receiving channel per flight platform, eliminating the need for complex attitude measurement equipment. This allows for higher positioning accuracy with current TDOA measurement precision. For example, patent application CN 113759313 A, entitled "A Time Difference / Frequency Difference Localization Method Based on Chaotic Sparrow Algorithm," discloses a time difference / frequency difference localization method based on the chaotic sparrow algorithm. This method first establishes a TDOA / FDOA positioning model under the condition of station errors on the flight platform. Then, it uses weighted least squares to obtain coarse estimates of multiple sets of radiation source location information and selects the one with the smallest cost function value as the initial estimate of the radiation source location information. Next, it initializes a population of Ligostic chaotic sequences using the initial estimate and employs a sparrow search algorithm to solve the TDOA / FDOA model for positioning. This method can locate radiation sources using only four flight platforms and solves the problem of poor positioning accuracy under low station errors. However, its drawbacks are that this invention directly uses all coarse estimates obtained by weighted least squares and then filters them. Furthermore, the sparrow search algorithm requires calculating the fitness of each individual in the population and iteratively finding the point with the optimal fitness, resulting in high computational complexity. The coarse estimate of the radiation source location information includes both fuzzy solutions and the true radiation source location. In the cost function value calculated from the coarse estimate, there are cases where the value of the fuzzy solution is less than the value of the true radiation source location, leading to the fuzzy solution being mistakenly identified as the radiation source location estimate, affecting the reliability of the positioning results. Summary of the Invention

[0003] The purpose of this invention is to overcome the defects of the prior art and propose a passive positioning method for ground motion radiation sources, which solves the technical problems of high computational complexity and poor positioning results in the prior art.

[0004] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0005] (1) Constructing a localization scenario for the motion radiation source:

[0006] Construct N flight platforms M = {m1, m2, ..., m} distributed in three-dimensional space, each equipped with passive sensors and information acquisition modules. n ,...,m N} and the location scene of moving radiation sources distributed on the ground, and one of the flying platforms m a As a reference platform, a∈{1,2,...,N}, m a It is equipped with an information processing module and a time-frequency difference information extraction module, where N≥4, m n This represents the nth flight platform;

[0007] (2) Construct pseudo-linear matrix equations:

[0008] The position and velocity vectors of the moving radiation source are initialized as θ, and the intermediate variable vector of θ is P. The electromagnetic wave signal radiated by the moving radiation source reaches the nth flight platform m. n and reference platform m a The time difference is τ na τ na rate of change And based on τ na and The passive localization model constructs a pseudo-linear matrix equation with respect to θ and P:

[0009] G1θ=h1+2KP

[0010] (3) Collect observation information for each flight platform:

[0011] Each flight platform m n The information collection module on the top collects m n Location observations s n =[x n ,y n ,z n ] T and velocity observations The set of location observations is obtained as S = {s1, s2, ..., s...} n ,...,s N} and velocity observation set And through the communication link between flight platforms, S and Send to the information processing module; where, [·] T Indicates the transpose operation, x n y n z n They represent s respectively n Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system;

[0012] (4) Extract the time-frequency difference measurement between the radiation source signal and the reference platform and each flight platform:

[0013] (4a) m per flight platform n The passive sensor on the device samples the electromagnetic wave signal from the moving radiation source L times and records the sampled values ​​I. n Transmitted to reference platform m via the communication link between flight platforms a Time-frequency difference information extraction module:

[0014] I n ={ξ n1 ,ξ n2 ,...,ξ nl ,...,ξ nL}

[0015] Where, ξ nl This represents the amplitude value of the electromagnetic wave signal from the moving radiation source sampled by the passive sensor on the nth flight platform for the lth time;

[0016] (4b) The time-frequency difference information extraction module extracts the sampled value I. n Electromagnetic wave signals from the medium-motion radiation source reach each flight platform m n and reference platform m a Time difference measurement τ na τ na Rate of change measurement τ na Error Δτ na , error The set of time difference measurements F = [τ] is obtained. 1a ,τ 2a ,...,τ na ,...,τ Na Set of time difference change rate measurements Time difference measurement error set ΔF=[Δτ 1a ,Δτ 2a ,...,Δτ na ,...,ΔτNa Time difference change rate measurement error set and F, ΔF Transmitted to the information processing module;

