A multi-target direct positioning method without source number estimation

Abstract

The application discloses a multi-target direct positioning method without source number estimation, comprising the following steps: collecting data of multiple targets by using distributed receiving stations, and constructing a joint receiving signal model of each observation station in a distributed array scene by using receiving signals of the targets; constructing a space-time correlation matrix by using autocorrelation coefficients of target signals in different time intervals and joint space steering vectors of each receiving station to the targets for the joint receiving signal model of each observation station; setting an interference parameter of position estimation, and constructing a direct positioning cost function by using the interference parameter, the space-time correlation matrix and joint space steering vectors at a hypothetical position; dividing an effective monitoring area of the receiving station into grid points, solving the direct positioning cost function for different grid points, and obtaining position estimation results of each target on the grid points. The application solves problems of low resolution, poor robustness and dependence on prior information of a classical algorithm in a current multi-target positioning scene.

Description

Technical Field

[0001] The present invention belongs to the field of target position estimation, and in particular relates to a multi-target direct positioning method without the need for signal source number estimation. Background Art

[0002] Passive positioning systems receive and intercept electromagnetic signals from space, locating them by analyzing parameters implicit in the signals related to the location of the radiating source. This system offers significant advantages in terms of concealment and anti-interference capabilities. With the advent of the concept of distributed swarm warfare, distributed collaborative passive positioning technology has rapidly developed. By intercepting space signals through multiple distributed receiving arrays, it offers advantages over single-station passive positioning systems, including stronger positioning capabilities, improved robustness, high fault tolerance, and greater reconfigurability. This technology is widely used in numerous military and civilian fields, including electronic reconnaissance, space early warning and surveillance systems, the Internet of Things, and smart logistics.

[0003] Classic passive location technology is based on a two-step processing strategy, known as two-step positioning. In the first step, parameters related to the emitter's location, such as the angle / direction of arrival (AOA / DOA) and time of arrival (TOA), are estimated from the sampled signals of each receiving station. In the second step, a nonlinear system of equations related to the emitter's location is established based on these parameters, and the equations are further solved to estimate the target's location. However, the two-step positioning method is a suboptimal estimation method. Position calculation is separated from parameter estimation, and positioning accuracy is directly affected by the accuracy of parameter estimation. Furthermore, it struggles to effectively utilize the correlation between the signals received by each station, leading to information loss and difficulty correlating positioning parameters in multi-target scenarios.

[0004] The Direct Position Determination (DPD) method, also known as a one-step positioning method, eliminates the need to estimate intermediate parameters. Instead, it processes the raw signals intercepted by the receiving station, constructs a positioning cost function based on the intercepted signals, and then achieves positioning by solving for the optimal value of the objective function. The DPD method fully exploits the correlation between received signals, ensuring effective coherent signal accumulation and avoiding the problems of position estimation error propagation and positioning parameter correlation caused by the inaccuracy of intermediate parameter estimation. It offers high positioning accuracy, strong resolution, and robustness, and performs better in low signal-to-noise ratio (SNR) and multi-target scenarios.

[0005] Classic direct positioning methods are based on the Maximum Likelihood (ML) criterion and theoretically achieve optimal positioning performance in single-source scenarios. However, this method fails in multi-target scenarios. Direct positioning methods based on the Minimum Variance Distortionless Response (MVDR) add MVDR constraints to the ML cost function to improve the resolution of the ML direct positioning algorithm. However, this algorithm is asymptotically biased, and its positioning accuracy is difficult to achieve the theoretical optimal value. Direct positioning methods based on the Multiple Signal Classification (MUSIC) algorithm utilize the orthogonality between the signal subspace and the noise subspace to effectively locate multiple target radiation sources in space. However, this method relies heavily on prior information about the number of radiation sources to determine the signal subspace dimension, and is less robust in unknown electromagnetic environments. Summary of the Invention

[0006] The purpose of the present invention is to provide a multi-target direct positioning method without the need for source number estimation, so as to solve the problems of low resolution, poor robustness and dependence on prior information of the current classical algorithms in multi-target positioning scenarios.

