A direct positioning method in presence of station site errors and external correction sources

Abstract

The present application relates to a kind of direct positioning method of station error and external calibration source, belong to radiation source positioning technical field, solve the problem of low precision of radiation source positioning in prior art.The direct positioning method includes: based on the observation station measurement position model and the measurement signal of each observation station of external calibration source, the measurement position of each observation station is corrected;Taylor series first order expansion is carried out to the observation station measurement signal model at the measurement position of each observation station after correction;According to the correction error model, the measurement signal of each observation station of radiation source and the correction position signal model, the cost function of radiation source position is constructed;According to each possible position of radiation source, the corresponding maximum eigenvalue is determined, and the possible position corresponding to the maximum maximum eigenvalue is regarded as the positioning position of radiation source.The high-precision positioning of radiation source position is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radiation source positioning, in particular to a direct positioning method with station site error and external calibration source. BACKGROUND

[0002] In the traditional two-step positioning method, signal parameters related to the position of the radiation source, such as the angle of arrival, time of arrival, time difference of arrival and frequency difference of arrival, are extracted from the received electromagnetic signals of the radiation source, and then the radiation source is positioned according to the extracted signal parameters. Direct positioning refers to the direct estimation of the position of the radiation source by the observation station based on the received electromagnetic signals of the radiation source.

[0003] The traditional two-step positioning method is not optimal because it ignores the potential constraint of the extracted signal parameters corresponding to a radiation source, while the direct positioning method can effectively utilize this potential constraint to improve the positioning of the position of the radiation source.

[0004] The direct positioning method for positioning the radiation source in the prior art cannot be adaptively changed with the application environment, and it is difficult to meet the requirements when performing high-precision positioning tasks.

[0005] Therefore, there is an urgent need for a technical solution for positioning the radiation source. SUMMARY

[0006] In view of the above analysis, the embodiments of the present application aim to provide a direct positioning method with station site error and external calibration source to solve the problem of low positioning accuracy of the radiation source in the prior art.

[0007] The embodiments of the present application provide a direct positioning method with station site error and external calibration source, which comprises:

[0008] Constructing an observation station measurement position model containing random position error and an observation station measurement signal model containing random signal error;

[0009] Correcting the measurement position of each observation station based on the observation station measurement position model and the external calibration source measurement signal of each observation station to obtain the corrected measurement position of each observation station;

[0010] Performing Taylor series first-order expansion on the observation station measurement signal model at the corrected measurement position of each observation station to obtain the expanded observation station measurement signal model; the expanded observation station measurement signal model comprises a corrected position signal model and a corrected error model;

[0011] Constructing a cost function of the position of the radiation source according to the corrected error model, the radiation source measurement signal of each observation station and the corrected position signal model;

[0012] 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 maximum maximum eigenvalue is taken as the positioning position of the radiation source.

[0013] Based on the above method, the measurement position of each observation station is corrected based on the observation station measurement position model and the measurement signal of the outer calibration source of each observation station, to obtain the corrected measurement position of each observation station, comprising:

[0014] According to the measurement signal of the outer calibration source of each observation station, a measurement distance difference equation of each observation station relative to the position of the outer calibration source is determined; the reference observation station is an optional observation station from all observation stations;

[0015] Based on the measurement position of each observation station, a theoretical distance difference equation of each observation station relative to the position of the outer calibration source is determined;

[0016] Using the measurement distance difference equation and the theoretical distance difference equation of each observation station relative to the position of the outer calibration source, a difference equation of the measurement distance difference and the theoretical distance difference is constructed, and the estimated random position error of each observation station is obtained by solving the difference equation;

[0017] According to the measurement position of each observation station and the estimated random position error of each observation station, the corrected measurement position of each observation station is calculated.