[0017] (5) Estimate the intermediate variable vector in the pseudo-linear matrix equation:

[0018] The information processing module calculates the distance difference covariance matrix Q based on the time difference measurement error set ΔF. t Based on the set of measurement errors according to the rate of change of time difference Calculate the relative radial velocity covariance matrix Q f And according to F, S, Q t Q f Calculate the estimated value of the intermediate distance variable r1 in the intermediate variable vector P. Then through Calculate the intermediate velocity variable in P respectively The estimated value Obtain the estimated vector of the intermediate variable vector P

[0019] (6) Calculate the initial estimated vectors of the position and velocity of the moving radiation source based on the weighted least squares algorithm:

[0020] The information processing module is based on the weighted least squares algorithm and uses the estimated vector of the intermediate variable vector P. Solving the pseudo-linear matrix equation yields... The estimated vector of the corresponding moving radiation source position and velocity vector Then from Select The vector with the smallest median value is used as the initial estimate of the position and velocity of the moving radiation source.

[0021]

[0022]

[0023]

[0024] Where |·| represents the absolute value operation, They represent The position vector and velocity vector of the moving radiation source in the image. They represent The position vector and velocity vector of the moving radiation source in the diagram. They represent The position vector and velocity vector of the moving radiation source in the diagram. They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system;

[0025] (7) Obtain the passive localization results of the moving radiation source:

[0026] (7a) The information processing module calculates the initial estimated vector based on the position and velocity of the moving radiation source. and the set of position observations S and the set of velocity observations Calculate the time-frequency difference weighted matrix W1′ and the time difference weighted matrix W t ′, and through W1′ and W t Initial estimation vector of the position and velocity of the moving radiation source. Perform a re-estimation to obtain the initial estimated vector.

[0027] (7b) The information processing module is based on the weighted least squares algorithm, and according to F, S, W1′、W t ′ and initial estimated vector The estimated vector of the error vector Δθ for calculating the position and velocity of a moving radiation source. and through right By performing deviation compensation, the passive localization result of the moving radiation source is obtained.

[0028] G2Δθ=h2

[0029]

[0030]

[0031] in, This represents the vector indicating the estimated location of the moving radiation source. This represents the velocity estimation vector of the moving radiation source.

[0032] Compared with the prior art, the present invention has the following advantages:

[0033] 1. This invention solves the pseudo-linear matrix equation using two estimated vectors of the intermediate variable vector, and selects the set of estimated values ​​with the lowest absolute value of the Z-axis component from the estimated vectors of the moving radiation source position and velocity corresponding to the two estimated vectors obtained from the solution as the initial estimated vectors of the moving radiation source position and velocity. This avoids the impact on the positioning effect caused by the existence of fuzzy solutions that are smaller than the true radiation source position value in the coarse estimation of radiation source position information in the prior art, and effectively improves the reliability of ground radiation source positioning.

[0034] 2. By considering the sign characteristics of the parameters in the calculation, this invention calculates two sets of intermediate variable estimation vectors, and then calculates a weighted matrix and performs re-estimation using a selected set of initial estimation vectors of the position and velocity of the moving radiation source. This avoids the impact on computational efficiency caused by calculating all coarse estimates and then filtering them, as is done in the prior art. At the same time, this invention estimates the estimated values ​​of the radiation source position and velocity errors by calculating the biased directional variables of the intermediate variables with respect to the position and velocity of the radiation source, and uses the results to correct the initial optimal solutions of the radiation source position and velocity. This avoids the computational complexity caused by the sparrow search algorithm in the prior art, and effectively improves positioning efficiency while ensuring positioning accuracy. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating the implementation of the present invention.

[0036] Figure 2 This is a distribution diagram of the results of 1000 Monte Carlo experiments in the embodiments of the present invention and the prior art.