[0007] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0008] A multi-target direct positioning method without the need for source number estimation includes:

[0009] Use distributed receiving stations to collect data from multiple targets, and use the received signals from the targets to build a joint receiving signal model for each observation station in a distributed array scenario;

[0010] For the joint receiving signal model of each observation station, a space-time correlation matrix is ​​constructed using the autocorrelation coefficients of the target signal at different time intervals and the joint spatial steering vectors of each receiving station to the target;

[0011] Setting interference parameters for position estimation, and constructing a direct positioning cost function using the interference parameters, the space-time correlation matrix, and the joint spatial steering vector at the assumed position;

[0012] The effective monitoring area of ​​the receiving station is divided into grid points, and the direct positioning cost function is solved for different grid points to obtain the position estimation results of each target at the grid points.

[0013] Furthermore, the signal receiving model of each observation station in the distributed array scenario is expressed as:

[0014] X(t)=As(t)+N(t), 0<t≤T

[0015] Where X(t)=[x1(t),x2(t),…,x L (t)] T , represents the joint spatial response matrix of L distributed receiving stations to Q targets, N(t) represents the vector of spatial transmission noise on the L receiving stations, and s(t) is the vector of complex envelopes of each target signal at time t;

[0016] The received signal x at the lth receiving station l (t) is expressed as:

[0017]

[0018] Among them, n l (t) represents the spatial transmission noise of the lth receiving station at time t, l = 1, 2, ... L; β l,q represents the channel fading coefficient when the qth target signal is transmitted to the lth station, T is the duration of each observation sampling; a l,q is the spatial steering vector of the qth target signal at the lth receiving station;

[0019]

[0020] s(t)=[s1(t),s2(t),…,s Q (t)] T

[0021] Among them, s q (t) represents the complex envelope of the target signal of the qth target at time t, q = 1, 2,…, Q.

[0022] Furthermore, for the joint receiving signal model of each observation station, a space-time correlation matrix is ​​constructed using the autocorrelation coefficients of the target signal at different time intervals and the joint spatial steering vectors of each receiving station to the target, including:

[0023] With time delay τ as the interval, the space-time correlation matrix of the joint receiving signal model X(t) of each receiving station is defined as:

[0024] R XX (τ) = E{X(t)X H (t-τ)}

[0025] Here, E{·} is the expectation of the elements in the brackets, and the superscript H of the parameter indicates the conjugate transpose of the parameter, the same below;

[0026] Since the spatial transmission noise is complex Gaussian white noise, the autocorrelation matrix of the spatial transmission noise is expressed as:

[0027]

[0028] Among them, I LM×LM represents the identity matrix of dimension LM×LM; for each receiving station, the space-time correlation matrix R of the joint receiving signal model X(t) XX (τ) has:

[0029] R XX (τ) = AR ss (τ)A H +R NN (τ)

[0030] Among them, R ss (τ) is the signal autocorrelation matrix; if the time interval τ≠0, then:

[0031] R XX (τ) = E{X(t)X H (t-τ)}=AR ss (τ)A H

[0032] Since each radiation source is independent of each other, the signal autocorrelation matrix R ss (τ) can be expressed as:

[0033] R ss (τ)=diag{r1(τ),r2(τ),…,r Q (τ)}

[0034] Where diag{·} represents the diagonal matrix consisting of the elements in the brackets, r q (τ) is the correlation coefficient of the target signal of the qth target at the time interval τ, which is expressed as:

[0035]

[0036] The superscript * indicates the conjugate of the parameter, the same below; for N different time intervals τ n ,n=1,...,N, construct N space-time correlation matrices R XX (τ n ),n=1,…,N,τ n The spatiotemporal correlation matrix R at time XX (τ n ) is expressed as:

[0037]

[0038] Among them, τ n represents the nth delay, r q (τ n ) represents the qth position target signal at a time interval of τn The correlation coefficient when is a column vector of dimension L×M, representing the joint spatial steering vector of all L distributed receiving stations to the qth target, expressed as:

[0039]

[0040] Among them, β L,q represents the channel fading coefficient when q target signals are transmitted to the Lth station, a L,q Represents the spatial steering vector of the qth position target signal at the Lth receiving station.