[0018] Based on the above method, the measurement distance difference equation of each observation station relative to the position of the outer calibration source is:

[0019]

[0020] Wherein, represents the measurement distance difference between the position of the i-th observation station and the reference observation station and the position of the outer calibration source, and v represents the speed of light, represents the time difference between the arrival of the outer calibration source measurement signal at the i-th observation station and at the reference observation station, and c o represents the position of the outer calibration source, respectively represent the actual position of the reference observation station and the actual position of the i-th observation station, represents the measurement error of the reference observation station and the i-th observation station;

[0021] The theoretical distance difference equation of each observation station relative to the position of the outer calibration source is:

[0022]

[0023] wherein, represents the theoretical distance difference between the ith observation station and the reference observation station, s i , s l respectively represent the measured position of the reference observation station, the measured position of the ith observation station.

[0024] Based on the further improvement of the above method, the difference equation of the measured distance difference and the theoretical distance difference is constructed, comprising:

[0025] At the measured position s i of each observation station, the Taylor series first-order expansion of is carried out to obtain:

[0026]

[0027]

[0028] wherein, represents the unit vector of the position c i pointing to the external calibration source from the measured position s o of the ith observation station;

[0029] The difference equation is:

[0030]

[0031] The Taylor series first-order expansion of is used to simplify the difference equation, and the simplified difference equation is:

[0032]

[0033] wherein, Ψ i , Ψ l are the random position errors of the ith observation station and the reference observation station respectively.

[0034] Based on the further improvement of the above method, the estimated random position error of each observation station is:

[0035]

[0036] wherein, represents the estimated random position error of each observation station, 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 being 1 and other elements being 0;

[0037] G cis a matrix of (M-1) x 3M and the (i-1)th row of is:

[0038]

[0039] wherein, Q c is a matrix of (M-1) x 1 and the (i-1)th element of is ;

[0040] wherein, h c is a matrix of (M-1) x 1 and the (i-1)th element of is

[0041] The corrected measurement position of each observation station is:

[0042]

[0043] wherein, represents the corrected measurement position of each observation station.

[0044] Based on the further improvement of the above method, the observation station measurement position model is:

[0045] s = s o + Ψ;

[0046]

[0047] wherein, M represents the number of observation stations, s, s o , Ψ represent the measurement position vector, the actual position vector, the random position error vector of the observation station; s i , Ψ i respectively represent the measurement position vector, the actual position vector, the random position error vector of the i th observation station;

[0048] The random position error vector Ψ conforms to zero mean, and the covariance matrix of Ψ is:

[0049]

[0050] wherein, 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 x 3M matrix with diagonal elements being 1 and other elements being 0;

[0051] The measurement position vector, the actual position vector, the random position error vector of the i th observation station are:

[0052] s i = [x i , y i , zi ] T ;

[0053]

[0054] where x i , y i , z i denote the X-axis measurement coordinate, the Y-axis measurement coordinate, and the Z-axis measurement coordinate of the i-th observation station, respectively; denote the X-axis actual coordinate, the Y-axis actual coordinate, and the Z-axis actual coordinate of the i-th observation station, respectively; denote the X-axis random error amount, the Y-axis random error amount, and the Z-axis random error amount of the i-th observation station, respectively.

[0055] Based on the further improvement of the above method, the observation station measurement signal model is:

[0056] z = ηQr + w;

[0057]

[0058] where z i denotes the sampling point signal vector of the i-th observation station, η i denotes the unknown path loss factor of the i-th observation station, and ||η i || = 1; w i denotes the random signal error vector of the i-th observation station; r denotes the radiation source signal vector, and ||r|| = 1; Q i denotes the discrete Fourier transform vector of the i-th observation station; I N denotes an N x N matrix with diagonal elements being 1 and other elements being 0, and N is the number of sampling points of the radiation source signal of each observation station;

[0059] z i = [z i [0], z i [1],..., z i [N-1]] T ;

[0060] w i = [w i [0], w i [1],..., w i [N-1]] T ;

[0061] r = [r[0], r[1],..., r[N-1]] T ;

[0062] The discrete Fourier transform vector of the i-th observation station is:

[0063]

[0064] n = [0, 1, …, N-1] T ;

[0065]

[0066] where j represents imaginary unit, Δ represents signal sampling interval of each observation station, u o represents actual position of radiation source, represents actual position of the i-th observation station.

[0067] Based on the further improvement of the above method, the unfolded observation station measurement signal model is:

[0068]

[0069] where, represents the corrected position signal model, w" represents the correction error model, diag{} represents a diagonal matrix.