[0037] Figure 3 This is a 95% confidence interval distribution of the results of 1000 Monte Carlo experiments conducted according to an embodiment of the present invention. Detailed Implementation

[0038] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0039] Reference Figure 1 The present invention includes the following steps:

[0040] Step 1) Construct a localization scenario for the moving radiation source:

[0041] Construct N flight platforms M = {m1, m2, ..., m} distributed in three-dimensional space, each equipped with passive sensors and information acquisition modules. n,...,m N} and the location scene of moving radiation sources distributed on the ground, and one of the flying platforms m a As a reference platform, a∈{1,2,...,N}, m a It is equipped with an information processing module and a time-frequency difference information extraction module, where N≥4, m n This represents the nth flight platform;

[0042] In this embodiment, the number of flight platforms N=4, and the first flight platform m1 is the reference platform, i.e., a=1;

[0043] Step 2) Construct pseudo-linear matrix equations:

[0044] The position and velocity vectors of the moving radiation source are initialized as θ, and the intermediate variable vector of θ is P. The electromagnetic wave signal radiated by the moving radiation source reaches the nth flight platform m. n and reference platform m a The time difference is τ na τ na rate of change And based on τ na and The passive localization model constructs a pseudo-linear matrix equation with respect to θ and P:

[0045] The passive localization model described above is expressed as follows:

[0046] r na =cτ na =r n -r a

[0047]

[0048]

[0049]

[0050] Where, τ na , These represent the electromagnetic wave signals radiated by the moving radiation source to the nth flight platform m at the same moment. n and reference platform m a Arrival time difference information, arrival frequency difference information, r n , These represent the radiation sources from the nth flight platform m, respectively. n Distance, relative radial velocity, r na , These represent the radiation sources from the nth flight platform m, respectively. n and reference platform m aThe distance difference and relative radial velocity difference, c and f0 represent the propagation speed and carrier frequency of the electromagnetic wave radiated by the moving radiation source, respectively, and x. n y n z n Let m represent the nth flight platform respectively. n Position vector s n Components on the X, Y, and Z axes of a spatial rectangular coordinate system Let m represent the nth flight platform respectively. n velocity vector The components of the position vector u of the moving radiation source on the X, Y, and Z axes of the spatial rectangular coordinate system, where x, y, and z represent the components of the position vector u of the moving radiation source on the X, Y, and Z axes of the spatial rectangular coordinate system, respectively. These represent the velocity vectors of the moving radiation source, respectively. Components on the X, Y, and Z axes of a spatial rectangular coordinate system;

[0051] The expression for the pseudolinear matrix equations of θ and P mentioned above is:

[0052] G1θ=h1+2KP

[0053]

[0054]

[0055] K = [K1 K2]

[0056]

[0057]

[0058]

[0059]

[0060] G 1t =-2[s2-s a s3-s a …s n -s a …s N -s a ] T

[0061]

[0062]

[0063]

[0064] Where G1 represents the coefficient matrix of the pseudolinear matrix equation, K represents the coefficient matrix of P, and h1 represents the constant matrix of the pseudolinear matrix equation.

[0065] Step 3) Collect observation information for each flight platform:

[0066] Each flight platform m n The information collection module on the top collects m n Location observations s n =[x n ,y n ,z n ] T and velocity observations The set of location observations is obtained as S = {s1, s2, ..., s...} n ,...,s N} and velocity observation set And through the communication link between flight platforms, S and Send to the information processing module; where, [·] T Indicates the transpose operation, x n y n z n They represent s respectively n Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system;

[0067] In this embodiment, the position observation vectors of the first flight platform m1 to the fourth flight platform m4 are s1 = (300, 100, 150) meters, s2 = (400, 150, 100) meters, s3 = (300, 500, 200) meters, and s4 = (350, 200, 100) meters, respectively. The velocity observation vectors of the first flight platform m1 to the fourth flight platform m4 are...

