Multi-target direct positioning method without signal source number estimation

Abstract

The invention discloses a multi-target direct positioning method without signal source number estimation, which comprises the following steps of: performing data acquisition on a plurality of targets by using a distributed receiving station, 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 the autocorrelation coefficients of the target signal at different time intervals and the joint space steering vector of each receiving station to the target according to the joint signal receiving model of each observation station; setting interference parameters of position estimation, and constructing a direct positioning cost function by using the interference parameters, the space-time correlation matrix and the joint space steering vector at the assumed position; and performing grid point division on the effective monitoring area of the receiving station, solving the direct positioning cost function for different grid points, and obtaining a position estimation result of each target on the grid points. According to the method, the problems of low resolution, poor robustness, priori information dependence and the like of a classic algorithm in a current multi-target positioning scene are solved.

Description

Technical Field

[0001] The 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] The passive positioning system receives and intercepts electromagnetic signals in space, and realizes positioning by analyzing the parameters related to the location of the radiation source implied in the signal. It has significant advantages in concealment and anti-interference ability. With the introduction of the concept of distributed cluster combat, distributed collaborative passive positioning technology has developed rapidly. It intercepts space signals through multiple distributed receiving arrays. Compared with the single-station passive positioning system, it has the advantages of strong positioning ability, good robustness, high fault tolerance, and strong reconfigurability. It is widely used in many military and civilian fields such as electronic reconnaissance, space early warning and surveillance systems, Internet of Things, and smart logistics.

[0003] The classic passive positioning technology is based on a two-step processing strategy, namely two-step positioning. In the first step, the parameters related to the position of the radiation source, such as the angle / direction of arrival (AOA / DOA) and the time of arrival (TOA), are estimated from the sampled signals of each receiving station; in the second step, a nonlinear equation group related to the position of the radiation source is established based on these parameters, and the equation group is further solved to obtain the target position estimation result. However, the two-step positioning method is a suboptimal estimation method, in which the position solution is separated from the parameter estimation, and the positioning accuracy is directly affected by the parameter estimation accuracy; in addition, it is difficult to effectively utilize the correlation between the received signals of each station, resulting in information loss and difficulty in associating positioning parameters in multi-target scenarios.

[0004] The direct positioning method (DPD) is also called a one-step positioning method. It does not need to estimate intermediate parameters. It directly processes the original signal intercepted by the receiving station, directly constructs the positioning cost function based on the intercepted signal, and then achieves positioning by solving the optimal value of the objective function. The DPD method can make full use of the correlation between the received signals, ensure the effective coherent accumulation of the signal, avoid the problem of position estimation error propagation and positioning parameter association difficulties caused by the accuracy of intermediate parameter estimation, and has the advantages of high positioning accuracy, strong resolution, and strong robustness. It performs better in low signal-to-noise ratio (SNR) and multi-target scenarios.

[0005] The classic direct positioning method is based on the maximum likelihood criterion (ML), and its positioning performance is theoretically optimal in a single radiation source scenario. However, this method fails in a multi-target scenario. The direct positioning method based on the minimum variance distortionless response (MVDR) adds MVDR constraints on the basis of the ML cost function to improve the resolution of the ML direct positioning algorithm. However, the algorithm is asymptotically biased, and its positioning accuracy is difficult to reach the theoretical optimal value. The direct positioning method based on the multiple signal classification algorithm (MUSIC) uses 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 the prior information of the number of radiation sources to determine the dimension of the signal subspace, and has poor robustness 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 reliance on prior information of classical algorithms in current 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, comprising:

[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 coefficient of the target signal at different time intervals and the joint spatial steering vector 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 result of each target at the grid point.

[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 composed of the spatial transmission noise on the L receiving stations, and s(t) is the vector composed of the complex envelope 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 coefficient of the target signal at different time intervals and the joint spatial steering vector of each receiving station to the target, including:

[0023] With the 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 unit 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 brackets, r q (τ) is the correlation coefficient of the target signal of the qth target at a time interval of τ, expressed as:

[0035]

[0036] The superscript * in the parameter 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 space-time correlation matrix R of the time XX (τ n ) is expressed as:

[0037]

[0038] Among them, τ n represents the nth delay, r q (τ n ) indicates that the target signal at the qth position is 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 space 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 value space spanned by the vector, 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 spatial 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 certain hypothetical position p is equal to a certain 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 used as 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 It means to find 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, represents the pseudo-inverse of the matrix F; Substituting into 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 of the maximization function value; the optimal estimate of the Q target positions can be obtained by solving the two-dimensional plane grid point position 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 obtain 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] means taking 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] A model building module is used to collect data from multiple targets using distributed receiving stations, and to construct 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, used for setting interference parameters of position estimation, and constructing a direct positioning cost function using the interference parameters, the space-time correlation matrix, and the joint space 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 information 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 information 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 position of the radiation source by solving the grid search method. In a multi-radiation source scenario, there is no need for prior information on the number of radiation sources, 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 It is a schematic diagram of the process of the present invention;

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

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

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

[0088] The present invention provides a multi-target direct positioning method without the need for signal source number estimation. The method adopts a distributed collaborative receiving positioning framework. Each distributed receiving station collects data on the target signal. Each receiving station is configured 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 receiving signal, 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. The 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 from the targets to build a joint receiving signal model for each observation station in a distributed array scenario.