[0070] Based on the further improvement of the above method, the cost function of the radiation source position is constructed according to the correction error model, the radiation source measurement signal of each observation station and the corrected position signal model, comprising:

[0071] Calculate the covariance matrix of the correction error model;

[0072] Based on the covariance matrix of the correction error model, the radiation source measurement signal of each observation station and the corrected position signal model, a weighted least squares solution equation of the radiation source position is constructed;

[0073] Based on the weighted least squares solution equation of the radiation source position, an estimated value of the radiation source signal is obtained;

[0074] 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.

[0075] Based on the further improvement of the above method, the covariance matrix of the correction error model is:

[0076]

[0077] where, is the largest element on the diagonal; I M represents an MxM matrix whose diagonal elements are 1 and the rest are 0; respectively represent the variance of the random signal error of the first observation station, the i-th observation station, …, and the M-th observation station.

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

[0079] 1. The position of each observation station is quickly corrected by using the measurement signal of the external calibration source of each observation station, the radiation source is directly positioned based on the corrected position of each observation station, the residual error of the station site of each observation station after correction is considered, and accurate positioning of the position of the radiation source is realized.

[0080] 2. The measurement distance difference equation of the reference observation station and other observation stations is determined according to the measurement signal of the external calibration source of each observation station, the theoretical distance difference equation of the reference observation station and other observation stations is determined based on the measurement position of each observation station, and finally the position of each observation station after correction is estimated according to the measurement distance difference equation and the theoretical distance difference equation, thereby improving the positioning accuracy of the radiation source.

[0081] 3. The observation station measurement signal model is expanded by using the position of each observation station after correction, a cost function of the position of the radiation source is constructed, and the positioning accuracy of the position of the radiation source is improved.

[0082] In the present application, the above technical solutions can be combined with each other to realize more preferred combination solutions. Other features and advantages of the present application will be described in the subsequent specification, and some advantages will become apparent from the specification or be understood through the implementation of the present application. The purpose and other advantages of the present application can be realized and obtained from the contents specifically pointed out in the specification and the drawings. BRIEF DESCRIPTION OF DRAWINGS

[0083] The accompanying drawings are included to provide a further understanding of the application and are incorporated herein and constitute a part of the application. The application will be described with reference to the drawings, and the same reference numbers in the drawings identify the same components.

[0084] Figure 1 A scene schematic diagram of M observation stations positioning a radiation source signal is provided for the embodiment of the present application.

[0085] Figure 2 A flowchart of a direct positioning method in the presence of station site error and external calibration source is provided for the embodiment of the present application.

[0086] Figure 3 A comparison diagram of application effects of a direct positioning method in the presence of station site error and external calibration source is provided for the embodiment of the present application. DETAILED DESCRIPTION

[0087] The preferred embodiments of the present application will be specifically described below with reference to the drawings, wherein the drawings constitute a part of the present application and are used to illustrate the principles of the embodiments of the present application, but are not used to limit the scope of the present application.

[0088] As shown in Figure 1 , in the positioning scenario, the position of the external calibration source is c o , and the position of the radiation source u o is The M observation stations include M observation stations, and the measurement positions of the M observation stations are s1, s2, s3…s M , and the actual positions of the M observation stations are Wherein, τ c1 represents the time of the external calibration source signal propagating from the external calibration source to the first observation station.

[0089] One specific embodiment of the present application discloses a direct positioning method with station address error and external calibration source, as shown in Figure 2 , the direct positioning method comprises:

[0090] Step S1: constructing an observation station measurement position model containing random position error and an observation station measurement signal model containing random signal error;

[0091] Step S2: correcting the measurement positions of each observation station based on the observation station measurement position model and the external calibration source measurement signal of each observation station, to obtain the corrected measurement positions of each observation station;

[0092] Step S3: performing Taylor series first-order expansion on the observation station measurement signal model at the corrected measurement positions of each observation station, to obtain an expanded observation station measurement signal model; the expanded observation station measurement signal model includes a corrected position signal model and a correction error model;

[0093] Step S4: constructing a radiation source position cost function according to the correction error model, the radiation source measurement signal of each observation station and the corrected position signal model;

[0094] Step S5: according to each possible position of the radiation source, using grid search method to determine the maximum eigenvalue corresponding to each possible position in the radiation source position cost function, and taking the possible position corresponding to the maximum maximum eigenvalue as the positioning position of the radiation source.