[0068] Step 4) Extract the radiation source signal to the time-frequency difference measurement values ​​between the reference platform and each flight platform:

[0069] 4a) Each flight platform m n The passive sensor on the device samples the electromagnetic wave signal from the moving radiation source L times and records the sampled values ​​I. n Transmitted to reference platform m via the communication link between flight platforms a Time-frequency difference information extraction module:

[0070] I n ={ξ n1 ,ξ n2 ,...,ξnl ,...,ξ nL}

[0071] Where, ξ nl This represents the amplitude value of the electromagnetic wave signal from the moving radiation source sampled by the passive sensor on the nth flight platform for the lth time;

[0072] (4b) The time-frequency difference information extraction module extracts the sampled value I. n Electromagnetic wave signals from the medium-motion radiation source reach each flight platform m n and reference platform m a Time difference measurement τ na τ na Rate of change measurement τ na Error Δτ na , error The set of time difference measurements F = [τ] is obtained. 1a ,τ 2a ,...,τ na ,...,τ Na Set of time difference change rate measurements Time difference measurement error set ΔF=[Δτ 1a ,Δτ 2a ,...,Δτ na ,...,Δτ Na Time difference change rate measurement error set and F, ΔF Transmitted to the information processing module;

[0073] In this embodiment, the measurement error of the time difference of arrival ΔF and the measurement error of the rate of change of the time difference of arrival are... The variables are independent and follow a mean of zero, with variances of respectively. and Gaussian distribution, These represent the distances from the motion radiation source to each flight platform, m respectively. n and reference platform m a The variance of the measurement errors for the distance difference and the relative radial velocity difference. square meters, The square of meters per second, c = 3.0 × 10 8 meters per second.

[0074] Step 5) Estimate the intermediate variable vectors in the pseudo-linear matrix equation:

[0075] The information processing module calculates the distance difference covariance matrix Q based on the time difference measurement error set ΔF. t Based on the set of measurement errors according to the rate of change of time difference Calculate the relative radial velocity covariance matrix Q f And according to F, S, Q t Q f Calculate the estimated value of the intermediate distance variable r1 in the intermediate variable vector P. Then through Calculate the intermediate velocity variable in P respectively The estimated value Obtain the estimated vector of the intermediate variable vector P The calculation formulas are as follows:

[0076]

[0077]

[0078]

[0079]

[0080]

[0081] Q t =c 2 E[(ΔF) T ΔF]

[0082]

[0083]

[0084]

[0085] r = [r 21 ,r 31 ,...,r N1 ] T

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093] W1 = Q -1

[0094]

[0095]

[0096] in,[·] -1 E[·] represents the matrix inversion operation, E[·] represents the mean operation, and W represents the matrix inversion operation. t Let Q represent the time difference weighted matrix. t The distance difference measurement covariance matrix between the moving radiation source and each passive sensor is represented by α. u β u and γ u These are vectors consisting of the first N-1 rows of α, β, and γ, respectively; α v ,β v and γ v These are vectors composed of the last N-1 rows of elements of α, β, and γ, where W1 represents the time-frequency difference weighted matrix, and Q... f This represents the covariance matrix of the relative radial velocity difference measurement between the moving radiation source and each passive sensor, where Q represents the result of Q... t With Q f A block diagonal matrix formed by successively using the main diagonals.

[0097] In this embodiment, the time difference weighting matrix Time Difference Change Rate Weighted Matrix V represents a 3×3 square matrix with 1 as the main diagonal element and 0.5 as the rest.

[0098] Step 6) Calculate the initial estimated vectors of the position and velocity of the moving radiation source based on the weighted least squares algorithm:

[0099] The information processing module is based on the weighted least squares algorithm and uses the estimated vector of the intermediate variable vector P. Solving the pseudo-linear matrix equation yields... The estimated vector of the corresponding moving radiation source position and velocity vector Then from Select The vector with the smallest median value is used as the initial estimate of the position and velocity of the moving radiation source.