[0041] Furthermore, the setting of interference parameters for position estimation and constructing a direct positioning cost function using the interference parameters, the space-time correlation matrix, and the joint spatial steering vector at the assumed position include:

[0042] According to the definition of space-time correlation matrix, for the k∈[1,…,Q] T A target is defined, and an L×M-dimensional column vector η is defined:

[0043]

[0044] Among them, range{·} represents the range space spanned by vectors, and the above formula represents the joint space guidance vector except the k-th target In addition, the vector η is perpendicular to the range space spanned by the joint space guidance vectors of the other Q-1 targets, that is:

[0045]

[0046] Then we have:

[0047]

[0048] in, is a scalar; the above formula is interpreted as the existence of an L×M-dimensional column vector η. When a hypothetical position p is equal to a target's true position, R XX (τ n )η and the joint spatial steering vector generated by each receiving station at position p Collinear:

[0049]

[0050] For all N space-time correlation matrices, define d = [d1, d2, ..., d N ] T ; The direct positioning cost function is expressed as:

[0051]

[0052] Among them, η and d are interference parameters for position estimation; when there is a position p that makes the cost function J(p,η,d) reach the minimum value, the position p is the possible location of the target.

[0053] Furthermore, the effective monitoring area of ​​the receiving station is divided into grid points, and the direct positioning cost function is solved for different grid points to obtain the position estimation result of each target at the grid point, including:

[0054] The direct positioning cost function J(p,η,d) can be further expressed as:

[0055] J(p,η,d)=η H Fη-η H G(p)dd H G H (p)η+LM

[0056] in:

[0057]

[0058]

[0059] According to the Lagrange multiplier method, the first-order derivative of J(p,η,d) with respect to the interference parameter η of positioning is:

[0060]

[0061] in Indicates finding the first-order derivative of the elements in the brackets with respect to η. is the symbol of the first-order partial derivative; let the first-order derivative is 0, and the solution is:

[0062]

[0063] in, represents the estimated value of parameter η, Denotes the pseudo-inverse of the matrix F; Bringing in the cost function, the following constraints are established:

[0064]

[0065] min(·) is the symbol of the minimized function value; for the interference parameter d, its estimated value d is equivalent to The eigenvector corresponding to the maximum eigenvalue of ; further, the cost function for position p estimation can be written as:

[0066]

[0067] Among them, λmax {·} means taking the maximum eigenvalue of the matrix, so the cost function of target position estimation can be further expressed as:

[0068]

[0069] max(·) is the symbol for the maximization function value; the optimal estimates of the Q target positions can be obtained by solving the two-dimensional plane grid point positions that can make the cost function f(p) obtain the first Q maximum values ​​through the two-dimensional grid search method.

[0070] Furthermore, by dividing the effective monitoring area of ​​L receiving stations into J grid points, the response of all L receiving stations to the jth (j=1,2,…,J) grid point p is calculated. j The joint spatial guidance vector , and solve G(p j ), and get the calculation result of the cost function f(p j ); For all J grid points, we can get the cost function f(p j ) is a set of f(p2),…,f(p J )}, the set of its first Q maximum values ​​f maxQ It can be expressed as:

[0071]

[0072] in, Represents the set of cost functions According to the function values, [1:Q] represents the first Q values ​​of the function after sorting; thus, the optimal position estimate of the qth target is It can be expressed as:

[0073]

[0074] A target positioning device, comprising:

[0075] The model building module is used to collect data from multiple targets using distributed receiving stations, and to build a joint receiving signal model of each observation station in a distributed array scenario using the received signals from the targets;

[0076] A matrix construction module is used to construct a space-time correlation matrix for the joint receiving signal model of each observation station using the autocorrelation coefficient of the target signal at different time intervals and the joint spatial steering vector of each receiving station to the target;

[0077] a cost function module, configured to set interference parameters for position estimation and construct a direct positioning cost function using the interference parameters, the space-time correlation matrix, and the joint spatial steering vector at the assumed position;

[0078] The position estimation module is used to divide the effective monitoring area of ​​the receiving station into grid points, solve the direct positioning cost function for different grid points, and obtain the position estimation result of each target at the grid point.

[0079] A positioning device comprises a processor, a memory and a computer program stored in the memory; when the processor executes the computer program, the multi-target direct positioning method without the need for signal source number estimation is implemented.

[0080] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the multi-target direct positioning method without the need for signal source number estimation is implemented.

[0081] A distributed receiving station adopts the multi-target direct positioning method without the need for signal source number estimation when performing target positioning.