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

[0096] s=s o +Ψ;

[0097]

[0098] Wherein, M represents the number of observation stations, s, s o , Ψ represent the measurement position vector, the actual position vector and the random position error vector of the observation station; si 、 Ψ i respectively represent the measurement position vector, the actual position vector and the random position error vector of the i-th observation station;

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

[0100]

[0101] wherein 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 being 1 and other elements being 0;

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

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

[0104]

[0105] wherein x i , y i , z i respectively represent the X-axis measurement coordinate, the Y-axis measurement coordinate and the Z-axis measurement coordinate of the i-th observation station; respectively represent the X-axis actual coordinate, the Y-axis actual coordinate and the Z-axis actual coordinate of the i-th observation station; respectively represent the X-axis random error, the Y-axis random error and the Z-axis random error of the i-th observation station.

[0106] It is worth noting that s i , Ψ i are all 3×1 matrices, and each row of the matrix is respectively the X-axis, Y-axis and Z-axis coordinate; s, s o , Ψ are all 3M×1 matrices.

[0107] Specifically, as shown in FIG. 1, the measurement signal model of the observation station constructed in step S1 is: Figure 2

[0108] z=ηQr+w;

[0109]

[0110] wherein z i ​z i = [z i [0], z i [1],..., z i [N-1]] i represents an unknown path loss factor of the i th observation station, and i || = 1; w i = [w i [0], w i [1],..., w i [N-1]] i represents a random signal error vector of the i th observation station; r represents a signal vector of a radiation source, and i represents a discrete Fourier transform vector of the i th observation station; I N represents an N * N matrix with diagonal elements being 1 and other elements being 0, N being the number of sampling points of the radiation source signal radiated by each observation station;

[0111] Specifically, T represents matrix transposition.

[0112] z i = [z i [0], z i [1],..., z i [N-1]] T ;

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

[0114] r = [r[0], r[1],..., r[N-1]] T .

[0115] It is worth noting that in Figure 1 , the M observation stations need to be sampled synchronously when sampling the signal radiated by the radiation source, and each observation station samples N points to obtain N signals of the radiation source signal.

[0116] Specifically, the radiation source signal in the present application is r, and there is only one, considering the potential constraint that the radiation source signal is only one.

[0117] Specifically, diag{} represents a diagonal matrix.

[0118] It can be understood that z and w are both MN * 1 matrices, representing the radiation source signal and the random signal error collected by the M observation stations.

[0119] Specifically, the discrete Fourier transform vector of the i th observation station is:

[0120]

[0121] n = [0, 1,..., N-1] T ;

[0122]

[0123] wherein j represents imaginary unit, Δ represents signal sampling interval of each observation station, u o represents actual position of radiation source, represents actual position of the i-th observation station.

[0124] Specifically, v represents light speed, F represents base function matrix of Fourier transform, n represents sampling point serial number matrix, τ i represents time for signal of radiation source to propagate to the i-th observation station, || || represents distance between two positions.

[0125] Specifically, as Figure 2 shown in step S2, the measured position of each observation station is corrected based on the observation station measured position model and the external calibration source measured signal of each observation station.

[0126] The external calibration source measured signal of each observation station needs to be synchronously sampled when acquired, and the number of sampling points can be the same as or different from the number of sampling points of the radiation source. The measured position of each observation station is the position obtained by each observation station measuring its own position.