[0100]

[0101]

[0102]

[0103] Where |·| represents the absolute value operation, They represent The position vector and velocity vector of the moving radiation source in the image. They represent The position vector and velocity vector of the moving radiation source in the diagram. They represent The position vector and velocity vector of the moving radiation source in the diagram. They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system;

[0104] In this embodiment, the position vector and velocity vector of the moving radiation source are u = (320, 150, 0) meters and...

[0105] Step 7) Obtain the passive localization results of the moving radiation source:

[0106] (7a) The information processing module calculates the initial estimated vector based on the position and velocity of the moving radiation source. and the set of position observations S and the set of velocity observations Calculate the time-frequency difference weighted matrix W1′ and the time difference weighted matrix W t ′, and through W1′ and W t Initial estimation vector of the position and velocity of the moving radiation source. Perform a re-estimation to obtain the initial estimated vector. The calculation formulas are as follows:

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] Where ||·||2 represents the 2-norm operation, 0 (N-1) Let N represent a square matrix of dimension N-1 containing all zeros.

[0113] (7b) The information processing module is based on the weighted least squares algorithm, and according to F, S, W1′、W t ′ and initial estimated vector The estimated vector of the error vector Δθ for calculating the position and velocity of a moving radiation source. and through right By performing deviation compensation, the passive localization result of the moving radiation source is obtained. The calculation formulas are as follows:

[0114] G2Δθ=h2

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124] Among them, 0 1×(N-1) This represents a row vector of all zeros with dimension N-1 columns. This represents the vector indicating the estimated location of the moving radiation source. This represents the velocity estimation vector of the moving radiation source.

[0125] The technical effects of this invention will be further explained below with reference to simulation experiments:

[0126] 1. Simulation conditions and content:

[0127] The hardware platform for the simulation experiment was: Intel(R) Core(TM) i5-6300HQ CPU@2.30GHz; the software platform was: Matlab R2016a simulation software under Windows 10 Home Chinese Edition 64-bit operating system.

[0128] Experiment 1 simulates the ability of the embodiments of the present invention and the prior art to screen the estimated positions and velocities of moving radiation sources. The results are as follows: Figure 2 and Figure 3 As shown;

[0129] 2. Analysis of experimental results:

[0130] Reference Figure 2 ,in This represents the mean of the estimated locations of the radiation sources from 1000 Monte Carlo experiments. The symbols represent the actual coordinates of the radiation sources, while "·" represents the estimated coordinates of 1000 radiation sources from the Monte Carlo experiment. Figure 2 (a) shows the distribution of estimated radiation source location coordinates for 1000 groups according to Embodiment 1 of the present invention. The estimated values ​​are concentrated around the true value (320, 150, 0) meters, and the mean of the estimated values ​​almost coincides with the true value. Figure 2 (c) is Figure 2 (a) is a magnified view of the area. The mean of the estimated values ​​deviates from the actual coordinates of the radiation source location in the X, Y, and Z axes by less than 0.1 meters. Figure 2 (b) shows the distribution of 1000 sets of estimated radiation source location coordinates when the parameters are set in the embodiments of the present invention. The estimation results are divided into two categories according to the aggregation and points in space. One category is... Figure 2 (b) The "·" in the lower right corner is concentrated around the actual location of the moving radiation source (320, 150, 0) meters. Another type is... Figure 2 (b) The "·" in the upper left corner is concentrated at coordinates (40, -88, 470) meters, while the mean of the estimated values ​​is The coordinates are (75.5, -58, 409) meters, which deviates greatly from the actual coordinates of the radiation source.

[0131] Reference Figure 3 , Figure 3 (a) shows the distribution of the 95% confidence intervals of the results of 1000 Monte Carlo experiments conducted in scenario 2 in three-dimensional space. Figure 3 (b) Figure 3 (c) Figure 3(d) shows the distribution of the projections of the results shown in 3(a) onto the XOZ, YOZ, and XOY planes. The present invention has nearly 97.5% of the estimated locations of moving radiation sources that fall within the 95% confidence interval, while the prior art has no estimated values ​​that fall within the 95% confidence interval because the estimated results are divided into two categories and have a large relative deviation.