[0082] Compared with the prior art, the present invention has the following technical features:

[0083] The present invention adopts a distributed collaborative positioning architecture, which improves the robustness, reconfigurability and fault tolerance of the positioning system and expands the application scenarios of the system; in addition, the present invention adopts a direct positioning method to solve the error propagation phenomenon caused by the separation of parameter estimation and position solution in the traditional two-step positioning method, thereby improving the positioning accuracy of the target; finally, the present invention establishes a positioning cost function by constructing a space-time autocorrelation matrix and obtains the radiation source position through a grid search method. In a multi-radiation source scenario, there is no need to know the prior information of the number of radiation sources in advance, and effective resolution of multiple targets can be achieved, thereby improving the scenario adaptability of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 Schematic diagram of the process of the present invention;

[0085] Figure 2 The distributed collaborative receiving and positioning framework involved in the method of the present invention;

[0086] Figure 3 This is a positioning spatial spectrum in a multi-target scenario according to an embodiment of the present invention;

[0087] Figure 4 The performance of an embodiment of the present invention in a multi-target scenario is compared with that of the MVDR direct positioning method (DPD-MVDR) and the MUSIC direct positioning method (DPD-MUSIC) under the influence of SNR. DETAILED DESCRIPTION

[0088] The present invention provides a multi-target direct positioning method that does not require the estimation of the number of signal sources. It adopts a distributed cooperative receiving positioning framework. Each distributed receiving station collects data on the target signal. Each receiving station is equipped with a multi-antenna array, thereby establishing a receiving signal model based on the signal arrival angle in a distributed multi-station receiving scenario; for the distributed joint received signals, multiple space-time correlation matrices are constructed, and a direct positioning cost function is established; finally, a two-dimensional grid search method is used to solve the cost function to obtain the target location; this method effectively improves the spatial resolution and algorithm accuracy of the direct positioning algorithm, and reduces the dependence on prior information on the number of radiation sources.

[0089] See attached Figure 1 The present invention provides a multi-target direct positioning method without the need for source number estimation, comprising the following steps:

[0090] Step 1: Use distributed receiving stations to collect data from multiple targets, and use the received signals of the targets to build a joint receiving signal model of each observation station in a distributed array scenario.

[0091] Assume that there are L stationary receiving stations distributed on the ground, where the spatial position of the lth receiving station is u l , each receiving station is equipped with an M-element uniform linear array; there are Q independent targets in space, and the spatial position of the qth target is p q , s q (t) represents the complex envelope of the target signal of the qth target at time t; therefore, the received signal x at the lth receiving station is l (t) is expressed as:

[0092]

[0093] Among them, n l (t) represents the spatial transmission noise of the lth receiving station at time t, which is set to have a mean of 0 and a variance of δ 2 Additive complex Gaussian white noise, β l,q represents the channel fading coefficient when the qth target signal is transmitted to the lth station, T is the duration of each observation sampling; a l,q is the spatial steering vector of the qth target signal at the lth receiving station, specifically expressed as

[0094]

[0095] Where e is a natural constant, j is an imaginary unit, the superscript T indicates transposition, and the same applies below; y is the array element spacing, λ is the signal wavelength, and θ l.q is the azimuth angle between the qth target and the lth receiving station.

[0096] At the lth receiving station, the received signals of all targets at time t can be jointly expressed in matrix form:

[0097] x l (t) = A l s(t)+n l (t),0<t≤T (3)

[0098] in, represents the spatial response of Q targets at the lth receiving station, represents the M×Q dimensional complex space, s(t) is the vector composed of the complex envelopes of each target signal at time t, which can be expressed as:

[0099]

[0100] The signal model X(t) received jointly by each observation station can be expressed as:

[0101] X(t)=As(t)+N(t),0<t≤T (5)

[0102] in:

[0103]

[0104] represents the joint spatial response matrix of L distributed receiving stations to Q targets, and N(t) represents the vector composed of spatial transmission noise on the L receiving stations.

[0105] Step 2: for the joint receiving signal model of each observation station, a space-time correlation matrix is ​​constructed using the autocorrelation coefficients of the target signal at different time intervals and the joint spatial steering vectors of each receiving station to the target.

[0106] With time delay τ as the interval, the space-time correlation matrix of the joint receiving signal model X(t) of each receiving station is defined as:

[0107]

[0108] Here, E{·} is the expectation of the elements in the brackets, and the superscript H on the parameter indicates the conjugate transpose of the parameter. The same applies below.