[0127] Preferably, the measured position of each observation station is corrected based on the observation station measured position model and the external calibration source measured signal of each observation station to obtain the corrected measured position of each observation station, comprising:

[0128] According to the external calibration source measured signal of each observation station, a measured distance difference equation of each observation station relative to the position of the external calibration source is determined; the reference observation station is an observation station selected from all observation stations;

[0129] Based on the measured position of each observation station, a theoretical distance difference equation of each observation station relative to the position of the external calibration source is determined;

[0130] Using the measured distance difference equation and the theoretical distance difference equation of each observation station relative to the position of the external calibration source, a difference equation of the measured distance difference and the theoretical distance difference is constructed, and the estimated random position error of each observation station is obtained by solving the difference equation;

[0131] According to the measured position of each observation station and the estimated random position error of each observation station, the corrected measured position of each observation station is calculated.

[0132] Specifically, according to the external calibration source measurement signals of each observation station, a measurement distance difference equation of the reference observation station and each of the other observation stations relative to the position of the external calibration source is determined. Optionally, one of the observation stations is taken as the reference observation station. For convenience, the first observation station can be taken as the reference observation station, and 1, 2,..., M as the other observation stations.

[0133] Preferably, the measurement distance difference equation of the reference observation station and each of the other observation stations relative to the position of the external calibration source is:

[0134]

[0135] wherein, represents the measurement distance difference between the i-th observation station and the reference observation station and the position of the external calibration source, and v represents the speed of light, represents the time difference between the arrival of the external calibration source measurement signal at the i-th observation station and at the reference observation station, and c represents the speed of light, o represents the position of the external calibration source, respectively represent the actual position of the reference observation station and the actual position of the i-th observation station, represents the measurement error of the reference observation station and the i-th observation station.

[0136] Specifically, the i-th observation station is taken as the reference observation station, and the measurement distance of the reference observation station relative to the position of the external calibration source is The measurement distance of the other observation stations relative to the position of the external calibration source is

[0137] It is worth noting that the time difference between the arrival of the external calibration source measurement signal at the i-th observation station and at the reference observation station is which can be obtained by the external calibration source signal received by each observation station using the known cross ambiguity function, and will not be described in detail here.

[0138] Specifically, based on the measurement positions of each observation station, a theoretical distance difference equation of the reference observation station and each of the other observation stations relative to the position of the external calibration source is determined. The theoretical distance difference equation of the reference observation station and each of the other observation stations relative to the position of the external calibration source is:

[0139]

[0140] wherein, represents the theoretical distance difference between the i-th observation station and the reference observation station, and s represents the speed of light, i , s l respectively represent the measurement position of the reference observation station and the measurement position of the i-th observation station.

[0141] Specifically, the theoretical distance between the reference observation station and the external correction source is ||c o -s l ||, the theoretical distance of other observation stations relative to the external correction source is ||c o -s i ||.

[0142] Specifically, constructing a difference equation between the measured distance difference and the theoretical distance difference. Preferably, constructing a difference equation between the measured distance difference and the theoretical distance difference includes:

[0143] The measurement position s at each observation station i Place Performing a first-order Taylor series expansion yields:

[0144]

[0145] in, represents the measurement position s of the i-th observation station i Pointing to the position c of the external correction source o The unit vector of

[0146] The difference equation is:

[0147]

[0148] Using the first-order expansion of the Taylor series The difference equation is simplified to:

[0149]

[0150] Among them, i , Ψ l are the random position errors of the i-th observation station and the reference observation station, respectively.

[0151] Specifically, according to the difference equation between the measured distance difference and the theoretical distance difference By constructing the difference equations corresponding to the reference observation station and each of the other observation stations, Ψ can be calculated using the linear minimum mean square error estimation.

[0152] Specifically, the estimated random position error of each observation station is calculated as:

[0153]

[0154] in, represents the estimated random position error of each observation station, Q β represents the covariance matrix of Ψ, It represents the variance of the random position error of the observation station, I 3MRepresents a 3M×3M matrix with diagonal elements set to 1 and the remaining elements set to 0;

[0155] G c It is a (M-1)×3M matrix and the (i-1)th row is:

[0156]

[0157] in, Q c for The covariance matrix of

[0158] Among them, h c is a (M-1)×1 matrix with the (i-1)th element being

[0159] Specifically, the measured position of each observation station is subtracted from the estimated random position error of each observation station to obtain the corrected measured position of each observation station. That is, the corrected measured position of each observation station is:

[0160]

[0161] in, Indicates the measurement position of each observation station after correction.