[0132] Based on the above simulation results, it is proven that the present invention has the best initial solution filtering capability and improves the reliability of the positioning results.

Claims

1. A passive positioning method for a ground-based motion radiation source, characterized in that, Includes the following steps: (1) Constructing a localization scenario for the motion radiation source: Construct N flight platforms M = {m1, m2, ..., m} distributed in three-dimensional space, each equipped with passive sensors and information acquisition modules. n ,...,m N } and the location scene of moving radiation sources distributed on the ground, and one of the flying platforms m a As a reference platform, a∈{1,2,...,N}, m a It is equipped with an information processing module and a time-frequency difference information extraction module, where N≥4, m n This represents the nth flight platform; (2) Construct pseudo-linear matrix equations: The position and velocity vectors of the moving radiation source are initialized as θ, and the intermediate variable vector of θ is P. The electromagnetic wave signal radiated by the moving radiation source reaches the nth flight platform m. n and reference platform m a The time difference is τ na τ na rate of change And based on τ na and The passive localization model constructs a pseudo-linear matrix equation with respect to θ and P: G1θ=h1+2KP (3) Collect observation information for each flight platform: Each flight platform m n The information collection module on the top collects m n Location observations s n =[x n ,y n ,z n ] T and velocity observations The set of location observations is obtained as S = {s1, s2, ..., s...} n ,...,s N } and velocity observation set And through the communication link between flight platforms, S and Send to the information processing module; where, [·] T Indicates the transpose operation, x n y n z n They represent s respectively n Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system; (4) Extract the time-frequency difference measurement values ​​between the radiation source signal and the reference platform and each flight platform: (4a) m per flight platform n The passive sensor on the device samples the electromagnetic wave signal from the moving radiation source L times and records the sampled values ​​I. n Transmitted to reference platform m via the communication link between flight platforms a Time-frequency difference information extraction module: I n ={ξ n1 ,x n2 ,...,x nl ,...,x nL } Where, ξ nl This represents the amplitude value of the electromagnetic wave signal from the moving radiation source sampled by the passive sensor on the nth flight platform for the lth time; (4b) The time-frequency difference information extraction module extracts the sampled value I. n Electromagnetic wave signals from the medium-motion radiation source reach each flight platform m n and reference platform m a Time difference measurement τ na τ na Rate of change measurement τ na Error Δτ na , error The set of time difference measurements F = [τ] is obtained. 1a ,τ 2a ,...,τ na ,...,τ Na Set of time difference change rate measurements Time difference measurement error set ΔF=[Δτ 1a ,Δτ 2a ,...,Δτ na ,...,Δτ Na Time difference change rate measurement error set and F, Transmitted to the information processing module; (5) Estimate the intermediate variable vector in the pseudo-linear matrix equation: The information processing module calculates the distance difference covariance matrix Q based on the time difference measurement error set ΔF. t Based on the set of measurement errors according to the rate of change of time difference Calculate the relative radial velocity covariance matrix Q f And according to F, Q t Q f Calculate the estimated value of the intermediate distance variable r1 in the intermediate variable vector P. Then through Calculate the intermediate velocity variable in P respectively The estimated value Obtain the estimated vector of the intermediate variable vector P (6) Calculate the initial estimated vectors of the position and velocity of the moving radiation source based on the weighted least squares algorithm: The information processing module is based on the weighted least squares algorithm and uses the estimated vector of the intermediate variable vector P. Solving the pseudo-linear matrix equation yields... The estimated vector of the corresponding moving radiation source position and velocity vector Then from Select The vector with the smallest median value is used as the initial estimate of the position and velocity of the moving radiation source. Where |·| represents the absolute value operation, They represent The position vector and velocity vector of the moving radiation source in the image. They represent The position vector and velocity vector of the moving radiation source in the diagram. They represent The position vector and velocity vector of the moving radiation source in the diagram. They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system They represent Components on the X, Y, and Z axes of a spatial rectangular coordinate system; (7) Obtain the passive localization results of the moving radiation source: (7a) The information processing module calculates the initial estimated vector based on the position and velocity of the moving radiation source. and the set of position observations S and the set of velocity observations Calculate the time-frequency difference weighted matrix W1′ and the time difference weighted matrix W t ′, and through W1′ and W t Initial estimation vector of the position and velocity of the moving radiation source. Perform a re-estimation to obtain the initial estimated vector. (7b) The information processing module is based on the weighted least squares algorithm, and according to F, S, W1′、W t ′ and initial estimated vector The estimated vector of the error vector Δθ for calculating the position and velocity of a moving radiation source. and through right By performing deviation compensation, the passive localization result of the moving radiation source is obtained. G2Δθ=h2 in, This represents the vector indicating the estimated location of the moving radiation source. This represents the velocity estimation vector of the moving radiation source.