[0109] Since the spatial transmission noise is complex Gaussian white noise, the autocorrelation matrix of the spatial transmission noise is expressed as:

[0110]

[0111] Among them, I LM×LM represents the identity matrix of dimension LM×LM; for each receiving station, the space-time correlation matrix R of the joint receiving signal model X(t) XX (τ) has:

[0112]

[0113] Among them, R ss (τ) is the signal autocorrelation matrix; according to formulas (8) and (9), if the time interval τ≠0, we have:

[0114] R XX (τ) = E{X(t)X H (t-τ)}=AR ss (τ)A H (10)

[0115] Since each radiation source is independent of each other, the signal autocorrelation matrix R ss (τ) can be expressed as:

[0116] R ss (τ)=diag{r1(τ),r2(τ),…,r Q (τ)} (11)

[0117] Where diag{·} represents the diagonal matrix consisting of the elements in the brackets, r q (τ) is the correlation coefficient of the target signal of the qth target at the time interval τ, which is expressed as:

[0118]

[0119] The superscript * in the parameter indicates the conjugate of the parameter, and the same applies below. Thus, for N different time intervals τ n ,n=1,...,N, construct N space-time correlation matrices R XX (τ n ),n=1,…,N,τ n The spatiotemporal correlation matrix R at time xx (τ n ) can be expressed as:

[0120]

[0121] Among them, τ n represents the nth delay, r q (τ n ) represents the qth position target signal at a time interval of τ n The correlation coefficient when is a column vector of dimension L×M, representing the joint spatial steering vector of all L distributed receiving stations to the qth target, expressed as:

[0122]

[0123] Among them, βL,q represents the channel fading coefficient when q target signals are transmitted to the Lth station, a L,q Represents the spatial steering vector of the qth position target signal at the Lth receiving station.

[0124] Step 3: Set interference parameters for position estimation, and construct a direct positioning cost function using the interference parameters, the space-time correlation matrix, and the joint spatial steering vector at the assumed position.

[0125] According to the definition of space-time correlation matrix, for the k∈[1,…,Q] T A target is defined, and an L×M-dimensional column vector η is defined:

[0126]

[0127] Where range{·} represents the range space spanned by vectors, and Equation (15) represents the joint space guidance vector except for the k-th target. In addition, the vector η is perpendicular to the range space spanned by the joint space guidance vectors of the other Q-1 targets, that is:

[0128]

[0129] According to the inference of formula (16), we have:

[0130]

[0131] in, is a scalar; Equation (17) can be interpreted as the existence of an L×M-dimensional column vector η. When a hypothetical position p is equal to a target's true position, R XX (τ n )η and the joint spatial steering vector generated by each receiving station at position p Collinear, that is:

[0132]

[0133] For all N space-time correlation matrices, define d = [d1, d2, ..., d N ] T , and both equation (18) hold true; therefore, the direct positioning cost function can be expressed as:

[0134]

[0135] Among them, η and d are interference parameters for position estimation, and the constraint ||d|| 2 The existence of =1 can avoid the influence of {η=0,d=0} on the solution cost function.

[0136] When there is a position p that makes the cost function J(p,η,d) take the minimum value, that is, for all delays τ n ,n=1,...,N, With R XX (τ n )η is the smallest vector angle, and at this time the position p is the possible location of the target.

[0137] Step 4: Divide the effective monitoring area of ​​the receiving station into grid points, solve the direct positioning cost function for different grid points, and obtain the position estimation result of each target at the grid point.

[0138] Expanding Equation (19), the positioning cost function J(p,η,d) in step 3 can be further expressed as:

[0139] J(p,η,d)=η H Fη-η H G(p)dd H G H (p)η+LM (20)

[0140] in:

[0141]

[0142]

[0143] According to the Lagrange multiplier method, the first-order derivative of the interference parameter η with respect to positioning in equation (20) is:

[0144]

[0145] in Indicates finding the first-order derivative of the elements in the brackets with respect to η. is the symbol of the first-order partial derivative; let the first-order derivative is 0, and the solution is:

[0146]

[0147] in, represents the estimated value of parameter η, Denotes the pseudo-inverse of the matrix F; Bringing in the cost function, the following constraints are established:

[0148]

[0149] min(·) is the symbol of the minimized function value; for the interference parameter d, its estimated value is Equivalent to The eigenvector corresponding to the maximum eigenvalue of ; further, the cost function for position p estimation can be written as:

[0150]

[0151] Among them, λ max {·} means taking the maximum eigenvalue of the matrix, so the cost function of target position estimation can be further expressed as:

[0152]

[0153] max(·) is the symbol of the maximization function value; the optimal estimate of the Q target positions can be obtained by solving the two-dimensional plane grid position that can make the cost function f(p) obtain the first Q maximum values ​​through the two-dimensional grid search method.