[0091] Assume that there are L stationary receiving stations distributed on the ground, and 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, which is 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, 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 the 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 coefficient of the target signal at different time intervals and the joint spatial steering vector of each receiving station to the target.

[0106] With the 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, and 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 unit 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 brackets, r q (τ) is the correlation coefficient of the target signal of the qth target at a time interval of τ, 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 space-time correlation matrix R of the time xx (τ n ) can be expressed as:

[0120]

[0121] Among them, τ n represents the nth delay, r q (τ n ) indicates that the target signal at the qth position is 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 formula (15) represents the joint space guidance vector except for the kth target In addition, the vector η is perpendicular to the range space spanned by the joint spatial 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; Formula (17) can be interpreted as there is an L×M-dimensional column vector η, when a certain hypothetical position p is equal to a certain target real 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; 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) reach the minimum value, that is, for all delays τ n ,n=1,...,N, With R XX (τ n )η is the smallest, 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 It means to find 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, represents the pseudo-inverse of the matrix F; Substituting into 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 p 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 the 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, there are 6 stationary receiving stations distributed on the ground, and their spatial positions are (1500, 0) m, (750, 1299) m, (-750, 1299) m, (-1500, 0) m, (-750, -1299) m, (750, -1299) m. An 8-element uniform linear array is installed on each receiving station. There are 2 independent target sources in the space, and the target spatial positions are (-200, 0) m and (400, 0) m. The sampling time of each observation is T = 0.04 μs. The spatial transmission noise on each receiving station is an additive complex Gaussian white noise with a mean of 0 and a variance of 1. The time interval is set to 4, that is, 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 embodiments of the present application, and should all be included in the protection scope 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 coefficient of the target signal at different time intervals and the joint spatial steering vector 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 result of each target at the grid point.

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 reception of signals by each observation station in the distributed array scenario is expressed as: X(t)=As(t)+N(t),0<t≤T 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 composed of the spatial transmission noise on the L receiving stations, and s(t) is the vector composed of the complex envelope of each target signal at time t; The received signal x at the lth receiving station l (t) is expressed as: 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; s(t)=[s1(t),s2(t), … ,s Q (t)] T Among them, s q (t) 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 source number estimation according to claim 1, characterized in that: For the joint receiving signal model of each observation station, a space-time correlation matrix is ​​constructed 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, including: Delay For interval, the space-time correlation matrix of the joint receiving signal model X(t) of each receiving station is defined as: 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; Since the spatial transmission noise is complex Gaussian white noise, the autocorrelation matrix of the spatial transmission noise is expressed as: Among them, I LM×LM represents the unit matrix of dimension LM×LM; for each receiving station, the space-time correlation matrix of the joint receiving signal model X(t) 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: Where diag{·} represents a diagonal matrix consisting of the elements in brackets. The target signal of the qth target is The correlation coefficient when is expressed as: The superscript * in the parameter indicates the conjugate of the parameter, the same below; for N different time intervals n=1,...,N, construct N space-time correlation matrices n=1,…,N, The space-time correlation matrix of the time It is expressed as: in, represents the nth delay, It means that the target signal at the qth position is at a time interval of 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: 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.

4. The multi-target direct positioning method without the need for source number estimation according to claim 1, 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 space steering vector at the assumed position include: 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: Among them, range{·} represents the value space spanned by the vector, 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 spatial guidance vectors of the other Q-1 targets, that is: Then we have: in, is a scalar; the above formula is interpreted as the existence of an L×M-dimensional column vector η. When a certain assumed position p is equal to a certain target's true position, The joint spatial steering vector generated by each receiving station at position p Collinear: For all N space-time correlation matrices, define d = [d1, d2, … ,d N ] T ; The direct positioning cost function is expressed as: Among them, η and d are used as 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.

5. The multi-target direct positioning method without source number estimation according to claim 1, 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: The direct positioning cost function J(p,η,d) can be further expressed as: J(p,η,d)=η H Fη-η H G(p)dd H G H (p)η+LM in: 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: in It means to find 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: in, represents the estimated value of parameter η, represents the pseudo-inverse of the matrix F; Substituting into the cost function, the following constraints are established: min(·) is the symbol of the minimized function value; for the interference parameter d, its estimated value is Equivalent to G H (p) The eigenvector corresponding to the maximum eigenvalue of ; further, the cost function for position p estimation can be written as: 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: max() is the symbol for maximizing the function value; by solving the two-dimensional plane grid point position that can make the cost function f(p) obtain the first Q maximum values ​​through the two-dimensional grid search method, the optimal estimate of the Q target positions can be obtained.

6. The multi-target direct positioning method without the need for source number estimation according to claim 5, characterized in that: 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 j The joint spatial guidance vector And solve G(p j ), and obtain 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 The set of its first Q maximum values ​​f maxQ It can be expressed as: in, Represents the set of cost functions According to the function values, [1:Q] means taking the first Q values ​​of the function after sorting; thus, the optimal position estimate of the qth target is It can be expressed as:

7. A target positioning device, characterized in that: include: A model building module is used to collect data from multiple targets using distributed receiving stations, and to construct 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, used for setting interference parameters of position estimation, and constructing a direct positioning cost function using the interference parameters, the space-time correlation matrix, and the joint space 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, it implements the multi-target direct positioning method without the need for signal source number estimation according to any one of claims 1-6.

9. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the multi-target direct positioning method without the need for 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.

Images