2. The passive positioning method according to claim 1, characterized in that, The passive localization model described in step (2), and the coefficient matrix G1 of the pseudolinear matrix equation, the coefficient matrix K of P, and the constant matrix h1 of the pseudolinear matrix equation, are expressed as follows: r na =cτ na =r n -r a K = [K1 K2] G 1t =-2[s2-s a s3 a ... and n -s a ... and N -s a ] T Where, τ na , These represent the electromagnetic wave signals radiated by the moving radiation source reaching the nth flight platform m. n and reference platform m a arrival time difference, τ na rate of change, r n , These represent the radiation sources from the nth flight platform m, respectively. n Distance, relative radial velocity, r na , These represent the radiation sources from the nth flight platform m, respectively. n and reference platform m a The distance difference and the relative radial velocity difference, where c represents the propagation speed of the electromagnetic wave radiated by the moving radiation source, and x... n y n z n Let m represent the nth flight platform respectively. n Position vector s n Components on the X, Y, and Z axes of a spatial rectangular coordinate system Let m represent the nth flight platform respectively. n velocity vector The components of the position vector u of the moving radiation source on the X, Y, and Z axes of the spatial rectangular coordinate system, where x, y, and z represent the components of the position vector u of the moving radiation source on the X, Y, and Z axes of the spatial rectangular coordinate system, respectively. These represent the components of the velocity vector u of the moving radiation source along the X, Y, and Z axes of the spatial rectangular coordinate system, respectively.

3. The passive positioning method according to claim 1, characterized in that, The estimated value of the intermediate distance variable r1 in the intermediate variable vector P mentioned in step (5). intermediate velocity variable in P The estimated value The calculation formulas are as follows: W t =Q t -1 Q t =c 2 E[(ΔF) T ΔF] r＝[r 21 ,r 31 ,...,r N1 ] T W1=Q -1 in,[·] -1 E[·] represents the matrix inversion operation, and E[·] represents the mean operation. 0 (N-1) Let W represent a square matrix of dimension N-1 containing all zeros. t Let α represent the time difference weighted matrix. u β u and γ u These are vectors consisting of the first N-1 rows of α, β, and γ, respectively; α v ,β v and γ v These are vectors composed of the last N-1 rows of elements of α, β, and γ, respectively, and W1 represents the time-frequency difference weighted matrix.

4. The passive positioning method according to claim 1, characterized in that, In step (6), the pseudo-linear matrix equation is solved using a weighted least squares algorithm to obtain the least squares estimate of the position and velocity vector θ of the moving radiation source. The calculation formula is:

5. The passive positioning method according to claim 1, characterized in that, The time-frequency difference weighting matrix W1′ and the time difference weighting matrix W mentioned in step (7a) t Initial estimated vector The calculation formulas are as follows: Where ||·||2 represents the 2-norm operation, They represent The vector formed by the first 3 rows of elements The vector consisting of the last three rows of elements.

6. The passive positioning method according to claim 1, characterized in that, The estimated vector of the error vector Δθ for calculating the position and velocity of the moving radiation source as described in step (7b). The calculation formula is: Among them, 0 1×(N-1) This represents a row vector of all zeros with dimension N-1 columns.

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