[0154] By dividing the effective monitoring area of ​​L receiving stations into J grid points, the p of all L receiving stations for the jth (j=1,2,…,J) grid point is calculated according to formula (14): j The joint spatial guidance vector , and solve G(p according to formula (22) j ), and substitute it into formula (27) to obtain f(p j ); For all J grid points, we can get the cost function f(p j ) is a set of f(p2),…,f(p J )}, the set of its first Q maximum values ​​f maxQ It can be expressed as:

[0155]

[0156] in, Represents the set of cost functions Arrange the function values ​​in descending order, [1:Q] means taking the first Q values ​​of the function geometry after arrangement, which is The first Q maximum values ​​of ; thus, the optimal position estimate of the qth target It can be expressed as:

[0157]

[0158] Example:

[0159] In one embodiment of the present invention, six stationary receiving stations are distributed on the ground, with their spatial locations being (1500, 0) m, (750, 1299) m, (-750, 1299) m, (-1500, 0) m, (-750, -1299) m, and (750, -1299) m, respectively. An 8-element uniform linear array is installed at each receiving station. Two independent target sources exist in space, with the target spatial locations being (-200, 0) m and (400, 0) m. Each observation sampling duration is T = 0.04 μs. The spatial transmission noise at each receiving station is additive complex Gaussian white noise with a mean of 0 and a variance of 1. Four time intervals are set, namely τ n ,n=1,...,4,τ1=1.25ns,τ2=2.5ns,τ3=3.75ns,τ4=5ns;the effective monitoring area is divided into J=100 grid points. The results are as follows Figure 3 and Figure 4 As shown; the test results show that the present invention effectively improves the positioning accuracy of the target and can achieve effective resolution of multiple targets.

[0160] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A multi-target direct positioning method without the need for source number estimation, characterized in that: include: Use distributed receiving stations to collect data from multiple targets, and use the received signals from the targets to build a joint receiving signal model for each observation station in a distributed array scenario; For the joint receiving signal model of each observation station, a space-time correlation matrix is ​​constructed using the autocorrelation coefficients of the target signal at different time intervals and the joint spatial steering vectors of each receiving station to the target; Setting interference parameters for position estimation, and constructing a direct positioning cost function using the interference parameters, the space-time correlation matrix, and the joint spatial steering vector at the assumed position; The effective monitoring area of ​​the receiving station is divided into grid points, and the direct positioning cost function is solved for different grid points to obtain the position estimation results of each target at the grid points.

2. The multi-target direct positioning method without the need for source number estimation according to claim 1, characterized in that: The model of joint signal reception at each observation station in the distributed array scenario is expressed as: in, , express Distributed receiving station pairs The joint spatial response matrix of the targets, express The vector of spatial transmission noise at the receiving station is is the vector composed of the complex envelopes of each target signal at time t; No. The received signal at the receiving station Expressed as: in, represents the spatial transmission noise of the lth receiving station at time t, l=1,2,…L; represents the channel fading coefficient when the qth target signal is transmitted to the lth station, is the sampling duration for each observation; is the spatial steering vector of the qth target signal at the lth receiving station; in, represents the complex envelope of the target signal of the qth target at time t, q=1,2,…,Q.

3. The multi-target direct positioning method without the need for source number estimation according to claim 2, characterized in that: For the joint receiving signal model of each observation station, a space-time correlation matrix is ​​constructed using the autocorrelation coefficients of the target signal at different time intervals and the joint spatial steering vectors of each receiving station to the target, including: Delay For intervals, each receiving station jointly receives the signal model The space-time correlation matrix of is defined as: Here, To find the expectation of the elements in the brackets, the superscript H indicates the conjugate transpose of the parameter, the same below; Since the spatial transmission noise is complex Gaussian white noise, the autocorrelation matrix of the spatial transmission noise is expressed as: in, represents the variance of additive complex Gaussian white noise, Indicates the dimension The unit matrix of each receiving station is The spatiotemporal correlation matrix of have: in, is the signal autocorrelation matrix; if the time interval ,have: Since each radiation source is independent of each other, the signal autocorrelation matrix It can be expressed as: in, represents a diagonal matrix consisting of the elements in the brackets, The target signal of the qth target is at the time interval The correlation coefficient when is expressed as: The superscript * on the parameter indicates the conjugate of the parameter, the same below; for N different time intervals ,structure spatiotemporal correlation matrix , The spatiotemporal correlation matrix of time Expressed as: in, represents the nth delay, Indicates that the qth position target signal is at a time interval of The correlation coefficient when The dimension is The column vector of The joint spatial guidance vector of the targets is expressed as: in, represents the channel fading coefficient when q target signals are transmitted to the Lth station, Represents the spatial steering vector of the qth position target signal at the Lth receiving station.