[0162] Specifically, Δs o The covariance matrix of

[0163]

[0164] Specifically, such as Figure 2 As shown, in step S3, the observation station measurement signal model is subjected to a first-order Taylor series expansion at the measurement position of each observation station after correction, and the obtained expanded observation station measurement signal model is:

[0165]

[0166] in, represents the correction position signal model, w″ represents the correction error model, and diag{} represents a diagonal matrix.

[0167] Specifically, such as Figure 2 As shown, in step S4, the cost function of the radiation source position is constructed using the correction error model, the correction position signal model and the radiation source measurement signal of each observation station.

[0168] Preferably, constructing a cost function of the radiation source position according to the correction error model, the radiation source measurement signal of each observation station and the correction position signal model includes:

[0169] a covariance matrix of the correction error model is calculated;

[0170] a weighted least squares solution equation of the emitter position is constructed based on the covariance matrix of the correction error model, the emitter measurement signals of each observation station and the correction position signal model;

[0171] an estimated value of the emitter signal is obtained based on the weighted least squares solution equation of the emitter position;

[0172] the estimated value of the emitter signal is substituted into the weighted least squares solution equation of the emitter position to obtain a cost function of the emitter position.

[0173] Specifically, the covariance matrix of the correction error model is calculated, and the covariance matrix of the correction error model is:

[0174]

[0175] wherein, is the maximum element on the diagonal line; I M denotes an MxM matrix whose diagonal elements are 1 and other elements are 0; denote the variances of the random signal errors of the first observation station, the i-th observation station, and the M-th observation station, respectively.

[0176] Specifically, the derivation process of the covariance matrix of the correction error model is as follows:

[0177]

[0178] Specifically, the weighted least squares solution equation of the emitter position is constructed based on the covariance matrix of the correction error model, the emitter measurement signals of each observation station and the correction position signal model, and the weighted least squares solution equation of the emitter position is:

[0179]

[0180] wherein, z denotes the emitter measurement signal vector of each observation station.

[0181] Specifically, argmin{} denotes the emitter position that makes{} take the minimum value, and the emitter position is taken as the positioning position of the emitter.

[0182] Specifically, the estimated value of the emitter signal is obtained based on the weighted least squares solution equation of the emitter position, including:

[0183] the first-order derivative of the emitter signal r is calculated, and the derivative is set to zero to obtain the estimated value of the emitter signal, i.e.

[0184]

[0185] Specifically, the estimated value of the radiation source signal Substitute the weighted least squares solution equation for the radiation source position The transfer equation of the cost function is obtained, namely:

[0186]

[0187] 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:

[0188]

[0189] 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:

[0190]

[0191] Among them, λ max {R(u o )} means R(u o )’s maximum eigenvalue.

[0192] Specifically, the cost function of the radiation source position only includes the position of the radiation source.

[0193] Specifically, such as Figure 2 As shown, in step S5, 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.

[0194] 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.

[0195] The following is a specific example demonstrating the technical effect of a direct positioning method with station address error and external correction source provided by an embodiment of the present invention.

[0196] 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 The position of the observation station is

[0197] and The position of the external calibration source is c o = [10, 90, 10] T The radiation source signal waveform modulation pattern is BPSK, the bandwidth is 25 kHz, the carrier frequency is set to 303 MHz, the sampling frequency is 100 kHz, and 2000 points of signal data are collected at each station for radiation source positioning.

[0198] For the convenience of description, the direct positioning method provided by the embodiment of the application in the presence of station address error and external calibration source is denoted as DPD 1CU As a comparison, the direct positioning algorithm ignoring the station address error is denoted as DPD NCNU The other direct positioning algorithm considering the station address error is denoted as DPD NCU .

[0199] As shown in Figure 3 , the root mean square error of DPD 1CU , DPD NCU and DPD NCNU based on 100 independent samples is given when the signal-to-noise ratio of the signal received by observation station 1 changes from -10 dB to 15 dB. In this embodiment, for each signal-to-noise ratio scenario, it is assumed that the covariance matrix of the station address error is equal to the covariance matrix of the range difference measurement error between observation station 1 and observation station 2 under the signal-to-noise ratio condition, wherein the range difference is defined as the product of the time difference and the wave speed.

[0200] As can be seen from Figure 3 , under various signal-to-noise ratio scenarios, the root mean square positioning error of DPD 1CU is always lower than that of DPD NCU and DPD NCNU , proving the effectiveness of the direct positioning method provided by the embodiment of the application in the presence of station address error and external calibration source.

[0201] Compared with the prior art, the direct positioning method provided by the embodiment of the present application utilizes the measurement signals of the external calibration source of each observation station to quickly correct the positions of each observation station, directly positions the radiation source based on the corrected positions of each observation station, considers the residual errors of the positions of each observation station after correction, and realizes accurate positioning of the position of the radiation source; meanwhile, the measurement distance difference equations of the reference observation station and other observation stations are determined according to the measurement signals of the external calibration source of each observation station, the theoretical distance difference equations of the reference observation station and other observation stations are determined based on the measurement positions of each observation station, and finally the positions of each observation station after correction are estimated according to the measurement distance difference equations and the theoretical distance difference equations, so as to improve the positioning accuracy of the radiation source; and the observation station measurement signal model is expanded using the positions of each observation station after correction, a cost function of the position of the radiation source is constructed, and the positioning accuracy of the position of the radiation source is improved.

[0202] Those skilled in the art can understand that all or part of the processes of the above-mentioned embodiments can be completed by a computer program instructing related hardware, 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.

[0203] The above is only a preferred embodiment of the present application, but the protection scope of the present application is not limited to this. Any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A direct positioning method in the presence of station location errors and external correction sources, characterized in that, The direct positioning method comprises: constructing an observation station measurement position model containing random position errors and an observation station measurement signal model containing random signal errors; correcting the measurement positions of the observation stations based on the observation station measurement position model and the measurement signals of the external calibration source of each observation station, to obtain the corrected measurement positions of the observation stations; performing Taylor series first-order expansion on the observation station measurement signal model at the corrected measurement positions of the observation stations, to obtain an expanded observation station measurement signal model; the expanded observation station measurement signal model comprises a corrected position signal model and a correction error model; constructing a cost function of the emitter position according to the correction error model, the measurement signals of the emitter of each observation station and the corrected position signal model; determining the maximum eigenvalue corresponding to each possible position in the cost function of the emitter position according to each possible position of the emitter, using a grid search method, and taking the possible position corresponding to the maximum maximum eigenvalue as the positioning position of the emitter.

2. The direct positioning method of claim 1, wherein, The method for correcting the measurement positions of the observation stations based on the observation station measurement position model and the measurement signals of the external calibration source of each observation station, to obtain the corrected measurement positions of the observation stations, comprises: determining a measurement distance difference equation of each observation station relative to the position of the external calibration source according to the measurement signals of the external calibration source of the observation stations; the reference observation station is an observation station selected from all the observation stations; determining a theoretical distance difference equation of each observation station relative to the position of the external calibration source based on the measurement positions of the observation stations; constructing a difference equation of the measurement distance difference and the theoretical distance difference by using the measurement distance difference equation and the theoretical distance difference equation of each observation station relative to the position of the external calibration source, and solving the difference equation to obtain the estimated random position error of each observation station; calculating the corrected measurement positions of the observation stations according to the measurement positions of the observation stations and the estimated random position error of each observation station.

3. The direct positioning method of claim 2, wherein, The measurement distance difference equation of each observation station relative to the position of the external calibration source is: wherein, represents the measured distance difference of the i-th observation station and the reference observation station from the position of the external correction source, v represents the speed of light, represents the time difference of the external correction source measurement signal arriving at the i-th observation station and arriving at the reference observation station, c o represents the position of the external correction source, respectively represent the actual position of the reference observation station, the actual position of the i-th observation station, represents the measurement error of the reference observation station and the i-th observation station; The theoretical distance difference equation of each observation station relative to the position of the external calibration source is: wherein, represents the theoretical distance difference between the ith observation station and the reference observation station, s i , s l respectively represent the measurement position of the reference observation station, the measurement position of the ith observation station.