4. The multi-target direct positioning method without the need for source number estimation according to claim 3, characterized in that: The setting of interference parameters for position estimation and constructing a direct positioning cost function using the interference parameters, the space-time correlation matrix, and the joint spatial steering vector at the assumed position include: According to the definition of space-time correlation matrix, for A goal, define a Dimensional column vector : in, Represents the range space spanned by vectors, and the above formula represents the joint space guidance vector except the k-th target Outside, vector Perpendicular to other The range space spanned by the joint space guidance vector of the targets is: Then we have: in, is a scalar; the above formula is interpreted as there is a Dimensional column vector , when a hypothetical position When is equal to a target's true position, Align positions with each receiving station The joint spatial guidance vector generated at Collinear: For all A space-time correlation matrix, defined as ; The direct positioning cost function is expressed as: in, 、 As an interference parameter for position estimation; when there is a certain position Make the cost function When the minimum value is obtained, the position This is where the target may be.

5. The multi-target direct positioning method without the need for source number estimation according to claim 4, characterized in that: The effective monitoring area of ​​the receiving station is divided into grid points, and the direct positioning cost function is solved for different grid points to obtain the position estimation result of each target at the grid point, including: Direct positioning cost function It can be further expressed as: in: According to the Lagrange multiplier method, Find the interference parameters for positioning The first-order derivatives of are: in Indicates that the elements in the brackets are about The first derivative of is the symbol of the first-order partial derivative; let the first-order derivative is 0, and the solution is: in, Representation parameters The estimated value of Representation matrix Pseudo-rebellion; Bringing in the cost function, the following constraints are established: is the symbol of the minimized function value; for the interference parameter , its estimated value Equivalent to The eigenvector corresponding to the maximum eigenvalue of The estimated cost function can be written as: in, Indicates taking the maximum eigenvalue of the matrix, so the cost function of target position estimation can be further expressed as: To maximize the function value symbol; solving the cost function by two-dimensional grid search method can make By obtaining the positions of the first Q maximum two-dimensional plane grid points, we can get the optimal estimates of the Q target positions.

6. The multi-target direct positioning method without the need for source number estimation according to claim 5, characterized in that: By The effective monitoring area of ​​each receiving station is divided into grid points, calculate all The receiving station (j=1,2,…,J) grid points The joint spatial guidance vector , and solve , and get the calculation result of the cost function ; for all grid points, we can get the cost function The collection of , the set of its first Q maximum values It can be expressed as: in, Represents the set of cost functions Arrange in descending order according to the function value, Indicates taking the first Q values ​​of the permutation function; thus, the optimal position estimate of the qth target is It can be expressed as: 。 7. A target positioning device, characterized in that: include: The model building module is used to collect data from multiple targets using distributed receiving stations, and to build a joint receiving signal model of each observation station in a distributed array scenario using the received signals from the targets; A matrix construction module is used to construct a space-time correlation matrix for the joint receiving signal model of each observation station using the autocorrelation coefficient of the target signal at different time intervals and the joint spatial steering vector of each receiving station to the target; a cost function module, configured to set interference parameters for position estimation and construct a direct positioning cost function using the interference parameters, the space-time correlation matrix, and the joint spatial steering vector at the assumed position; The position estimation module is used to divide the effective monitoring area of ​​the receiving station into grid points, solve the direct positioning cost function for different grid points, and obtain the position estimation result of each target at the grid point.

8. A positioning device comprising a processor, a memory, and a computer program stored in the memory; characterized in that: When the processor executes the computer program, the multi-target direct positioning method without the need for signal source number estimation according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium storing a computer program; wherein: When the computer program is executed by a processor, the multi-target direct positioning method without the need for signal source number estimation according to any one of claims 1 to 6 is implemented.

10. A distributed receiving station, characterized in that: When performing target positioning, the receiving station adopts the multi-target direct positioning method without the need for signal source number estimation according to any one of claims 1-6.

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