4. The direct positioning method of claim 3, wherein, The method for constructing the difference equation of the measurement distance difference and the theoretical distance difference comprises: At the measurement position s of each observation station i The first order expansion of the Taylor series at the measurement position s of each observation station gives:​ wherein, denotes the measurement position s i points to the position c o of the unit vector; The difference equation is: By using the first order expansion of Taylor series Simplifying the difference equation, the simplified difference equation is: where Ψ i , Ψ l are the random position errors of the i-th observation station, the reference observation station, respectively.

5. The direct positioning method of claim 4, wherein, The estimated random position error of each observation station is: wherein represents the estimated random position error of each observation station, Q β represents the covariance matrix of Ψ, represents the variance of the amount of random position error of the observation station, I 3M represents a 3M x 3M matrix whose diagonal elements are 1 and whose other elements are 0; G c is a matrix of size (M - 1) x 3M and the (i - 1)-th row is: wherein Q c is covariance matrix; where h c is a (M-1) x 1 matrix and the (i-1)th element is The corrected measurement position of each observation station is: wherein, represents the corrected measurement position of each observation station.

6. The direct positioning method of claim 1, wherein, The observation station measurement position model is: s = s o + Ψ; wherein, M represents the number of observation stations, s, s o , Ψ represents the measurement position vector, actual position vector, random position error vector of the observation station; s i 、 Ψ i respectively represent the measurement position vector, actual position vector, random position error vector of the i-th observation station; The random position error vector Ψ satisfies zero mean, and the covariance matrix of Ψ is: where Q β denotes the covariance matrix of Ψ, denotes the variance of the random position error of the observation station, I 3M denotes a 3M x 3M matrix with diagonal elements equal to 1 and the remaining elements equal to 0; The measurement position vector, the actual position vector and the random position error vector of the i-th observation station are: s i = [x i , y i , z i ] T ; wherein x i , y i , z i respectively represent the X-axis measurement coordinate, the Y-axis measurement coordinate, the Z-axis measurement coordinate of the i-th observation station; respectively represent the X-axis actual coordinate, the Y-axis actual coordinate, the Z-axis actual coordinate of the i-th observation station; respectively represent the X-axis random error amount, the Y-axis random error amount, the Z-axis random error amount of the i-th observation station.

7. The direct positioning method of claim 6, wherein, The observation station measurement signal model is: z = ηQr + w; where 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 signal vector of the radiation source, and ||r|| = 1; Q i represents the discrete Fourier transform vector of the i-th observation station; I N represents an N x N matrix with diagonal elements being 1 and other elements being 0, N being the number of sampling points of the radiation source signal radiated by each observation station; z i = [z i [0], z i [1],..., z 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 ； The discrete Fourier transform vector of the i-th observation station is: n = [0, 1,..., N-1] T ; where j denotes the imaginary unit, Δ denotes the signal sampling interval of each observation station, u o denotes the actual position of the radiation source, denotes the actual position of the i-th observation station.

8. The direct positioning method of claim 4, wherein, The expanded observation station measurement signal model is: wherein represents the corrected position signal model, w" represents the correction error model, and diag{} represents a diagonal matrix.

9. The direct positioning method of claim 8, wherein, The method for constructing the cost function of the emitter position according to the correction error model, the measurement signals of the emitter of each observation station and the corrected position signal model comprises: calculating the covariance matrix of the correction error model; constructing a weighted least squares solution equation of the emitter position based on a covariance matrix of the correction error model, the radiation source measurement signals of each observation station and the correction position signal model; obtaining an estimated value of the radiation source signal based on the weighted least squares solution equation of the emitter position; substituting the estimated value of the radiation source signal into the weighted least squares solution equation of the emitter position to obtain a cost function of the emitter position.

10. The direct positioning method of claim 9, wherein, The covariance matrix of the correction error model is: wherein, is the largest element on the diagonal; I M denotes an M x M matrix with 1 on the diagonal and 0 elsewhere; denotes the variance of the random signal error of the 1st observation station, the i-th observation station,... the M-th observation station, respectively.

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